# Best applied mathematics books according to redditors

We found 2,147 Reddit comments discussing the best applied mathematics books. We ranked the 845 resulting products by number of redditors who mentioned them. Here are the top 20.

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## Subcategories:

Differential equations books
Game theory books
Graph theory books
Linear programming books
Probability & statistics books
Vector analysis mathematics books
Stochastic modeling books
Biomathematics books
Statistics books

Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.

Amazon search for Dover Books on mathematics

There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

Pre-Calculus / Problem-Solving

u/[deleted] · 49 pointsr/math

You need to develop an "intuition" for proofs, in a crude sense.

I would suggest these books to do that:

Proof, Logic, and Conjecture: The Mathematician's Toolbox by Robert Wolf. This was the book I used for my own proof class at Stony Brook - (edit: when I was a student.) This book goes down to the logic level. It is superbly well written and was of an immense use to me. It's one of those books I've actually re-read entirely, in a very Wax-on Wax-off Mr. Miyagi type way.

How to Read and Do Proofs by Daniel Slow. I bought this little book for my own self study. Slow wrote a really excellent, really concise, "this is how you do a proof" book. Teaching you when to look to try a certain technique of proof before another. This little book is a quick way to answer your TL:DR.

How to Solve it by G. Polya is a classic text in mathematical thinking. Another one I bought for personal collection.

Mathematics and Plausible Reasoning, Vol 1 and Mathematics and Plausible Reasoning, Vol 2 also by G. Polya, and equally classic, are two other books on my shelf of "proof and mathematical thinking."

u/beaverteeth92 · 29 pointsr/math

Stay away from Numberphile. Numberphile oversimplifies mathematical concepts to the point where they will give you misconceptions about common mathematical notions that will greatly impact your learning later on. I'm noticing this happening a lot with the "1+2+... = -1/12" video because it doesn't explain that they aren't using the standard partial sum definition of series convergence.

Not sure how "mathematical" it is, but Secrets of Mental Math is a great, useful book that will help you do really fast calculations in your head.

u/Redrot · 29 pointsr/math

He's my major advisor, and he loves occasionally showing off (who wouldn't?). I find it very entertaining. As far as I can tell, it's just a lot of practice plus some pattern recognition. For multiplying large numbers he just uses the distributive property combined with a certain method of remembering numbers in his head he uses.

I also read his book Secrets of Mental Math back in high school. He outlines some of the techniques there although its more basic.

u/vantu · 27 pointsr/LifeProTips

This is the work of Abraham Wald. If you're interested in survivorship bias, and thinking mathematically in general, please consider reading this book, which discusses this exact story, among others. I just read it last week, and I recommend it.

u/krtcl · 24 pointsr/learnmachinelearning

I've wasted too much time trying to find the so-called "right" statistics book. I'm still early in my journey, going through calculus using Prof. Leonards videos while working through a Linear Algebra book all in prep for tackling a stats book. Here's a list of books that I've had a look at so far.

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• Probability and Statistical Inference by Hogg, Tanis and Zimmerman
• Mathematical Statistics with Applications by Wackerly

These seem to be of a similar level with regards to rigour, as they aren't that rigourous. That's not to say you can get by without the calculus prereq and even linear algebra

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The other two I've been looking at which seem to be a lot more complex are

• Introduction to Mathematical Statistics by Hogg as well. I'd think it's the more rigorous version of the book mentioned above by the same author
• All of Statistics by Wasserman which seems to require a lot of prior knowledge in statistics, but I think tackles just the perfect topics for machine learning

And then there's Casella and Berger's Statistical inference, which I looked at once and decided not to look at again until I can manage at least one of the aforementioned books. I think I'm leaning most to the first book listed. Whichever one you decide to use, good luck with your journey.

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u/Aethec · 19 pointsr/skeptic

A lot of it is probably confirmation bias, but yes, it does happen.

HP used to have expiry dates on their cartridges claiming they degraded printing after a certain time: http://www.hp.com/pageyield/articles/uk/en/InkExpiration.html

Another example from the software development world: Red Gate announced that one of their products (Reflector) would no longer be free starting from the next version and disabled all existing free copies, a move that upset many developers: http://www.infoq.com/news/2011/02/NET-Reflector-Not-Free

College textbooks are the most literal example of planned obsolescence; the new editions often contain very few new material and cost a lot while all older versions can be bought for almost nothing... and of course most classes require the new version.
For instance, Kenneth Rosen's "Discrete Mathematics and its Applications" currently sells for $125 if you want the [latest edition] (http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090/),$100 for the one before that and $16 for an older one even though the number of pages only increased by 100 each time. Thankfully, my teacher gave us the page numbers for both the latest and the second-latest editions... u/misplaced_my_pants · 17 pointsr/math You could read Timothy Gowers' welcome to the math students at Oxford, which is filled with great advice and helpful links at the bottom. You could read this collection of links on efficient study habits. You could read this thread about what it takes to succeed at MIT (which really should apply everywhere). Tons of great discussion in the lower comments. You could read How to Solve It and/or How to Prove It. If you can work your way through these two books over the summer, you'll be better prepared than 90% of the incoming math majors (conservatively). They'll make your foundation rock solid. u/Aman_Fasil · 15 pointsr/xkcd This book has a nice ELI5-style chapter on these voting systems. And it's just generally a really good book. https://smile.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535/ref=sr_1_1?ie=UTF8&amp;amp;qid=1496252174&amp;amp;sr=8-1&amp;amp;keywords=how+not+to+be+wrong u/acetv · 14 pointsr/math You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me. Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good. • The Nature and Power of Mathematics, Donald M. Davis. This book seems to be a survey of some history of mathematics and various modern topics. Check out the table of contents to get an idea. You'll notice a few of the subjects in the list below. It seems like this would be a good buy if you want to taste a few different subjects to see what pleases your palate. • Introduction to Graph Theory, Richard J. Trudeau. Check out the Wikipedia entry on graph theory and the one defining graphs to get an idea what the field is about and some history. The reviews on Amazon for this book lead me to believe it would be a perfect match for an interested high school student. • Game Theory: A Nontechnical Introduction, Morton D. Davis. Game theory is a very interesting field with broad applications--check out the wiki. This book seems to be written at a level where you would find it very accessible. The actual field uses some heavy math but this seems to give a good introduction. • An Introduction to Information Theory, John R. Pierce. This is a light-on-the-maths introduction to a relatively young field of mathematics/computer science which concerns itself with the problems of storing and communicating data. Check out the wiki for some background. • Lady Luck: The Theory of Probability, Warren Weaver. This book seems to be a good introduction to probability and covers a lot of important ideas, especially in the later chapters. Seems to be a good match to a high school level. • Elementary Number Theory, Underwood Dudley. Number theory is a rich field concerned with properties of numbers. Check out its Wikipedia entry. I own this book and am reading through it like a novel--I love it! The exposition is so clear and thorough you'd think you were sitting in a lecture with a great professor, and the exercises are incredible. The author asks questions in such a way that, after answering them, you can't help but generalize your answers to larger problems. This book really teaches you to think mathematically. • A Book of Abstract Algebra, Charles C. Pinter. Abstract algebra formalizes and generalizes the basic rules you know about algebra: commutativity, associativity, inverses of numbers, the distributive law, etc. It turns out that considering these concepts from an abstract standpoint leads to complex structures with very interesting properties. The field is HUGE and seems to bleed into every other field of mathematics in one way or another, revealing its power. I also own this book and it is similarly awesome. The exposition sets you up to expect the definitions before they are given, so the material really does proceed naturally. • Introduction to Analysis, Maxwell Rosenlicht. Analysis is essentially the foundations and expansion of calculus. It is an amazing subject which no math student should ignore. Its study generally requires a great deal of time and effort; some students would benefit more from a guided class than from self-study. • Principles of Statistics, M. G. Bulmer. In a few words, statistics is the marriage between probability and analysis (calculus). The wiki article explains the context and interpretation of the subject but doesn't seem to give much information on what the math involved is like. This book seems like it would be best read after you are familiar with probability, say from Weaver's book linked above. • I have to second sellphone's recommendation of Naive Set Theory by Paul Halmos. It's one of my favorite math books and gives an amazing introduction to the field. It's short and to the point--almost a haiku on the subject. • Continued Fractions, A. Ya. Khinchin. Take a look at the wiki for continued fractions. The book is definitely terse at times but it is rewarding; Khinchin is a master of the subject. One review states that, "although the book is rich with insight and information, Khinchin stays one nautical mile ahead of the reader at all times." Another review recommends Carl D. Olds' book on the subject as a better introduction. Basically, don't limit yourself to the track you see before you. Explore and enjoy. u/jboyd88 · 13 pointsr/GetStudying I'll share my reading list for the next 12 months as it's how I plan to become a better learner: &amp;nbsp; Learning u/debteater · 12 pointsr/financialindependence Anyone have any book recommendations for a 26 year old? No topic in particular, not necessarily financial/business or otherwise, just any suggestions? I'm currently reading: https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535 I'm not far into it, but it's basically on how to properly apply mathematics and logic to problem-solving. It's not exactly a new strategy for life or anything, but it's probably a good idea to read if you're analytical. I got it off Bill Gates reading list. https://www.amazon.com/How-Lie-Statistics-Darrell-Huff/dp/0393310728 Found through the reading list- This one I've finished and can't recommend enough. It's from the 50's and it's intended reader were investment bankers. The main suggestion is hide yourself from bad information because you can't eliminate the impact it'll have on your decision making, and we aren't exactly equipped to know what's good or bad if we don't have experience in that realm already. It's a lot of common stuff people use stats for to push a product service policy etc. https://www.amazon.com/Starship-Troopers-Robert-Heinlein/dp/0441783589/ I'm really into it. I love sci-fi. I don't necessarily love philosophy, but I'm really enjoying this book. It's hard for me to read a lot of at once but I don't ever want to put it down. The mindset of the character and narration really gets me. Since reading this, I've heard or noticed many many recommendations for Heinlein, though I'm unsure. He seems to be a proponent of fascism, but I guess he could just be writing down the fantasy of the particular fascist society he created and not necessarily saying "ya know this is how we should be" I don't know. I see conflicting things. u/M_from_Austin · 12 pointsr/learnmath Ordinary Differential Equations from the Dover Books on Mathematics series. I Just took my final for Diff Eq a few days ago and the book was miles better than the one my school suggested and is the best written math textbook I have encountered during my math minor. My Diff Eq course only covered about the first 40% of the book so there's still a TON of info that you can learn or reference later. It is currently$14 USD on amazon and my copy is almost 3" thick so it really is a great deal. A lot of the reviewers are engineering and science students that said the book helped them learn the subject and pass their classes no problem. Highly Highly recommend. ISBN-10: 9780486649405

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https://www.amazon.com/gp/product/0486649407/ref=ppx_yo_dt_b_asin_title_o08_s00?ie=UTF8&amp;psc=1

u/FraterAleph · 12 pointsr/occult

In the case of this paper, it's referring to dimensions in a mathematical sense, not a physical "space-like" or "time-like" sense. In that regard, the more abstract mathematical notion of "dimension" is used all the time to describe things on a computational level that most people wouldn't associate with their idea of "dimension". For example, a picture on the computer can be thought of as a single point in some extremely high dimensional space (Im talking on the scale of millions of dimensions).

Personally, I'd find a more interesting occult correlation between the neural network structure shapes being directed/undirect simplices. If anyone is curious about learning about some of the mathematics behind those sorts of structures (called graphs) I'd recommend Introduction to Graph Theory by Dover books on the subject. It's a great introduction and has a great preface on the subject of mathematics.

u/Croc600 · 12 pointsr/sociology

R for Data Science is great, especially because it teaches tidyverse.

Another good book is Learning Statistics with R: A tutorial for psychology students and other beginners, which also teaches the implementation of basic statistical techniques, like ANOVA or linear regression.

If you have some time spare, you can follow it by Data Analysis Using Regression and Multilevel/Hierarchical Models, which is also (mostly) based on R.

The Visual Display of Quantitative Information is a good book on the principles of data visualization. It’s theoretical, so no R examples.

Complex Surveys: A Guide to Analysis Using R is great if you work with survey data, especially if you work with complex designs (which nowdays is pretty much all the time).

Personaly, I would also invest some time learning methodology. Sadly, I can’t help you here, because I didn’t used textbook for this, but people seem to like books from Earl Babbie.

u/DaxACTN · 11 pointsr/ucf

The textbook is usually Discrete Mathematics and It's Applications. Don't let the bookstore fool you, the sell the "UCF Edition" for an inflated price. The only difference is an additional introduction. Here is an Amazon link where you should be able to find a reasonably priced used copy. Alternatively, here is a link to a PDF copy that you can have for free! Enjoy =)

u/paultypes · 11 pointsr/programming

Of course efforts like this won't fly because there will be people who sincerely want to can them because it's "computerized racial profiling," completely missing the point that, if race does correlate with criminal behavior, you will see that conclusion from an unbiased system. What an unbiased system will also do is not overweight the extent to which race is a factor in the analysis.

Of course, the legitimate concern some have is about the construction of prior probabilities for these kinds of systems, and there seems to be a great deal of skepticism about the possibility of unbiased priors. But over the last decade or two, the means of constructing unbiased priors have become rather well understood, and form the central subject matter of Part II of E.T. Jaynes' Probability Theory: The Logic of Science, which I highly recommend.

u/MRItopMD · 11 pointsr/medicalschool

Sure! I have a lot of resources on this subject. Before I recommend it, let me very quickly explain why it is useful.

Bayes Rule basically means creating a new hypothesis or belief based on a novel event using prior hypothesis/data. So I am sure you can already see how useful it would be in medicine to think about. The Rule(or technically theorem) is in fact an entire field of statisitcs and basically is one of the core parts of probability theory.

Bayes Rule explains why you shouldn't trust sensitivity and specificity as much as you think. It would take too long to explain here but if you look up Bayes' Theorem on wikipedia one of the first examples is about how despite a drug having 99% sensitivity and specificity, even if a user tests positive for a drug, they are in fact more likely to not be taking the drug at all.

Ok, now book recommendations:

Basic: https://www.amazon.com/Bayes-Theorem-Examples-Introduction-Beginners-ebook/dp/B01LZ1T9IX/ref=sr_1_2?ie=UTF8&amp;amp;qid=1510402907&amp;amp;sr=8-2&amp;amp;keywords=bayesian+statistics

https://www.amazon.com/Bayes-Rule-Tutorial-Introduction-Bayesian/dp/0956372848/ref=sr_1_6?ie=UTF8&amp;amp;qid=1510402907&amp;amp;sr=8-6&amp;amp;keywords=bayesian+statistics

Intermediate/Advanced: Only read if you know calculus and linear algebra, otherwise not worth it. That said, these books are extremely good and are a thorough intro compared to the first ones.

https://www.amazon.com/Bayesian-Analysis-Chapman-Statistical-Science/dp/1439840954/ref=sr_1_1?ie=UTF8&amp;amp;qid=1510402907&amp;amp;sr=8-1&amp;amp;keywords=bayesian+statistics

https://www.amazon.com/Introduction-Probability-Chapman-Statistical-Science/dp/1466575573/ref=sr_1_12?s=books&amp;amp;ie=UTF8&amp;amp;qid=1510403749&amp;amp;sr=1-12&amp;amp;keywords=probability

$9.36 and free shipping. Honestly. You'll be improving yourself while being able to amaze others at your "magic". u/analysis1837 · 10 pointsr/math At the moment, psychology is largely ad-hoc, and not a modicum of progress would've been made without the extensive utilization of statistical methods. To consider the human condition does not require us to simply extrapolate from our severely limited experiences, if not from the biases of limited datasets, datasets for which we can't even be certain of their various e.g. parameters etc.. For example, depending on the culture, the set of phenotypical traits with which increases the sexual attraction of an organism may be different - to state this is meaningless and ad-hoc, and we can only attempt to consider the validity of what was stated with statistical methods. Still, there comes along social scientists who would proclaim arbitrary sets of phenotypical features as being universal for all humans in all conditions simply because they were convinced by limited and biased datasets (e.g. making extreme generalizations based on the United States' demographic while ignoring the entire world etc.). In fact, the author(s) of "Probability Theory: The Logic of Science" will let you know what they think of the shaky sciences of the 20th and 21st century, social science and econometrics included, the shaky sciences for which their only justifications are statistical methods. _ With increasing mathematical depth and the increasing quality of applied mathematicians into such fields of science, we will begin to gradually see a significant improvement in the validity of said respective fields. Otherwise, currently, psychology, for example, holds no depth, but the field itself is very entertaining to me; doesn't stop me from enjoying Michael's "Mind Field" series. For mathematicians, physics itself lacks rigour, let alone psychology. _ Note, the founder of "psychoanalysis", Sigmund Freud, is essentially a pseudo-scientist. Like many social scientists, he made the major error of extreme extrapolation based on his very limited and personal life experiences, and that of extremely limited, biased datasets. Sigmund Freud "proclaimed" a lot of truths about the human condition, for example, Sigmund Fraud is the genius responsible for the notion of "Penis Envy". In the same century, Einstein would change the face of physics forever after having published the four papers in his miracle year before producing the masterpiece of General Relativity. And, in that same century, incredible progress such that of Gödel's Incompleteness Theorem, Quantum Electrodynamics, the discovery of various biological reaction pathways (e.g. citric acid cycle etc.), and so on and so on would be produced while Sigmund Fraud can be proud of his Penis Envy hypothesis. u/CrazyStatistician · 10 pointsr/statistics Bayesian Data Analysis and Hoff are both well-respected. The first is a much bigger book with lots of applications, the latter is more of an introduction to the theory and methods. u/idroppedmyapple · 10 pointsr/datascience So off the top off my head, I can’t think of any courses. Here are three books that include exercieses that are relatively comprehensive and explain their material well. They all touch upon basic methods that are good to know but also how to do analyses with them. • Hands-On Machine Learning with Scikit-Learn and TensorFlow. General machine learning and intro to deep learning (python) - link • The Elements of Statistical Learning. Basic statistical modelling (R) link • Statistical rethinking. Bayesian statistics (R) link - there are lectures to this book as well But there are many many others. Then there are plenty of tutorials to python, R or how to handle databases (probably the core programming languages, unless you want to go the GUI route). u/COOLSerdash · 9 pointsr/statistics u/statmama · 9 pointsr/statistics Seconding /u/khanable_ -- most of statistical theory is built on matrix algebra, especially regression. Entry-level textbooks usually use simulations to explain concepts because it's really the only way to get around assuming your audience knows linear algebra. My Ph.D. program uses Casella and Berger as the main text for all intro classes. It's incredibly thorough, beginning with probability and providing rigorous proofs throughout, but you would need to be comfortable with linear algebra and at least the basic principles of real analysis. That said, this is THE book that I refer to whenever I have a question about statistical theory-- it's always on my desk. u/siddboots · 9 pointsr/statistics It is hard to provide a "comprehensive" view, because there's so much disperate material in so many different fields that draw upon probability theory. Feller is an approachable classic that covers all of the main results in traditional probability theory. It certainly feels a little dated, but it is full of the deep central limit insights that are rarely explained in full in other texts. Feller is rigorous, but keeps applications at the center of the discussion, and doesn't dwell too much on the measure-theoretical / axiomatic side of things. If you are more interested in the modern mathematical theory of probability, try Probability with Martingales. On the other hand, if you don't care at all about abstract mathematical insights, and just want to be able to use probabilty theory directly for every-day applications, then I would skip both of the above, and look into Bayesian probabilistic modelling. Try Gelman, et. al.. Of course, there's also machine learning. It draws on a lot of probability theory, but often teaches it in a very different way to a traditional probability class. For a start, there is much more emphasis on multivariate models, so linear algebra is much more central. (Bishop is a good text). u/CoreyN · 8 pointsr/math Tenenbaum and Pollard's ODE book made the subject come quite easily when all my$150 textbook did was confuse me.

u/zifyoip · 8 pointsr/math

Here is the book I always recommend for people who want an introduction to graph theory:

• Introduction to Graph Theory, Richard J. Trudeau

It's super cheap (only 3.99 on Amazon) and I think it's really a good introduction to the subject. It doesn't go as far in depth as more advanced books, but Kuratowski's theorem is covered in Chapter&amp;nbsp;3. u/tiii · 8 pointsr/econometrics Both time series and regression are not strictly econometric methods per se, and there are a range of wonderful statistics textbooks that detail them. If you're looking for methods more closely aligned with econometrics (e.g. difference in difference, instrumental variables) then the recommendation for Angrist 'Mostly Harmless Econometrics' is a good one. Another oft-prescribed econometric text that goes beyond Angrist is Wooldridge 'Introductory Econometrics: A Modern Approach'. For a very well considered and basic approach to statistics up to regression including an excellent treatment of probability theory and the basic assumptions of statistical methodology, Andy Field (and co's) books 'Discovering Statistics Using...' (SPSS/SAS/R) are excellent. Two excellent all-rounders are Cohen and Cohen 'Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences' and Gelman and Hill 'Data Analysis Using Regression and Multilevel/Hierarchical Modelling' although I would suggest both are more advanced than I am guessing you need right now. For time series I can recommend Rob Hyndman's book/s on forecasting (online copy freely available) For longitudinal data analysis I really like Judith Singer's book 'Applied Longitudinal Data Analysis'. It sounds however as if you're looking for a bit of a book to explain why you would want to use one method over another. In my experience I wanted to know this when I was just starting. It really comes down to your own research questions and the available data. For example I had to learn Longitudinal/fixed/random effects modelling because I had to do a project with a longitudinal survey. Only after I put it into practice (and completed my stats training) did I come to understand why the modelling I used was appropriate. u/DiogenicOrder · 8 pointsr/statistics How would you rather split beginner vs intermediate/advanced ? My feeling was that Ben Lambert's book would be a good intro and that Bayesian Data Analysis would be a good next ? u/raubry · 8 pointsr/math Practical Algebra: A Self-Teaching Guide really helped me a couple of years ago when I had to get up to speed on algebra quickly. Beyond that, you can hardly do better in the best-bang-for-the-buck department than the Humongous Books series. 1000 problems in each book, annotated and explained, and he has an entertaining style. The Humongous Book of Algebra Problems: Translated for People Who Don't Speak Math The Humongous Book of Geometry Problems: Translated for People Who Don't Speak Math The Humongous Book of Calculus Problems: For People Who Don't Speak Math u/rast_7 · 7 pointsr/learnprogramming You won't get a hang of anything until and unless you practice. Since you are having Object Oriented Programming, go on and make a project. This will give you a sense of accomplishment and on the way you will learn a lot of things. Talking about data structures, you will need the concepts of this course everywhere. I would suggest you to strengthen your basics by refering to CLRS or some other resource, that is totally your choice. But, implement the data structure you have learned. There are a lot of resources out there, I am listing some of my favorites: &gt;https://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P &gt;https://www.coursera.org/specializations/algorithms I would also suggest you to read discrete mathematics. The book that I use is &gt;https://www.amazon.com/Discrete-Mathematics-Applications-Seventh-Higher/dp/0073383090/ref=sr_1_1?ie=UTF8&amp;amp;qid=1492831532&amp;amp;sr=8-1&amp;amp;keywords=discrete+mathematics+kenneth+rosen You can also go through the discrete mathematics course from MIT OCW. In case you need some help, PM me. I'll be more than happy to help :) u/Shemptacular · 7 pointsr/CollegeBasketball Also about the relationship between statistical analyses and building narratives. There's a super good book that breaks a lot of this down in detail: https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535 u/tikael · 7 pointsr/AskPhysics Get a copy of Div, Grad, Curl. It will walk you through the math you need. u/fatangaboo · 7 pointsr/AskEngineers 1. Vector Calculus isn't just a required math course, and the often-suggested supplementary textbook Div, Grad, Curl, and All That has a terribly misleading title - VC's not just a temporary annoyance, you'll actually need this stuff later. 2. Same for probability. If you skate thru probability hoping you can forget it right away, you're gonna have a bad time in your Signals classes and your Communications classes later. Stochastic Processes will strangle you and urinate on your corpse. 3. During your internship(s), do your best to befriend the engineers you work around &amp; with. They have much to teach you and can give you excellent advice after your internship is over. Plus they can write letters of reference that are a lot more influential than your Logic Design professor can write. 4. No matter how much you enjoyed your Chemistry classes, and no matter how well you did in them, it turns out that Chemistry is 99% irrelevant to EE. Sorry. 5. Programming and software are a fact of EE life. Become a good coder and don't let your skills atrophy. Learn Linux or at least UNIX or at least the UNIX underpinnings of MAC OSX. Learn command line tools. 6. Often the best EEs are the ones with the most bravery, the least afraid of the unknown. "I've never done that before" is a reason to jump in and try something, NOT an excuse to back away. 7. Analysis Paralysis really does exist. Avoid it. u/Puckered_Sphincter · 7 pointsr/math An Introduction to Manifolds by Tu is a very approachable book that will get you up to Stokes. Might as well get the full version of Stokes on manifolds not just in analysis. From here you can go on to books by Ramanan, Michor, or Sharpe. A Guide to Distribution Theory and Fourier Transforms by Strichartz was my introduction to Fourier analysis in undergrad. Probably helps to have some prior Fourier experience in a complex analysis or PDE course. Bartle's Elements of Integration and Legesgue Measure is great for measure theory. Pretty short too. Intro to Functional Analysis by Kreysig is an amazing introduction to functional analysis. Don't know why you'd learn it from any other book. Afterwards you can go on to functional books by Brezis, Lax, or Helemskii. u/dargscisyhp · 7 pointsr/AskScienceDiscussion I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done. If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try. Basics I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW. Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving. From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done. This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on. Intermediate At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better. This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point. Advanced Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev. Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time. Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject. u/crypto_ha · 7 pointsr/learnmachinelearning Since you are already going to take Machine Learning and want to build a good statistical foundation, I highly recommend Mathematical Statistics with Applications by Wackerly et al. u/Blizzarex · 7 pointsr/PhilosophyofScience If you like logic and the scientific method, I recommend E. T. Jaynes' Probability Theory: The Logic of Science. You can buy it here: http://www.amazon.com/Probability-Theory-The-Logic-Science/dp/0521592712/ or read a PDF here: http://shawnslayton.com/open/Probability%2520book/book.pdf u/de_shrike · 7 pointsr/india It can't be helped, the price is almost the same for the first book on amazon.com and I assume a similar trend for the others. Hardcovers in general are more expensive due to the intrinsic higher cost of manufacturing. What you may have observed is that other books have lower cost Asian editions that make them more affordable for nations with smaller economies, but these research books do not serve such a niche as such. What is interesting though is that state of the art Machine Learning is usually not in these books, and is simply being published in papers and blog posts as of late. u/Robin_Banx · 7 pointsr/learnmath Reposted from this thread: http://www.reddit.com/r/IWantToLearn/comments/mqoxx/iwtl_math/ "Had a very similar path. Decided to bite the bullet and take my school's remedial algebra course, as I cheated through middle and high school and thus knew nothing. Failed remedial algebra and retook it. Now I'm graduating with a math minor and am taking a calc-based probability theory course. Have hope! Advice: 1. Find something to motivate you. I was inspired partially by a friend explaining couple of high-level concepts to me. What little I understood sounded fascinating, and I wanted to know more. Part of the reason math can get tough is that there might be no "light at the end of the tunnel" that will reward your hard work. 2. While immersing yourself in cool stuff can be good to keep you motivated, remember to do the "boring parts" too. Unfortunately, not everything can be awesome serendipity. There is no going around the fact that you're going to have to spend some time just going through practice problems. Way past the point when it stops being fun. You need to develop intuitions about certain things in order for the profundity of later things to really sink, and there's no way to do that aside from doing a bunch of problems. 3. Khan Academy's great. Right now they have tons of practice problems too. I highly recommend this book: http://www.amazon.com/Humongous-Book-Algebra-Problems-Translated/dp/1592577229 Lots of problems broken down step-by-step. Skipped steps are one of the hardest things to deal with when you don't yet have much mathematical knowledge, especially during self-study. Look for other books by the author, W. Michael Kelly. 4. This blog has a lot of useful general study advice: http://calnewport.com/blog/ An interesting take on math and math education, though a little bitter: http://www.maa.org/devlin/LockhartsLament.pdf Godspeed, sir!" u/MyMoon0hMyMoon · 7 pointsr/learnmath Do not enroll in a precalculus class until you have a solid grasp on the foundations of precalculus. Precalculus is generally considered to be the fundamentals required for calculus and beyond (obviously), and a strong understanding of precalculus will serve you well, but in order to do well in precalculus you still need a solid understanding of what comes before, and there is quite a bit. I do not mean to sound discouraging, but I was tutoring a guy in an adult learning program from about December 2017-July 2018...I helped him with his homework and answered any questions that he had, but when he asked me to really get into the meat of algebra (he needed it for chemistry to become a nurse) I found a precalculus book at the library and asked him to go over the prerequisite chapter and it went completely over his head. Perhaps this is my fault as a tutor, but I do not believe so. What I am saying is that you need a good foundation in the absolute basics before doing precalculus and I do not believe that you should enroll in a precalculus course ASAP because you may end up being let down and then give up completely. I would recommend pairing Basic Mathematics by Serge Lang with The Humongous Book of Algebra Problems (though any book with emphasis on practice will suffice) and using websites like khanacademy for additional practice problems and instructions. Once you have a good handle on this, start looking at what math courses are offered at your nearest CC and then use your best judgment to decide which course(s) to take. I do not know how old you are, but if you are anything like me, you probably feel like you are running out of time and need to rush. Take your time and practice as much as possible. Do practice problems until it hurts to hold the pencil. u/lbkulinski · 6 pointsr/Purdue CS182 is a discrete mathematics course. It has a lot to do with logic and proofs, and less to do with algebra and calculus. Most have never really seen what you will be covering. If you can, I would get the book and work through some of the problems before the start of the semester. CS240 is similar to CS180, but it is taught in C — a much lower-level language. Once again, I recommend getting the book (I assume it will be The C Programming Language) and doing some of the exercises. Java syntax comes from C/C++, so that part will be somewhat familiar. C is pretty barebones, though. There are no classes, only functions. There is no ArrayList, LinkedList, etc. You have to build it all yourself. And when you allocate memory using malloc() (similar to calling new), you have to remember to free it when you’re done using free(). There is no garage collection. Good luck! u/rednarg · 6 pointsr/booksuggestions memory, just pick one book the basics are the same: A Sheep Falls Out of the Tree, Quantum Memory Power, not just memory techniques but with a section on Improve your intelligence math: secrets of mental math Among many others who can be given the title of the world's most intelligent person is Marilyn vos Savant: one of her books u/InfinityFlat · 6 pointsr/learnmath You may find Kreyszig's Introductory Functional Analysis with Applications interesting. EDIT: NoLemurs suggested Shankar as a good text that proceeds from first principles. Another book famous for deriving beautiful results from basic physical ideas is Landau's Quantum Mechanics, though it is quite dense and not at all pedagogical. u/gerschgorin · 6 pointsr/math An Introduction to Ordinary Differential Equations -7.62

Ordinary Differential Equations - $14.74 Partial Differential Equations for Scientists and Engineers -$11.01

Dover books on mathematics have great books for very cheap. I personally own the second and third book on this list and I thought they were a great resource, especially for the price.

u/schmook · 6 pointsr/MachineLearning

Imagine you have a dataset without labels, but you want to solve a supervised problem with it, so you're going to try to collect labels. Let's say they are pictures of dogs and cats and you want to create labels to classify them.

One thing you could do is the following process:

1. Get a picture from your dataset.
2. Show it to a human and ask if it's a cat or a dog.
3. If the person says it's a cat or dog, mark it as a cat or dog.
4. Repeat.

(I'm ignoring problems like pictures that are difficult to classify or lazy or adversarial humans giving you noisy labels)

That's one way to do it, but is it the most efficient way? Imagine all your pictures are from only 10 cats and 10 dogs. Suppose they are sorted by individual. When you label the first picture, you get some information about the problem of classifying cats and dogs. When you label another picture of the same cat, you gain less information. When you label the 1238th picture from the same cat you probably get almost no information at all. So, to optimize your time, you should probably label pictures from other individuals before you get to the 1238th picture.

How do you learn to do that in a principled way?

Active Learning is a task where instead of first labeling the data and then learning a model, you do both simultaneously, and at each step you have a way to ask the model which next example should you manually classify for it to learn the most. You can than stop when you're already satisfied with the results.

You could think of it as a reinforcement learning task where the reward is how much you'll learn for each label you acquire.

The reason why, as a Bayesian, I like active learning, is the fact that there's a very old literature in Bayesian inference about what they call Experiment Design.

Experiment Design is the following problem: suppose I have a physical model about some physical system, and I want to do some measurements to obtain information about the models parameters. Those measurements typically have control variables that I must set, right? What are the settings for those controls that, if I take measurements on that settings, will give the most information about the parameters?

As an example: suppose I have an electric motor, and I know that its angular speed depends only on the electric tension applied on the terminals. And I happen to have a good model for it: it grows linearly up to a given value, and then it becomes constant. This model has two parameters: the slope of the linear growth and the point where it becomes constant. The first looks easy to determine, the second is a lot more difficult. I'm going to measure the angular speed at a bunch of different voltages to determine those two parameters. The set of voltages I'm going to measure at is my control variable. So, Experiment Design is a set of techniques to tell me what voltages I should measure at to learn the most about the value of the parameters.

I could do Bayesian Iterated Experiment Design. I have an initial prior distribution over the parameters, and use it to find the best voltage to measure at. I then use the measured angular velocity to update my distribution over the parameters, and use this new distribution to determine the next voltage to measure at, and so on.

How do I determine the next voltage to measure at? I have to have a loss function somehow. One possible loss function is the expected value of how much the accuracy of my physical model will increase if I measure the angular velocity at a voltage V, and use it as a new point to adjust the model. Another possible loss function is how much I expect the entropy of my distribution over parameters to decrease after measuring at V (the conditional mutual information between the parameters and the measurement at V).

Active Learning is just iterated experiment design for building datasets. The control variable is which example to label next and the loss function is the negative expected increase in the performance of the model.

So, now your procedure could be:

• a model to predict if the picture is a cat or a dog. It's probably a shit model.
• a dataset of unlabeled pictures
• a function that takes your model and a new unlabeled example and spits an expected reward if you label this example
6. Do:
1. For each example in your current unlabeled set, calculate the reward
2. Choose the example that have the biggest reward and label it.
3. Continue until you're happy with the performance.
7. ????
8. Profit

Or you could be a lot more clever than that and use proper reinforcement learning algorithms. Or you could be even more clever and use "model-independent" (not really...) rewards like the mutual information, so that you don't over-optimize the resulting data set for a single choice of model.

I bet you have a lot of concerns about how to do this properly, how to avoid overfitting, how to have a proper train-validation-holdout sets for cross validation, etc, etc, and those are all valid concerns for which there are answers. But this is the gist of the procedure.

You could do Active Learning and iterated experiment design without ever hearing about bayesian inference. It's just that those problems are natural to frame if you use bayesian inference and information theory.

About the jargon, there's no way to understand it without studying bayesian inference and machine learning in this bayesian perspective. I suggest a few books:

• Information Theory, Inference, and Learning Algorithms, David Mackay - for which you can get a pdf or epub for free at this link.

Is a pretty good introduction to Information Theory and bayesian inference, and how it relates to machine learning. The Machine Learning part might be too introductory if already know and use ML.

• Bayesian Reasoning and Machine Learning by David Barber - for which you can also get a free pdf here

Some people don't like this book, and I can see why, but if you want to learn how bayesians think about ML, it is the most comprehensive book I think.

• Probability Theory, the Logic of Science by E. T. Jaynes. Free pdf of the first few chapters here.

More of a philosophical book. This is a good book to understand what bayesians find so awesome about bayesian inference, and how they think about problems. It's not a book to take too seriously though. Jaynes was a very idiosyncratic thinker and the tone of some of the later chapters is very argumentative and defensive. Some would even say borderline crackpot. Read the chapter about plausible reasoning, and if that doesn't make you say "Oh, that's kind of interesting...", than nevermind. You'll never be convinced of this bayesian crap.

u/M_Bus · 6 pointsr/statistics

Wellll I'm going to speak in some obscene generalities here.

There are some philosophical reasons and some practical reasons that being a "pure" Bayesian isn't really a thing as much as it used to be. But to get there, you first have to understand what a "pure" Bayesian is: you develop reasonable prior information based on your current state of knowledge about a parameter / research question. You codify that in terms of probability, and then you proceed with your analysis based on the data. When you look at the posterior distributions (or posterior predictive distribution), it should then correctly correspond to the rational "new" state of information about a problem because you've coded your prior information and the data, right?

WELL let's touch on the theoretical problems first: prior information. First off, it can be very tricky to code actual prior information into a true probability distribution. This is one of the big turn-offs for frequentists when it comes to Bayesian analysis. "Pure" Bayesian analysis sees prior information as necessarily coming before the data is ever seen. However, suppose you define a "prior" whereby a parameter must be greater than zero, but it turns out that your state of knowledge is wrong? What if you cannot codify your state of knowledge as a prior? What if your state of knowledge is correctly codified but makes up an "improper" prior distribution so that your posterior isn't defined?

Now'a'days, Bayesians tend to think of the prior as having several purposes, but they also view it as part of your modeling assumptions - something that must be tested to determine if your conclusions are robust. So you might use a weakly regularizing prior for the purposes of getting a model to converge, or you might look at the effects of a strong prior based on other studies, or the effects of a non-informative prior to see what the data is telling you absent other information. By taking stock of the differences, you can come to a better understanding of what a good prediction might be based on the information available to you. But to a "pure" Bayesian, this is a big no-no because you are selecting the prior to fit together with the data and seeing what happens. The "prior" is called that because it's supposed to come before, not after. It's supposed to codify the current state of knowledge, but now'a'days Bayesians see it as serving a more functional purpose.

Then there are some practical considerations. As I mentioned before, Bayesian analysis can be very computationally expensive when data sets are large. So in some instances, it's just not practical to go full Bayes. It may be preferable, but it's not practical. So you wind up with some shortcuts. I think that in this sense, modern Bayesians are still Bayesian - they review answers in reference to their theoretical understanding of what is going on with the distributions - but they can be somewhat restricted by the tools available to them.

As always with Bayesian statistics, Andrew Gelman has a lot to say about this. Example here and here and he has some papers that are worth looking into on the topic.

There are probably a lot of other answers. Like, you could get into how to even define a probability distribution and whether it has to be based on sigma algebras or what. Jaynes has some stuff to say about that.

If you want a good primer on Bayesian statistics that has a lot of talking and not that much math (although what math it does have is kind of challenging, I admit, though not unreachable), read this book. I promise it will only try to brainwash you a LITTLE.

u/GeneralEbisu · 6 pointsr/math

I'm also planning on doing a Masters in Math or CS. What do you plan to write for your masters?

&gt; Anybody else feels like this?

I think its natural to doubt yourself, sometimes. I dont know what else to say, but just try to be objective and emotionless about it (when you get stuck in a problem).

The following books that helped me improve my math problem solving skills when I was an undergrad:

u/david55555 · 6 pointsr/math

I think this is the recommended replacement for Polya's "How to Solve It"

http://www.amazon.com/How-Solve-It-Mathematical-Princeton/dp/069111966X

Seriously what do you want to be "modernized?"

u/yagsuomynona · 6 pointsr/math
u/bit_pusher · 5 pointsr/personalfinance

Link to Dave Ramsey on credit cards

I am not a fan of Dave Ramsey in many specific cases and this is one of them.

First, having access to a ready line of credit is important to financial security if you do not have access to a similar amount of immediate cash. Even forms of liquid capital may require to much time for conversion in an emergency. This can be overcome, obviously, with a large emergency savings pool but then this savings isn't working for you in an index fun, etc. As such, having access to an emergency line of credit is important even if you never plan on using a credit card day to day.

Second, building credit is necessary for long term savings on loans and mortgages. While it is possible to build credit without a credit card it is more difficult.

Third, avoiding rewards is leaving money on the table similar to not contributing to a 401k when match is available.

Ramsey's advice is often about eliminating options for risky behavior which is one way to reduce your possible debt burden, but it is not the only way. The more obvious way, which requires personal self discipline.

Dave Ramsey quotes:

"Even by paying the bills on time, you are not beating the system!". It isn't about beating the system, it is about using the system as intended and getting the rewards the system put in place to encourage your use of their credit card over others. Credit card companies make their profit off vendors and consumers. Credit card companies bank on a pool of consumers having some who do not pay their bills on time and some who do, similar to insurance, and offset their risk with rewards with one group over another. The problem with Ramsey's statement is that we are making individual decisions as individual actors within the context of a "system" built around a large pool of participants. The two are disjointed ideas and make no sense in the context of each other.

"A study of credit card use at McDonald’s found that people spent 47% more when using credit instead of cash." This is one of those statements I would refer people to How Not to Be Wrong: The Power of Mathematical Thinking where a statistic has been taking out of context to support a point but is, likely, unrelated. We live in a relatively cashless society and people are more likely to make larger purchases on a card rather than with cash so relative size of purchases will always favor a credit card.

"Personal finance is 80% behavior. You need to cut out habits that make you spend more. You do not build wealth with credit cards. Use common sense." And this is completely true. Personal finance is about personal behavior and creating good habits. If you habitually pay off your credit card month over month, never spending more credit than you have cash reserves, then you are at no greater risk than if you used cash for those same purchases.

u/blueboybob · 5 pointsr/Physics

To me its about what you can do in your head. Get a book for example, BOOK is good.

Also, subscribe to /r/math. Finally, ANYTIME you see a number do something with it. Factor it, think of a historical significance, etc.

u/mrburrows · 5 pointsr/IWantToLearn

First off, I'd recommend looking into a book like this.

Second, when doing something like multiplication, it always helps to break a problem down into easier steps. Typically, you want to be working with multiples of 10/100/1000s etc.

For multiplying 32 by 32, I would break it into two problems: (32 x 30) + (32 x 2). With a moderate amount of practice, you should quickly be able to see that the first term is 960, and the second is 64. Adding them together gives the answer: 1024. It can be tricky to keep all these numbers in your head at once, but that honestly just comes down to practice.

Also, that same question can be expressed as 32^2 . These types of problems have a whole bunch of neat tricks. One that I recall from the book I linked above has to do with squaring any number ending in a 5, like 15 or 145. First, the number will always end in 25. For the leading digits, take the last 5 off the number, and multiply the remaining digits by their value +1. So, for 15 we just have 1x2=2. For 145, we have 14x15=210. Finally, tack 25 on the end of that, so you have 15^2 = (1x2)25 = 225, and 145^2 = (14x15)25 = 21025. Boom! Now you can square any number ending in 5 really quick.

Edit: Wanted to add some additional comments that have helped me out through the years. First, realize that

(1) Addition is easier than subtraction,

(2) Addition and subtraction are easier than multiplication,

(3) Multiplication is easier than division.

Let's go through these one by one. For (1), try to rewrite a subtraction problem as addition. Say you're given 31 - 14; then rephrase the question as, what plus 14 equals 31? You can immediately see that the ones digit is 7, since 4+7 = 11. We have to remember that we are carrying the ten over to the next digit, and solve 1 + (1 carried over) + what = 3. Obviously the tens digit for our answer is 1, and the answer is 17. I hope I didn't explain that too poorly.

For (2), that's pretty much what I was originally explaining at the start. Try to break a multiplication problem down to a problem of simple multiplication plus addition or subtraction. One more example: 37 x 40. Here, 40 looks nice and simple to work with; 37 is also pretty close to it, so let's add 3 to it and just make sure to subtract it later. That way, you end up with 40 x 40 - (3 x 40) = 1600 - 120 = 1480.

I don't really have any hints with division, unfortunately. I don't really run into it too often, and when I do, I just resort to some mental long division.

u/HigherMathHelp · 5 pointsr/math

Good question OP! I drafted a blog article on this topic a while back but haven't published it yet. An excerpt is below.
--------

With equations, I sometimes just visualize what I'd usually do on paper. For arithmetic, there are actually a lot of computational methods that are better suited to mental computation than the standard pencil-and-paper algorithms.

There are tons of different options, often for the same problem. The main thing is to understand some general principles, such as breaking a problem down into easier sub-problems, and exploiting special features of a particular problem.

Below are some basic methods to give you an idea. (These may not all be entirely different from the pencil-and-paper methods, but at the very least, the format is modified to make them easier to do mentally.)

(1) Separate into place values: 27+39= (20+30)+(7+9)=50+16=66

We've reduced the problem into two easier sub-problems, and combining the sub-problems in the last step is easy, because there is no need to carry as in the standard written algorithm.

(2) Exploit special features: 298+327 = 300 + 327 -2 = 625

We could have used the place value method, but since 298 is close to 300, which is easy to work with, we can take advantage of that by thinking of 298 as 300 - 2.

SUBTRACTION

(1) Number-line method: To find 71-24, you move forward 6 units on the number line to get to 30, then 41 more units to get to 71, for a total of 47 units along the number line.

(2) There are other methods, but I'll omit these, since the number-line method is a good starting point.

MULTIPLICATION

(1) Separate into place values: 18*22 = 18*(20+2)=360+36=396.

(2) Special features: 18*22=(20-2)*(20+2)=400-4=396

Here, instead of using place values, we use the feature that 18*22 can be written in the form (a-b)*(a+b) to obtain a difference of squares.

(3) Factoring method: 14*28=14*7*4=98*4=(100-2)*4=400-8=392

Here, we've turned a product of two 2-digit numbers into simpler sub-problems, each involving multiplication by a single-digit number (first we multiply by 7, then by 4).

(4) Multiplying by 11: 11*52= 572 (add the two digits of 52 to get 5+2=7, then stick 7 in between 5 and 2 to get 572).

This can be done almost instantaneously; try using the place-value method to see why this method works. Also, it can be modified slightly to work when the sum of the digits is a two digit number.

DIVISION
(1) Educated guess plus error correction: 129/7 = ? Note that 7*20=140, and we're over by 11. We need to take away two sevens to get back under, which takes us to 126, so the answer is 18 with a remainder of 3.

(2) Reduce first, using divisibility rules. Some neat rules include the rules for 3, 9, and 11.

The rules for 3 and 9 are probably more well known: a number is divisible by 3 if and only if the sum of its digits is divisible by 3 (replace 3 with 9 and the same rule holds).

For example, 5654 is not divisible by 9, since 5+6+5+4=20, which is not divisible by 9.

The rule for 11 is the same, but it's the alternating sum of the digits that we care about.

Using the same number as before, we get that 5654 is divisible by 11, since 5-6+5-4=0, and 0 is divisible by 11.

PRACTICE
I think it's kind of fun to get good at finding novel methods that are more efficient than the usual methods, and even if it's not that fun, it's at least useful to learn the basics.

If you want to practice these skills outside of the computations that you normally do, there's a nice online arithmetic game I found that's simple and flexible enough for you to practice any of the four operations above, and you can set the parameters to work on numbers of varying sizes.

Happy calculating!
Greg at Higher Math Help

Edit: formatting

u/cannonballism · 5 pointsr/math
u/shivstroll · 5 pointsr/Physics

A commonly used book for this exact purpose is Div, Grad, Curl by Schey.

u/Edelsonc · 5 pointsr/math

For multivariable calculus I cannot recommend Div, Grad, Curl and All That enough. It’s got wonderful physically motivated examples and great problems. If you work through all the problems you’ll have s nice grasp on some central topics of vector calculus. It’s also rather thin, making it feel approachable for self learning (and easy to travel with).

u/Banach-Tarski · 5 pointsr/math

Hey I'm a physics BSc turned mathematician.

I would suggest starting with topology and functional analysis. Functional analysis is the foundation of quantum mechanics, and topology is necessary to properly understand manifolds, which are the foundation of relativity.

I would suggest Kreyszig for functional analysis. It's probably the most gentle functional analysis book out there.

For topology, I would suggest John Lee. This topology text is unique because it teaches general topology with a view towards manifolds. This makes it ideal for a physicist. If you want to know about Lie algebras and Lie groups, the sequel to this text discusses them.

u/clarinetist001 · 5 pointsr/statistics

If you are really good at calculus, learn some probability first. My personal favorite is Wackerly et al.'s Mathematical Statistics with Applications. This covers both the probability and mathematical stats background that you will see in college. The book is quite pricey, so I recommend buying it on half (dot) com.

You might notice that this text has a lot of negative reviews. This review of the above text explains the prerequisites quite well - this is not an AP-stats type of textbook:

&gt; I believe that this book is designed to teach statistics to those who plan on actually using it professionally (and not just to pass a required course) while continuing to develop one's own mathematical maturity. While Wackerly is not as rigorous as Ross's Probability book, it is taught at a completely different level than a non-calculus-based statistics course that are often taken by students who simply want to know which formula to use for the exam. I think of it as the ideal text for anyone in the sciences, engineering, or economics. The level of rigor is similar to the 2 Calculus courses online at MIT-Open Course Ware.
&gt;
&gt; [...]
&gt;
&gt; this book derives virtually every formula, allowing students to continue to develop their mathematical maturity which will be required for higher-level courses on bootstrapping, pattern recognition, statistical learning, etc. In order to follow these proofs (and also in order to solve problems from about 4 chapters) one must have a firm grasp of calculus. That not only means that one can integrate, differentiate, work with series, use L-Hopital's rule and integration-by-parts, but also that one understands the concepts of calculus very well.
&gt;
&gt; The proofs are all broken down so as to not really skip many steps, but as someone away from math for over 25 years, I must write down each step myself and make sure that I understand it before moving on. If a few steps are skipped, I must connect the dots myself using plenty of scratch paper. My math background was the Calculus series, ordinary differential equations, and linear algebra. About 1/5 of all problems are proof-based.

&gt; I will concede that you can't come at this book without an understanding of at least integral calculus (and since so many people get turned off by Algebra, well...), so I suspect a lot of the negative reviews here are written by people who jumped in the deep end of the pool without having a few swimming lessons. If you know the calculus and basic set theory, the book is exceedingly easy to follow.

Some of what you learned in AP Stats will transfer to calculus-based statistics, but a lot of what you learn in your undergrad will not be like anything you learned in AP Stats. Hence I'm recommending that you start from scratch on probability.

Generally speaking, I agree with /u/Akillees89 that you should get a head start in developing your math background. However, I don't agree that Strang or Axler are good for linear algebra for statistics. See my post here.

u/jonnydedwards · 5 pointsr/math

Bayes is the way to go: Ed Jayne's text Probability Theory is fundamental and a great read. Free chapter samples are here. Slightly off topic, David Mackay's free text is also wonderfully engaging.

u/shujaa-g · 5 pointsr/statistics

You're pretty good when it comes to linear vs. generalized linear models--and the comparison is the same regardless of whether you use mixed models or not. I don't agree at all with your "Part 3".

My favorite reference on the subject is Gelman &amp; Hill. That book prefers to the terminology of "pooling", and considers models that have "no pooling", "complete pooling", or "partial pooling".

One of the introductory datasets is on Radon levels in houses in Minnesota. The response is the (log) Radon level, the main explanatory variable is the floor of the house the measurement was made: 0 for basement, 1 for first floor, and there's also a grouping variable for the county.

Radon comes out of the ground, so, in general, we expect (and see in the data) basement measurements to have higher Radon levels than ground floor measurements, and based on varied soil conditions, different overall levels in different counties.

We could fit 2 fixed effect linear models. Using R formula psuedocode, they are:

1. radon ~ floor
2. radon ~ floor + county (county as a fixed effect)

The first is the "complete pooling" model. Everything is grouped together into one big pool. You estimate two coefficients. The intercept is the mean value for all the basement measurements, and your "slope", the floor coefficient, is the difference between the ground floor mean and the basement mean. This model completely ignores the differences between the counties.

The second is the "no pooling" estimate, where each county is in it's own little pool by itself. If there are k counties, you estimate k + 1 coefficients: one intercept--the mean value in your reference county, one "slope", and k - 1 county adjustments which are the differences between the mean basement measurements in each county to the reference county.

Neither of these models are great. The complete pooling model ignores any information conveyed by the county variable, which is wasteful. A big problem with the second model is that there's a lot of variation in how sure we are about individual counties. Some counties have a lot of measurements, and we feel pretty good about their levels, but some of the counties only have 2 or 3 data points (or even just 1). What we're doing in the "no pooling" model is taking the average of however many measurement there are in each county, even if there are only 2, and declaring that to be the radon level for that county. Maybe Lincoln County has only two measurements, and they both happen to be pretty high, say 1.5 to 2 standard deviations above the grand mean. Do you really think that this is good evidence that Lincoln County has exceptionally high Radon levels? Your model does, it's fitted line goes straight between the two Lincoln county points, 1.75 standard deviations above the grand mean. But maybe you're thinking "that could just be a fluke. Flipping a coin twice and seeing two heads doesn't mean the coin isn't fair, and having only two measurements from Lincoln County and they're both on the high side doesn't mean Radon levels there are twice the state average."

Enter "partial pooling", aka mixed effects. We fit the model radon ~ floor + (1 | county). This means we'll keep the overall fixed effect for the floor difference, but we'll allow the intercept to vary with county as a random effect. We assume that the intercepts are normally distributed, with each county being a draw from that normal distribution. If a county is above the statewide mean and it has lots of data points, we're pretty confident that the county's Radon level is actually high, but if it's high and has only two data points, they won't have the weight to pull up the measurement. In this way, the random effects model is a lot like a Bayesian model, where our prior is the statewide distribution, and our data is each county.

The only parameters that are actually estimated are the floor coefficient, and then the mean and SD of the county-level intercept. Thus, unlike the complete pooling model, the partial pooling model takes the county info into account, but it is far more parsimonious than the no pooling model. If we really care about the effects of each county, this may not be the best model for us to use. But, if we care about general county-level variation, and we just want to control pretty well for county effects, then this is a great model!

Of course, random effects can be extended to more than just intercepts. We could fit models where the floor coefficient varies by county, etc.

Hope this helps! I strongly recommend checking out Gelman and Hill.
u/klaxion · 5 pointsr/statistics

Recommendation - don't learn statistics through "statistics for biology/ecology".

Go straight to statistics texts, the applied ones aren't that hard and they usually have fewer of the lost-in-translation errors (e.g. the abuse of p-values in all of biology).

Try Gelman and Hill -

http://www.amazon.com/Analysis-Regression-Multilevel-Hierarchical-Models/dp/052168689X/ref=sr_1_1?ie=UTF8&amp;amp;qid=1427768688&amp;amp;sr=8-1&amp;amp;keywords=gelman+hill

Faraway - Practical Regression and Anova using (free)

http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf

Categorical data analysis

http://www.amazon.com/Categorical-Data-Analysis-Alan-Agresti/dp/0470463635/ref=sr_1_1?ie=UTF8&amp;amp;qid=1427768746&amp;amp;sr=8-1&amp;amp;keywords=categorical+data+analysis

u/bmike210 · 5 pointsr/Physics

For mathematical statistics: Statistical Inference.

Bioinformatics and Statistics: Statistical Methods in Bioinformatics.

R: R in a Nutshell.

Edit: The Elements of Statistical Learning (free PDF!!)

ESL is a great book, but it can get very difficult very quickly. You'll need a solid background in linear algebra to understand it. I find it delightfully more statistical than most machine learning books. And the effort in terms of examples and graphics is unparalleled.

u/Darumana · 5 pointsr/selfhelp

I hope I am not too late.

You can post this to /r/suicidewatch.

Here is my half-baked attempt at providing you with some answers.

First of all let's see, what is the problem? Money and women. This sounds rather stereotypical but it became a stereotype because a lot of people had this kind of problems. So if you are bad at money and at women, join the club, everybody sucks at this.

Now, there are a few strategies of coping with this. I can tell you what worked for me and perhaps that will help you too.

I guess if there is only one thing that I would change in your attitude that would improve anything is learning the fact that "there is more where that came from". This is really important in girl problems and in money problems.

When you are speaking with a girl, I noticed that early on, men tend to start being very submissive and immature in a way. They start to offer her all the decision power because they are afraid not to lose her. This is a somehow normal response but it affects the relationship negatively. She sees you as lacking power and confidence and she shall grow cold. So here lies the strange balance between good and bad: you have to be powerful but also warm and magnanimous. You can only do this by experimenting without fearing the results of your actions. Even if the worst comes to happen, and she breaks up with you .... you'll always get a better option. There are 3.5 billion ladies on the planet. The statistics are skewed in your favor.

Now for the money issue. Again, there is more where that came from. The money, are a relatively recent invention. Our society is built upon them but we survived for 3 million years without them. The thing you need to learn is that your survival isn't directly related to money. You can always get food, shelter and a lot of other stuff for free. You won't live the good life, but you won't die. So why the anxiety then?

Question: It seems to me you are talking out of your ass. How do I put into practice this in order to get a girlfriend?

Answer: Talk to people. Male and female. Make the following your goals:
Talk to 1 girl each day for one month.
Meet a few friends each 3 days.
Make a new friend each two weeks.
Post your romantic encounters in /r/seduction.
This activities will add up after some time and you will have enough social skill to attract a female. You will understand what your female friend is thinking. Don't feel too bad if it doesn't work out.

Question: The above doesn't give a lot of practical advice on getting money. I want more of that. How do I get it?

Answer: To give you money people need to care about you. People only care about you when you care about them. This is why you need to do the following:
Start solving hard problems.
Start helping people.
Problems aren't only school problems. They refer to anything: start learning a new difficult subject (for example start learning physics or start playing an instrument or start writing a novel). Take up a really difficult project that is just above the verge of what you think you are able to do. Helping people is something more difficult and personal. You can work for charity, help your family members around the house and other similar.

Question: I don't understand. I have problems and you are asking me to work for charity, donate money? How can giving money solve anything?

Answer: If you don't give, how can you receive? Helping others is instilling a sense of purpose in a very strange way. You become superior to others by helping them in a dispassionate way.

Question: I feel like I am going to cry, you are making fun of me!
Answer: Not entirely untrue. But this is not the problem. The problem is that you are taking yourself too serious. We all are, and I have similar problems. The true mark of a person of genius is to laugh at himself. Cultivate your sense of humor in any manner you can.

Question: What does it matter then if I choose to kill myself?

Answer: There is this really good anecdote about Thales of Miletus (search wiki). He was preaching that there is no difference between life and death. His friends asked him: If there is no difference, why don't you kill yourself. At this, he instantly answered: I don't kill myself because there is no difference.

Question: Even if I would like to change and do the things you want me to do, human nature is faulty. It is certain that I would have relapses. How do I snap out of it?

Answer: There are five habits that you should instill that will keep bad emotions away. Either of this habits has its own benefits and drawbacks:

1. Mental contemplation. This has various forms, but two are the best well know: prayer and meditation. At the beginning stage they are quite different, but later they begin to be the same. You will become aware that there are things greater than you are. This will take some of the pressure off of your shoulders.
2. Physical exercise. Build up your physical strength and you will build up your mental strength.
3. Meet with friends. If you don't have friends, find them.
4. Work. This wil give you a sense of purpose. Help somebody else. This is what I am doing here. We are all together on this journey. Even though we can't be nice with everyone, we need to at least do our best in this direction.
5. Entertainment. Read a book. Play a game. Watch a movie. Sometimes our brain needs a break. If not, it will take a break anyway and it will not be a pretty one. Without regular breaks, procrastination will occur.

Question: Your post seems somewhat interesting but more in an intriguing kind of way. I would like to know more.

Answer: There are a few good books on these subjects. I don't expect you to read all of them, but consider them at least.

For general mental change over I recommend this:
http://www.amazon.com/Learned-Optimism-Change-Your-Mind/dp/1400078393/ref=sr_1_1?ie=UTF8&amp;amp;qid=1324795853&amp;amp;sr=8-1

http://www.amazon.com/Generous-Man-Helping-Others-Sexiest/dp/1560257288

For girl issues I recommend the following book. This will open up a whole bag of worms and you will have an entire literature to pick from. This is not going to be easy. Remember though, difficult is good for you.
http://www.amazon.com/GAME-UNDERCOVER-SOCIETY-PICK-UP-ARTISTS/dp/1841957518/ref=sr_1_1?ie=UTF8&amp;amp;qid=1324795664&amp;amp;sr=8-1 (lately it is popular to dish this book for a number of reasons. Read it and decide for yourself. There is a lot of truth in it)

Regarding money problem, the first thing is to learn to solve problems. The following is the best in my opinion
http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X
The second thing about money is to understand why our culture seems wrong and you don't seem to have enough. This will make you a bit more comfortable when you don't have money.
http://www.amazon.com/Story-B-Daniel-Quinn/dp/0553379011/ref=sr_1_3?ie=UTF8&amp;amp;qid=1324795746&amp;amp;sr=8-3 (this one has a prequel called Ishmael. which people usually like better. This one is more to my liking.)

For mental contemplation there are two recommendations:
http://www.urbandharma.org/udharma4/mpe.html . This one is for meditation purposes.
http://www.amazon.com/Way-Pilgrim-Continues-His/dp/0060630175 . This one is if you want to learn how to pray. I am an orthodox Christian and this is what worked for me. I cannot recommend things I didn't try.

For exercising I found bodyweight exercising to be one of the best for me. I will recommend only from this area. Of course, you can take up weights or whatever.
http://www.amazon.com/Convict-Conditioning-Weakness-Survival-Strength/dp/0938045768/ref=sr_1_1?ie=UTF8&amp;amp;qid=1324795875&amp;amp;sr=8-1 (this is what I use and I am rather happy with it. A lot of people recommend this one instead: http://www.rosstraining.com/nevergymless.html )

Regarding friends, the following is the best bang for your bucks:
http://www.amazon.com/How-Win-Friends-Influence-People/dp/1439167346/ref=sr_1_1?ie=UTF8&amp;amp;qid=1324796461&amp;amp;sr=8-1 (again, lots of criticism, but lots of praise too)

The rest of the points are addressed in the above books. I haven't given any book on financial advices. Once you know how to solve problems and use google and try to help people money will start coming, don't worry.

I hope this post helps you, even though it is a bit long and cynical.

Merry Christmas!
u/ccondon · 5 pointsr/math

On a more serious note, this book by Polya is wonderful.

u/mkat5 · 5 pointsr/math

In the lead up to calc first thing you want to do is just make sure you're algebra skills are pretty solid. A lot of people neglect it and then find the course to be harder than it needed to be because you really use algebra throughout.

Beyond that, if you want an extra book to study with and get practice problems from The Calculus Lifesaver is a big book of calculus you can use from now and into a first year college calculus course. If you do get it, don't worry about reading the whole thing from cover to cover, or doing all of the problems in it. It is a big book for a reason, it definitely covers more than you need to know for now, so don't get overwhelmed, it all comes with time.

Best of luck

u/kypronite · 5 pointsr/learnprogramming

I highly recommend this book for learning calculus.
I faced same problem as yours with calculus and this book helped me alot.

u/skier_scott · 5 pointsr/math

As everyone else is saying, Gilbert Strang's book. He also has a [great course][1] on MIT's OCW.

[1]:http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm

u/timshoaf · 5 pointsr/education

&gt; Elementary Statistics
http://ftp.cats.com.jo/Stat/Statistics/Elementary%20Statistics%20%20-%20Picturing%20the%20World%20(gnv64).pdf

Presuming you mean this book, I am still at an absolute loss to understand how you think this doesn't somehow require algebra as a prerequisite.

All the manipulations about gaussian distributions, student t distributions, binomial distribution etc... or even the bit on regression, right there on page 502, how is that not algebra. It literally makes reference to the general form of a line in 2-space. Are they just expected to memorize those outright with no regard to their derivation?

How do you treat topics like expected value? Because it seems like right there on page 194 that they've given the general algebraic formula for discrete, real valued, random variable.

They seem to elide the treatment of continuous random variables. So I presume they won't even be going through the exercise of the mean of a Poisson.

All of that granted, this book still heavily relies on the ability to perform algebraic permutations. Right there on page 306 is the very z-score transform I explicitly mentioned earlier.

As far as where I teach, I don't, excepting the odd lecture to clients or coworkers. Typically, however, our domain does not fit prettily into the packaged up parameterized distributions of baccalaureate statistics. We deal in a lot of probabilistic graphical models, in manifold learning, in non-parametrics, etc.

The books I recommend to my audience (which is quite different than those who haven't a basic grasp on algebra) are:

u/Bambo222 · 5 pointsr/OMSCS

I can offer my two cents. I’m a Googler who uses machine learning to detect abuse, where my work is somewhere between analyst and software engineer. I’m also 50% done through the OMSCS program. Here’s what I’ve observed:

Yes, Reinforcement Learning, Computer Vision, and Machine Learning are 100% relevant for a career in data science. But data science is vague; it means different things depending on the company and role. There are three types of data science tasks and each specific job may be weighted more heavily in one of these three directions: (1) data analytics, reporting, and business intelligence focused, (2) statistical theory and model prototyping focused and (3) software engineering focused by launching models into production, but with less empathsis on statistical theory.

I've had to do a bit of all three types of work. The two most important aspects are (1) defining your problem as a data science/machine learning problem, and (2) launching the thing in a distributed production environment.

If you already have features and labeled data, you should be able to get a sense of what model you want to use within 24 hours on your laptop based on a sample of the data (this can be much much harder when you can't actually sample the data before you build the prod job because the data is already distributed and hard to wrangle). Getting the data, ensuring it represents your problem, and ensuring you have processes in place to monitor, re-train, evaluate, and manage FPs/FNs will take a vast majority of your time. Read this paper too: https://papers.nips.cc/paper/5656-hidden-technical-debt-in-machine-learning-systems.pdf

Academic classes will not teach you how to do this in a work environment. Instead, expect them to give you a toolbox of ideas to use, and it’s up to you to match the tool with the problem. Remember that the algorithm will just spit out numbers. You'll need to really understand what's going on, and what assumptions you are making before you use each model (e.g. in real life few random variables are nicely gaussian).

I do use a good amount of deep learning at work. But try not to - if a logistic regression or gradient boosted tree works, then use it. Else, you will need to fiddle with hyper parameters, try multiple different neural architectures (e.g. with time series prediction, do you start with a CNN with attention? CNN for preprocessing then DNN? LSTM-Autoencoder? Or LSTM-AE + Deep Regressor, or classical VAR or SARIMAX models...what about missing values?), and rapidly evaluate performance before moving forward. You can also pick up a deep learning book or watch Stanford lectures on the side; first have the fundamentals down. There are many, many ways you can re-frame and tackle the same problem. The biggest risk is going down a rabbit hole before you can validate that your approach will work, and wasting a lot of time and resources. ML/Data Science project outcomes are very binary: it will work well or it won’t be prod ready and you have zero impact.

I do think the triple threat of academic knowledge for success in this area would be graduate level statistics, computer science, and economics. I am weakest in theoretical statistics and really need to brush up on bayesian stats (https://www.amazon.com/Statistical-Rethinking-Bayesian-Examples-Chapman/dp/1482253445). But 9/10 times a gradient boosted tree with good features (it's all about representation) will work, and getting it in prod plus getting in buy-in from a variety of teams will be your bottleneck. In abuse and fraud; the distributions shift all the time because the nature of the problem is adversarial, so every day is interesting.

One of the post-docs in my department did his dissertation with Bayesian stats and he essentially had to teach himself! He strongly recommended this as a place to start if you are interested in that topic -- https://www.amazon.com/gp/product/1482253445/ref=oh_aui_detailpage_o09_s00?ie=UTF8&amp;amp;psc=1 (I have not read it yet.)

One of our computer science profs teaches Bayes for the CS folks and said he would be willing to put together a class for psych folks in conjunction with some other people, so that's a place where I am hoping to develop some competency at some point. I strongly recommend reaching outside of your department, especially if you are at a larger university!

u/Tabuhli · 5 pointsr/learnmath

I really believe that Michael Kelly's "Humongous Book of" series are the best resources for getting through all math classes up to Calculus II. These books contain every single type of problem you will ever encounter in Algebra I &amp; II, Geometry, Trig, and Calc I &amp; II, all solved in great detail. They are like Schaums Outlines but much more reliable.

https://www.amazon.com/Humongous-Basic-Pre-Algebra-Problems-Books/dp/1615640835

https://www.amazon.com/Humongous-Book-Algebra-Problems-Books/dp/1592577229

https://www.amazon.com/Humongous-Book-Geometry-Problems-Books/dp/1592578640

https://www.amazon.com/Humongous-Book-Trigonometry-Problems-Comprehensive/dp/1615641823

https://www.amazon.com/Humongous-Book-Calculus-Problems-Books/dp/1592575129

u/Rock0rSomething · 4 pointsr/aviation

How Not To Be Wrong explores this vignette in some detail - highly recommend the book!

u/Santarini · 4 pointsr/IWantToLearn

Check this book out!

It absolutely changed my mental math ability. Arthur Benjamin also has videos all over the Internet with some quick mental math tricks.

u/justdmg · 4 pointsr/math

I have a book on mental math, and this is essentially the technique that the author uses to square numbers mentally really quickly.

In other words,

x^2 = (x+k)(x-k) + k^2

where you substitute x's into the equation you gave.

This is the book.

u/NotherDayAnotherDoug · 4 pointsr/wholesomememes

What I love about David Foster Wallace is how profound his writing is across all topics. Whether he's writing about tennis, or exploring deep mathematical + philosophical concepts, it's always incredibly insightful. If anyone reading this enjoys the above quote and wants to read more DFW, but doesn't wish to attempt the intimidating tome that is Infinite Jest, I recommend wetting one's feet with his magazine article Consider the Lobster (footnotes on page 8, they're important).

u/joshuahutt · 4 pointsr/math

Not sure if they qualify as "beautifully written", but I've got two that are such good reads that I love to go back to them from time to time:

u/Aeschylus_ · 4 pointsr/Physics

You're English is great.

I'd like to reemphasize /u/Plaetean's great suggestion of learning the math. That's so important and will make your later career much easier. Khan Academy seems to go all through differential equations. All of the more advanced topics they have differential and integral calculus of the single variable, multivariable calculus, ordinary differential equations, and linear algebra are very useful in physics.

As to textbooks that cover that material I've heard Div, Grad, Curl for multivariable/vector calculus is good, as is Strang for linear algebra. Purcell an introductory E&amp;M text also has an excellent discussion of the curl.

As for introductory physics I love Purcell's E&amp;M. I'd recommend the third edition to you as although it uses SI units, which personally I dislike, it has far more problems than the second, and crucially has many solutions to them included, which makes it much better for self study. As for Mechanics there are a million possible textbooks, and online sources. I'll let someone else recommend that.

u/brmj · 4 pointsr/probabilitytheory

I'm only part way through it myself, but here's one I've been recomended in the past that I've been enjoying so far:

Probability Theory: The Logic of Science by E.T. Jaynes

http://www.amazon.com/Probability-Theory-The-Logic-Science/dp/0521592712

http://omega.albany.edu:8008/JaynesBook.html

The second link only appears to have the first three chapters in pdf (though it has everything as postscript files), but I would be shocked if you couldn't easilly find a free pdf off the whole thing online with a quick search.

u/lykonjl · 4 pointsr/statistics

Jaynes: Probability Theory. Perhaps 'rigorous' is not the first word I'd choose to describe it, but it certainly gives you a thorough understanding of what Bayesian methods actually mean.

u/gmarceau · 4 pointsr/science
u/placemirror · 4 pointsr/statistics

Try the two:

https://www.amazon.com/Introduction-Mathematical-Statistics-Robert-Hogg/dp/0321795431

https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

introduction to mathematical statistics by craig and statistical inference by george casella.

u/RAPhisher · 4 pointsr/statistics

In addition to linear regression, do you need a reference for future use/other topics? Casella/Berger is a good one.

For linear regression, I really enjoyed A Modern Approach to Regression with R.

u/dustlesswalnut · 4 pointsr/todayilearned

Innumeracy

u/marmle · 4 pointsr/statistics

The short version is that in a bayesian model your likelihood is how you're choosing to model the data, aka P(x|\theta) encodes how you think your data was generated. If you think your data comes from a binomial, e.g. you have something representing a series of success/failure trials like coin flips, you'd model your data with a binomial likelihood. There's no right or wrong way to choose the likelihood, it's entirely based on how you, the statistician, thinks the data should be modeled. The prior, P(\theta), is just a way to specify what you think \theta might be beforehand, e.g. if you have no clue in the binomial example what your rate of success might be you put a uniform prior over the unit interval. Then, assuming you understand bayes theorem, we find that we can estimate the parameter \theta given the data by calculating P(\theta|x)=P(x|\theta)P(\theta)/P(x) . That is the entire bayesian model in a nutshell. The problem, and where mcmc comes in, is that given real data, the way to calculate P(x) is usually intractable, as it amounts to integrating or summing over P(x|\theta)P(\theta), which isn't easy when you have multiple data points (since P(x|\theta) becomes \prod_{i} P(x_i|\theta) ). You use mcmc (and other approximate inference methods) to get around calculating P(x) exactly. I'm not sure where you've learned bayesian stats from before, but I've heard good things , for gaining intuition (which it seems is what you need), about Statistical Rethinking (https://www.amazon.com/Statistical-Rethinking-Bayesian-Examples-Chapman/dp/1482253445), the authors website includes more resources including his lectures. Doing Bayesian data analysis (https://www.amazon.com/Doing-Bayesian-Data-Analysis-Second/dp/0124058884/ref=pd_lpo_sbs_14_t_1?_encoding=UTF8&amp;amp;psc=1&amp;amp;refRID=58357AYY9N1EZRG0WAMY) also seems to be another beginner friendly book.

u/bashfulbear · 3 pointsr/OSUOnlineCS

I have not taken the class yet (I'm taking 161 and 225 in January), but I looked at the syllabi already and here's the textbook for the class:

http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090/ref=sr_1_1?ie=UTF8&amp;amp;qid=1417826968&amp;amp;sr=8-1&amp;amp;keywords=Rosen+Discrete+Math

You may want to go ahead and pick this up and start looking through it prior to January. I already grabbed a copy; I finish Calculus II tomorrow at my community college and I am going to be starting Rosen very soon.

This book is also commonly recommended:

http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_1?ie=UTF8&amp;amp;qid=1417827137&amp;amp;sr=8-1&amp;amp;keywords=Epp

I'm not sure what your math background is, but one of the most important success factors (in my experience) in math classes is a lot of practice. If you start working through either of those books now, you'll probably be in a good place once class starts in January.

We could also probably get a study group going on in here; I'm pretty comfortable with math, so I am happy to help out anyone else who needs help.

u/lmtstrm · 3 pointsr/learnmath

I took a Discrete Mathematics class in College, and this was the textbook the professor recommended:

http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090/ref=la_B001IGOE0C_1_1/189-4818032-4394023?s=books&amp;amp;ie=UTF8&amp;amp;qid=1382239523&amp;amp;sr=1-1

I can't honestly say I ever touched it, because the class was actually very easy, and you could study for it using only the professor's lecture notes.

MIT's OCW also has some material available (it includes video lectures, assignments and a textbook):

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010

u/haroldburgess · 3 pointsr/math

I recently started reading How Not To Be Wrong (The Power of Mathematical Thinking), by Jordan Ellenberg, and while the material is probably way too simple for most on this thread, it's very engaging and informative, relating real world examples to simple math concepts. It's especially good at pointing out how math is used and abused by people to come to inaccurate or sometimes completely false conclusions.

But I think math geniuses aside, everyone can get something out of this book. It's good.

u/FNGMedia · 3 pointsr/politics

That's certainly one of the issues. There is a great book that covers this and other topics. How Not To Be Wrong by Jordan Ellenberg.

u/duuuh · 3 pointsr/careerguidance

It's possible without college, but it's not possible without education (leaving aside the incredibly rare exceptions like being a professional athlete.) That education can be apprenticeships; it can be on the job training (which is very hard to get in the US); it can be self taught; it can be college. Usually college is easiest.

Mathematics actually has very wide applicability although I'll grant you that many or most courses don't go out of their way to make that clear.

However, I'm not suggesting you should follow a math program. But you will need some form of education that's in demand to not live paycheck to paycheck. (This was much less true 40 years ago but it's true today, and getting more true with each passing year.)

u/MattB148 · 3 pointsr/Sat

I have the same problem. Its a lot about efficiency. Ive been reading secrets to mental math and that's helpful.
https://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

u/__Pers · 3 pointsr/IWantToLearn

If you want to learn to calculate quickly in your head, probably the most fruitful thing is to pick up a bunch of tricks for mental math. One good video course for this is Secrets of Mental Math put out by The Great Courses. The same lecturer published out a very good book on the subject as well.

Of course, if you want to go old school, then it's hard to beat the utility of memorizing logarithm tables...

u/Wacholez · 3 pointsr/IWantToLearn

The book The Secrets of Mental Math has some great tricks in it to help you along.

u/Danikar · 3 pointsr/learnmath

I read this book a few years ago, and it is pretty much the way I do any basic arithmetic in my head now. http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?ie=UTF8&amp;amp;qid=1333153637&amp;amp;sr=8-1

u/benEggers · 3 pointsr/mathematics

My pleasure :\^) It's hard to say what a local community college would have, since courses seem to vary a lot from school to school. The best thing you could find would probably be a class on something like "Set Theory" or "Mathematical Thinking" (those usually tend to touch on subjects like this without being pathologically rigorous), but a course in Discrete Math could do the trick, since you often talk about counting which leads naturally to countable vs uncountable sets. If you really want to learn the hardcore math, a course in Real Analysis is what you want. And if you don't know where to begin or are too busy, I can't recommend this book enough: http://www.amazon.com/Everything-More-Compact-History-Infinity/dp/0393339289. It's DFW so you know it's good ;)

I'm actually an undergrad studying Computer Science and Math but yes, I plan to end up a teacher after some other sort of career. Feel free to PM me if you have any more questions.

u/poopstixPS2 · 3 pointsr/EngineeringStudents

I looked at the free pages on Amazon and it does seem a bit wordier than the physics books I remember. It could just be the chapter. Maybe it reads like a book; maybe it's incredibly boring :/

If money isn't an issue (or if you're resourceful and internet savvy ;) you can try the book by Serway &amp; Jewett. It's fairly common.

http://www.amazon.com/Physics-Scientists-Engineers-Raymond-Serway/dp/1133947271

As for DE, this book really resonated with me for whatever reason. Your results may vary.

http://www.amazon.com/Course-Differential-Equations-Modeling-Applications/dp/1111827052/ref=sr_1_2?s=books&amp;amp;ie=UTF8&amp;amp;qid=1372632638&amp;amp;sr=1-2&amp;amp;keywords=differential+equations+gill

If your issue is with the technical nature of textbooks in general, then you'll either have to deal with it or look for some books that simplify/summarize the material in some way. The only example I can come up with is:

Although Div, Grad, Curl, and all That is intended for students in an Electromagnetics course (not Physics 2), it might be helpful. It's an informal overview of Calculus 3 integrals and techniques. The book uses electromagnetism in its examples. I don't think it covers electric circuits, which are a mess of their own. However, there are tons of resources on the internet for circuits. I hope all this was helpful :)

u/darkwing42 · 3 pointsr/ElectricalEngineering
u/freireib · 3 pointsr/Physics

Are you familiar with Div, Grad, Curl, &amp; All That. If not you'd probably enjoy it.

let me give you a shortcut.

You want to know how partial derivatives work? Consider a function with two variables: f(x,y) = x^2 y^3, for a simple example.

here's what you do. Let's take the partial derivative with respect to x. What you do, is you consider all the other variables to be constant, and just take the standard derivative with respect to x. In this case, the partial derivative with respect to x is: 2xy^3. That's it, it's really that easy.

What about taking with respect to y? Same thing, now x is constant, and your answer is 3x^2 y^2.

This is an incredibly deep topic, but getting enough of an understanding to tackle gradient descent is really pretty simple. If you want to full on jump in though and get some exposure to way more than you need, check out div curl and grad and all that. It covers a lot, including a fair amount that you won't need for any ML algorithm I've ever seen (curl, divergence theorem, etc) but the intro section on the gradient at the beginning might be helpful... maybe see if you can find a pdf or something. There's probably other good intros too, but seriously... the mechanics of actually performing a partial derivative really are that easy. If you can do a derivative in one dimension, you can handle partial derivatives.

edit: I misread, didn't see you were a junior in highschool. Disregard div curl grad and all that, I highly recommend it, but you should be up through calc 3 and linear algebra first.

To change my advice to be slightly more relevant, learn how normal derivatives work. Go through the Kahn Academy calc stuff if the format appeals to you. Doesn't matter what course you go through though, you just need to go through a few dozen exercises (or a few hundred, depending on your patience and interest) and you'll get there. Derivatives aren't too complicated really, if you understand the limit definition of the derivative (taking the slope over a vanishingly small interval) then the rest is just learning special cases. How do you take the derivative of f(x)g(x)? f(g(x))? There's really not too many rules, so just spend a while practicing and you'll be right where you need to be. Once you're there, going up to understanding partial derivatives is as simple as I described above... if you can take a standard derivative, you can take a partial derivative.

Also: props for wading into the deep end yourself! I know some of this stuff might seem intimidating, but if you do what you're doing (make sure you understand as much as you can instead of blowing ahead) you'll be able to follow this trail as far as you want to go. Good luck, and feel free to hit me up if you have any specific questions, I'd be happy to share.

u/TheMiamiWhale · 3 pointsr/MachineLearning
1. Not sure what exactly the context is here but usually it is the space from which the inputs are drawn. For example, if your inputs are d dimensional, the input space may be R^d or a subspace of R^d

2. The curse of dimensionality is important because for many machine learning algorithms we use the idea of looking at nearby data points for a given point to infer information about the respective point. With the curse of dimensionality we see that our data becomes more sparse as we increase the dimension, making it harder to find nearby data points.

3. The size of the neighbor hood depends on the function. A function that is growing very quickly may require a smaller, tighter neighborhood than a function that has less dramatic fluctuations.

If you are interested enough in machine learning that you are going to work through ESL, you may benefit from reading up on some math first. For example:

u/sakattack · 3 pointsr/math

Hmm I'm surprised you've had point-set topology, linear algebra, and basic functional analysis but have yet to encounter locally convex topological vector spaces! No worries, you have most likely developed all oft the machinery to understand them. I agree with G-Brain, Rudin's function analysis will do. Most functional analysis books should cover this at some point. The only I use is Kreyszig. Hope that helps!

u/Hilbert84 · 3 pointsr/math

If you enjoy analysis, maybe you'd like to learn some more?

I really enjoyed learning introductory functional analysis, which is presented incredibly well in Kreyszig's book Introductory Functional Analysis with Applications. It's very easy to read, and covers a lot and assumes very little on the part of the reader (basic concepts from analysis and linear algebra). This will teach you about doing analysis on finite and infinite dimensional spaces and about operators between such spaces. It's incredibly interesting, and I highly recommend it if you enjoy analysis and linear algebra.

Another great analysis topic is Fourier Analysis and wavelets. I enjoyed the books by Folland Fourier Analysis and Its Applications. I don't believe that book has any wavelets in it, so if you're interested in learning Fourier analysis plus wavelet theory, then I highly recommend the very approachable and fun book by Boggess and Narcowich A First Course in Wavelets with Fourier Analysis. If you have any interest at all in applications (like signals processing), this subject is fundamental.

u/EulerANDBernoulli · 3 pointsr/math
u/BattleFriendly · 3 pointsr/EngineeringStudents

Definitely split up the load and take classes over the summer. I often hear people say Calculus II is the hardest of the EPIC MATH TRILOGY. I certainly agree. If you've done well in Calc I and II and have a notion of what 3d vectors are (physics should of covered this well) then you'll have no problem with Calc III (though series' and summations can be tough).

Differential equations will be your first introduction to hard "pure"-style math concepts. The language will take some time to understand and digest. I highly recommend you purchase this book to supplement your textbook. If you take notes on each chapter and work through the derivations, problems, and solutions, you'll be golden.

In my experience, materials is not math heavy for ME's. All of my tests were multiple choice and more concept based. It's not too bad.

Thermodynamics and Engineering Dynamics will be in the top three as far as difficulty goes. Circuits or Fluids will also be in there somewhere. Make sure you allow plenty of time to study these topics.

Good luck!

u/DomMk · 3 pointsr/math

I used Tenenbaum. One of my favorite undergrad books. Only downside that it doesn't use any Linear Algebra

u/commutant · 3 pointsr/math

The second book that gerschgorin listed is very good, though a little old fashioned.

Since you are finishing up your math major, I'd recommend Hirsch &amp; Smale &amp; Devaney, an excellent book if you have a little bit of mathematical background.

There is also a video series I'm making meant to be a quick overview of many of the key topics. Maybe useful, maybe not. Also, the MIT lectures are excellent.

u/mjedm6 · 3 pointsr/math

They may not be the best books for complete self-learning, but I have a whole bookshelf of the small introductory topic books published by Dover- books like An Introduction to Graph Theory, Number Theory, An Introduction to Information Theory, etc. The book are very cheap, usually $4-$14. The books are written in various ways, for instance the Number Theory book is highly proof and problem based if I remember correctly... whereas the Information Theory book is more of a straightforward natural-language summary of work by Claude Shannon et al. I still find them all great value and great to blast through in a weekend to brush up to a new topic. I'd pair each one with a real learning text with problem sets etc, and read the Dover book first quickly which introduces the reader to any unfamiliar terminology that may be needed before jumping into other step by step learning texts.

u/agconway · 3 pointsr/math

He really should be starting with the Trudeau, much better bed side reading.

u/belarius · 3 pointsr/statistics

Casella &amp; Berger is the go-to reference (as Smartless has already pointed out), but you may also enjoy Jaynes. I'm not sure I'd say it's quick but if gaps are your concern, it's pretty drum-tight.

u/MohKohn · 3 pointsr/math

it most certainly is! There's a whole approach to statistics based around this idea of updating priors. If you're feeling ambitious, the book Probability theory by Jaynes is pretty accessible.

u/vyaas · 3 pointsr/math

If you can find this at your library, I suggest you pour over it in the weekend. You will not regret it.

u/POWAHHH · 3 pointsr/ECE

I've had a few colleagues recommend A Student's Guide to Maxwell's Equations.

u/complexsystems · 3 pointsr/econometrics

The important part of this question is what do you know? By saying you're looking to learn "a little more about econometrics," does that imply you've already taken an undergraduate economics course? I'll take this as a given if you've found /r/econometrics. So this is a bit of a look into what a first year PhD section of econometrics looks like.

My 1st year PhD track has used
-Casella &amp; Berger for probability theory, understanding data generating processes, basic MLE, etc.

-Greene and Hayashi for Cross Sectional analysis.

-Enders and Hamilton for Time Series analysis.

These offer a more mathematical treatment of topics taught in say, Stock &amp; Watson, or Woodridge's Introductory Econometrics. C&amp;B will focus more on probability theory without bogging you down in measure theory, which will give you a working knowledge of probability theory required for 99% of applied problems. Hayashi or Greene will mostly cover what you see in an undergraduate class (especially Greene, which is a go to reference). Hayashi focuses a bit more on general method of moments, but I find its exposition better than Greene. And I honestly haven't looked at Enders or Hamilton yet, but they will cover forecasting, auto-regressive moving average problems, and how to solve them with econometrics.

It might also be useful to download and practice with either R, a statistical programming language, or Python with the numpy library. Python is a very general programming language that's easy to work with, and numpy turns it into a powerful mathematical and statistical work horse similar to Matlab.

u/jmcq · 3 pointsr/statistics

I was an Actuary (so I took the Financial Engineering exams) before I went back to get my PhD in Statistics. If you're familiar with:

• Real Analysis (limits, convergence, continuity etc)
• Basic Probability (Random variables, discrete vs. continuous, expectation, variance)
• Multivariate Calculus

You should be fine in a PhD stats program. It's easy enough to learn the statistics but harder to learn the math (specifically you're going to want strong analysis and calculus skills).

Check out Statistical Inference - Casella &amp; Berger it's a pretty standard 1st year theory text in Statistics, flip through the book and see how challenging the material looks to you. If it seems reasonable (don't expect to know it -- this is stuff you're going to learn!) then you ought to be fine.

This is a classic. I took a grad level course with this textbook and every problem is nasty. But yes, it is really a classic.

Also, I just begun Data Analysis Using Regression and Multilevel/Hierarchical Models by Andrew Gelman and Jennifer Hill. Love his interpretation of linear regression. Linear regression might sound like basics, but it lays the foundation work for everything else and from time to time I feel compelled to review it. This book gave me a new way to look at a familiar topic.

If you are familiar with any statistical programming language/packages, I would highly suggest you implement the learnings from any books you have.

Beginner Resources: These are fantastic places to start for true beginners.

Introduction to Probability is an oldie but a goodie. This is a basic book about probability that is suited for the absolute beginner. Its written in an older style of english, but other than that it is a great place to start.

Bayes Rule is a really simple, really basic book that shows only the most basic ideas of bayesian stats. If you are completely unfamiliar with stats but have a basic understanding of probability, this book is pretty good.

A Modern Approach to Regression with R is a great first resource for someone who understands a little about probability but wants to learn more about the details of data analysis.

&amp;#x200B;

Advanced resources: These are comprehensive, quality, and what I used for a stats MS.

Statistical Inference by Casella and Berger (2nd ed) is a classic text on maximum likelihood, probability, sufficiency, large sample properties, etc. Its what I used for all of my graduate probability and inference classes. Its not really beginner friendly and sometimes goes into too much detail, but its a really high quality resource.

Bayesian Data Analysis (3rd ed) is a really nice resource/reference for bayesian analysis. It isn't a "cuddle up by a fire" type of book since it is really detailed, but almost any topic in bayesian analysis will be there. Although its not needed, a good grasp on topics in the first book will greatly enhance the reading experience.

u/animalcrossing · 3 pointsr/cscareerquestions

You received A's in your math classes at a major public university, so I think you're in pretty good shape. That being said, have you done proof-based math? That may help tremendously in giving intuition because with proofs, you are giving rigor to all the logic/theorems/ formulas, etc that you've seen in your previous math classes.

Statistics will become very important in machine learning. So, a proof-based statistics book, that has been frequently recommended by /r/math and /r/statistics is Statistical Inference by Casella &amp; Berger: https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

I've never read it myself, but skimming through some of the beginning chapters, it seems pretty solid. That being said, you should have an intro to proof-course if you haven't had that. A good book for starting proofs is How to Prove It: https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995

u/trijazzguy · 3 pointsr/statistics

See Casella and Berger chapter 2, theorem 2.1.5

u/CodeNameSly · 3 pointsr/statistics

Casella and Berger is one of the go-to references. It is at the advanced undergraduate/first year graduate student level. It's more classical statistics than data science, though.

Good statistical texts for data science are Introduction to Statistical Learning and the more advanced Elements of Statistical Learning. Both of these have free pdfs available.

u/Galphanore · 3 pointsr/atheism

It is detailed. It just doesn't seem logical to me. His entire position is that since the odds against things being the way they are are so high, there must be a god that arranged them. It's a fundamental misunderstanding of probability. The chance of things being the way they are is actually 100%, because they are that way. We don't know how likely they were before they happened because we only have one planet and one solar system to examine. For all we know there could be life in most solar systems.

Even if that wasn't the case, even if we did have enough information to actually conclude that our existence here and now has a .00000000000000000000000000000001% chance of happening he then makes the even more absurd jump to saying "there being a God is the only thing that makes sense". God, especially the Christian God, is even less likely than the already unlikely chance of us existing at all. If it's extremely unlikely that we could evolve into what we are naturally, how is it less unlikely that an all-powerful, all-knowing, all-good being could exist for no discernible reason?

You should get him a copy of this book. It's great and will help him with these misconceptions. If you haven't read it, I highly suggest you do as well.

I think this book, Innumeracy, does a good job at explaining the odds of these kind of things happening to people.

u/magnanimous_xkcd · 3 pointsr/books

Innumeracy is pretty entertaining (and useful), even if you're not a math person. It's only about 150 pages, so it's a quick read.

u/pinxox · 3 pointsr/learnmath

As long as you have a solid foundation in algebra (and basic trig), you should be fine. However, you have to put in the study time. If you want supplementary material, I'd recommend The Calculus Lifesaver, which was a tremendous help for me, although it only covers single-variable calculus (i.e., Calc I and II). The cool thing about this book is that its author (a Princeton University professor) also has video lectures posted online.

u/Airballp · 3 pointsr/princeton

The single best resource for 103/104 is The Calculus Lifesaver by Adrian Banner. There's a book and a series of recorded review sessions. I stopped showing up to 104 lectures when I found these because they were so much more thorough than the classes. Banner also did review sessions for 201/202 when you reach that point, which are equally good.

u/sordidarray · 3 pointsr/math

Check out Adrian Banner's The Calculus Lifesaver for a companion to a typical undergrad introductory calculus sequence and the accompanying videos from Princeton.

This has been pretty much the standard textbook on Bayes
https://www.amazon.com/Bayesian-Analysis-Chapman-Statistical-Science/dp/1439840954/

u/ginger_beer_m · 3 pointsr/science

May I recommend this book to you then, Statistical Rethinking: A Bayesian Course with Examples in R and Stan (Chapman &amp; Hall/CRC Texts in Statistical Science) https://www.amazon.co.uk/dp/1482253445/ref=cm_sw_r_cp_apa_Iu6.BbJE7EECQ

u/futrawo · 3 pointsr/BayesianProgramming

There seem to be a few options. I've had this and this on my reading list for a while, but haven't got further than that.

I'm also interested in recommendations.

Here's mine

To understand life, I'd highly recommend this textbook that we used at university http://www.amazon.com/Campbell-Biology-Edition-Jane-Reece/dp/0321558235/ That covers cell biology and basic biology, you'll understand how the cells in your body work, how nutrition works, how medicine works, how viruses work, where biotech is today, and every page will confront you with what we "don't yet" understand too with neat little excerpts of current science every chapter. It'll give you the foundation to start seeing how life is nothing special and just machinery (maybe you should do some basic chemistry/biology stuff on KhanAcademy first though to fully appreciate what you'll read).

For math I'd recommend doing KhanAcademy aswell https://www.khanacademy.org/ and maybe a good Algebra workbook like http://www.amazon.com/The-Humongous-Book-Algebra-Problems/dp/1592577229/ and after you're comfortable with Algebra/Trig then go for calc, I like this book http://www.amazon.com/Calculus-Ron-Larson/dp/0547167024/ Don't forget the 2 workbooks so you can dig yourself out when you get stuck http://www.amazon.com/Student-Solutions-Chapters-Edwards-Calculus/dp/0547213093/ http://www.amazon.com/Student-Solutions-Chapters-Edwards-Calculus/dp/0547213107/ That covers calc1 calc2 and calc3.

Once you're getting into calc Physics is a must of course, Math can describe an infinite amount of universes but when you use it to describe our universe now you have Physics, http://www.amazon.com/University-Physics-Modern-12th/dp/0321501217/ has workbooks too that you'll definitely need since you're learning on your own.

At this point you'll have your answers and a foundation to go into advanced topics in all technical fields, this is why every university student who does a technical degree must take courses in all those 3 disciplines.

If anything at least read that biology textbook, you really won't ever have a true appreciation for the living world and you can't believe how often you'll start noticing people around you spouting terrible science. If you could actually get through all the work I mentioned above, college would be a breeze for you.

u/mtVessel · 2 pointsr/compsci

I've only browsed Concrete Mathematics, but others have said it might not be sufficient. My uni used Rosen's Discrete Mathematics and its Applications. I think it's a fairly standard text. Pricey, but older editions might be just as useful.

u/cbarrick · 2 pointsr/computing

Sipser's Introduction to the Theory of Computation is the standard textbook. The book is fairly small and quite well written, though it can be pretty dense at times. (Sipser is Dean of Science at MIT.)

You may need an introduction to discrete math before you get started. In my udergrad, I used Rosen's Discrete Mathematics and Its Applications. That book is very comprehensive, but that also means it's quite big.

Rosen is a great reference, while Sipser is more focused.

u/MtSopris · 2 pointsr/learnmath

I should note that topics like graph theory, combinatorics, areas otherwise under the "discrete math" category, don't really require calculus, analysis, and other "continuous math" subjects to learn them. Instead, you can get up to college level algebra, then get a book like
Discrete Mathematics and Its Applications Seventh Edition (Higher Math) https://www.amazon.com/dp/0073383090/ref=cm_sw_r_cp_api_U6Zdzb793HMA7

Or the more highly regarded but less problem set answers,
Discrete Mathematics with Applications https://www.amazon.com/dp/0495391328/ref=cm_sw_r_cp_api_d7ZdzbQ77B65P

This will be enough to tackle ideas from discrete math. I'd recommend reading a book on logic to help with proof techniques and the general idea for rigorously proving statements.
Gensler is a great one but can require a computer if you want more extensive feedback and problem sets.

u/sachal10 · 2 pointsr/learnmath

since you are a computer science student, you can start with proofs in Discrete Mathematics fo this you can look at Kenneth Rosen's book, it can help you with a lot of basic concepts, constructing proofs. Its a good book for those who want to go in algorithms or theoretical cs or a even want to work on pure maths problems. I had this same confusion I wanted to do maths but also cs with it. After this you can try "The art of computer programming"(this has 4 volumes) by Donald Knuth but CLRS is a must along with Rosen's if you want to take cs and maths side by side. If you want to explore further you can look at Design of Approximation Algorithms and Randomised Algorithms. These book can help you with concepts of probability, number theory, geometry, linear algebra etc. But then if you want pure math problems then search for them, go though different journals, SIAM and Combinatorica are really good ones, search them pick a problem you like, then find text relevant to problem and try to give better solutions.

u/ILCaragiale · 2 pointsr/Romania

Mulțumesc mult pentru recomandări și pentru răspunsul elaborat!

Împreună cu cartea linkuită de tine am mai luat și Discrete Mathematics and Its Applications, Kenneth H Rosen.

u/captain_zerg · 2 pointsr/iamverysmart

Could be. I took discrete math last semester, and we spent a few weeks on cryptography. We used this book.

u/bayhack · 2 pointsr/learnmachinelearning

Hey I'm very very new to machine learning.
BUT I am very familiar with your situation. School didn't teach me anything and I don't think I can take the topics I should know into the workforce.

https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535

And it has put a lot into perspective.

A lot of my education (this is at least for me going to school in the US) has been more about rote memorization and just glossing over concepts. Not really about the logic behind it, I doubt my grade school teachers even understood the concepts better than I did. But now I'm older I'm sucking it up and actually teaching myself the basics all the way up. Going to extremes as learning the Common Core math basics (and I mean the basics!) even though I have no kids.
While it seems like a lot to relearn, your actually going to be working on understanding the concept more and less about solving the problems and getting the right answer, so it's quicker than you can believe.

I say get some books that put stats into perspective, even in a fun way like the book I'm reading. Anything putting you to sleep is cause you are forcing yourself, so read something interesting in the field even if it's for people without any stats knowledge.
Go back and see your old coursework from new eyes. Do side projects and analyze things on your own and ask for help in forums.

Well, that's what I'm doing at least with all math and CS topics.

Yeah, school sucks. I think I understand why (I think) Mark Twain said "I don't let schooling get in the way of my education"

u/bbqfap · 2 pointsr/wholesomememes

This is a thing. I read a decent book with a lot of cool math tricks
https://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

u/freudian_nipple_slip · 2 pointsr/science

My favorite book that has a ton of these is this book. I remember seeing the author do all kinds of math tricks on talk shows. My favorite was determining what day of the week any date in history was (or at least, after the start of the Gregorian calendar)

u/MeridianJP · 2 pointsr/math

The following easy to read book teaches kids (and adults) you how to do it. Its actually really easy:

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

u/rrsmitto · 2 pointsr/matheducation

When you say everyday calculations I'm assuming you're talking about arithmetic, and if that's the case you're probably just better off using you're phone if it's too complex to do in you're head, though you may be interested in this book by Arthur Benjamin.

I'm majoring in math and electrical engineering so the math classes I take do help with my "everyday" calculations, but have never really helped me with anything non-technical. That said, the more math you know the more you can find it just about everywhere. I mean, you don't have to work at NASA to see the technical results of math, speech recognition applications like Siri or Ok Google on you're phone are insanely complex and far from a "solved" problem.

Definitely a ton of math in the medical field. MRIs and CT scanners use a lot of physics in combination with computational algorithms to create images, both of which require some pretty high level math. There's actually an example in one of my probability books that shows how important statistics can be in testing patients. It turns out that even if a test has a really high accuracy, if the condition is extremely rare there is a very high probability that a positive result for the test is a false positive. The book states that ~80% of doctors who were presented this question answered incorrectly.

u/the_resident_skeptic · 2 pointsr/videos

A lot of these tricks are very easy. He explains them all in his book Secrets of Mental Math

u/turd__burgleson · 2 pointsr/learnmath

Secrets of Mental Math May be helpful for filling in some gaps. Also A Mind for Numbers gives helpful meta learning info: how to study, etc.

u/Maristic · 2 pointsr/science

I began doing it in my head the same way. For clarity, my thought processes were based on the idea of "don't do something hard, do something easier instead and then fix it up afterwards", roughly:

• 251 = 250 + 1 = 1000/4 + 1 (probably easier to work with)
• 973 = 972 + 1 (useful because 972 is divisible by 4)
• 972/4 = 900/4+72/4 = 450/2 + 36/2 = 225 + 18 = 235+8 = 240+3 = 243
• 973/4 = 243 + 1/4 = 243.25
• 973/4 1000 = oh screw this, I'm convinced I could do it, but this is not fun any more

(I stopped there because I just wasn't looking forward to adding 973 to 243250, but was pretty sure I could slog my way through it if I actually had to.)

But there are lots of tricks you can do to make mental math easier. I don't know them, but like the above, I know that I
could* go and learn them. For example, here is a book by one of the world's best people at mental arithmetic, Arthur Benjamin; the book is filled with techniques you can use to make mental arithmetic easier. See him on TED here.
u/Ozzy_ · 2 pointsr/GetStudying

I'm only a high school sophomore, so I can't really help you with most of your questions, but if you want to improve your mental math, buy "Secrets of Mental Math" by Arthur Benjamin.

It's written in a way that makes sitting in your room doing mental calculations seem fun and it is very accessible. I have only gotten through 3 chapters (the addition/subtraction/multiplication chapters) and I can confidently add and subtract 3-digit numbers in seconds. I can even mentally cube two-digit numbers in a few minutes.

[Anyway, here's a link to the book] (http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?s=books&amp;amp;ie=UTF8&amp;amp;qid=1381633585&amp;amp;sr=1-1&amp;amp;keywords=mental+math)

[If you don't want to buy it, you can use this PDF version of the book] (http://www.uowm.gr/mathslife/images/fbfiles/files/Secrets_of_Mental_Math___Michael_Shermer___Arthur_Benjamin.pdf)

[And here is the author, Arthur Benjamin, performing what he likes to call "Mathemagics"] (http://www.youtube.com/watch?v=e4PTvXtz4GM)

I hope this has been helpful and you succeed in whatever uni you go to :)

u/casact921 · 2 pointsr/teaching

Check out Secrets of Mental Math by Arthur Benjamin. Benjamin is amazing, I've seen him at MAA meetings. He does lightning fast calculations in his head, and his book shows you how to do it. Your students may or may not think this is cool, but I do :) And the bonus is that they will never learn this kind of thing in school at any grade, so you won't be stepping on anybody's toes by teaching it to them now.

Also, the "third grade team" sucks. Screw those guys.

It depends on what kind of math you want to learn. If you want to get up to speed on your basic math, khan academy is the way to go. However, I think that is probably a waste of your time. The math that you will see in high school and the first year or too of college has very little to do with what a mathematician might consider 'real math.' Frankly I found it boring as hell and I majored in math undergrad and grad.

If I were you, I would start with something interesting and if you end up really liking math, go back and pick up algebra and calculus. So check out the two books below:

This book will walk you through really high level stuff in an easy to understand way. As a grad student I would hang out in this class because it was rather fun.

This book is a history of math/pop math book. As an undergrad it put the field into perspective. Lots and lots of really useful information for anyone, especially someone who is interested in being well learned.

I have to disagree a bit with your second pick, Everything and More by David Foster Wallace. His somewhat chaotic writing style [footnote footnote footnote] is more suited to essays and fiction than describing mathematical ideas. Clear and concise he is not.

That said, it is an interesting read. I just don't see it as a great introduction to someone who has had trouble with math in the past. It can be confusing.

u/PrurientLuxurient · 2 pointsr/philosophy

I'd just throw in that the late David Foster Wallace has a fun little book about this stuff. I'd recommend it as an accessible introduction; I am a complete layman when it comes to advanced mathematics and I found it to be an enjoyable read. I'm sure it isn't quite as comprehensive as what you'd get in a pure math course, but it might be useful nevertheless.

Edit: I should add that it is written in DFW's characteristic style--full of digressions, self-consciously and ironically pedantic footnotes, etc.--which plenty of people find unbelievably annoying. Be forewarned, then, that if you've never read anything by him, you may find the style irritating.

u/MedPhysPHD · 2 pointsr/berkeley

Math 53 isn't heavy on proofs at all except possibly near the tail end of the course. Actually, the whole purpose of Math 53 really is the last 2 weeks when it gets into the Stoke's and Divergence Theorem. If you want to get started early on that I recommend the excellent Div, Grad, Curl, and All That which is a short text you can get online or the library that really makes the topic more manageable. Be prepared for it because it will hit you right at the end of the semester although the curve is generally nicer than Math 1B.

Math 54, or linear algebra in general, is for a lot of people the "intro to proofs" course. Right around the time Math 53 goes at breakneck speed, Math 54 finishes up with fourier analysis. It's doable but you have to stay on top of things the whole semester or have a miserable few weeks near the end.

u/testcase51 · 2 pointsr/PhysicsStudents

As others have mentioned, there are a lot of good books on Math Methods of Physics out there (I used Hassani's Mathematical Methods: For Students of Physics and Related Fields).

That said, if you're having trouble with calculus, I'd recommend going back and really understanding that well. It underlies more or less all the mathematics found in physics, and trying to learn vector calculus (essential for E&amp;M) without having a solid understanding of single-variable calculus is just asking for trouble.

There are a number of good books out there. Additionally, Khan Academy covers calculus very well. The videos on this page cover everything you'd encounter in your first year, and maybe a smidge more.

Once you move on to vector calculus, Div, Grad, Curl and All That is without equal.

u/Antagonist360 · 2 pointsr/math

I found the book Div Grad Curl and All That to explain it pretty well. The book is short enough to read through in a couple hours.

u/mrcmnstr · 2 pointsr/Physics

I thought of some books suggestions. If you're going all in, go to the library and find a book on vector calculus. You're going to need it if you don't already know spherical coordinates, divergence, gradient, and curl. Try this one if your library has it. Lots of good books on this though. Just look for vector calculus.

Griffiths has a good intro to E&amp;M. I'm sure you can find an old copy on a bookshelf. Doesn't need to be the new one.

Shankar has a quantum book written for an upper level undergrad. The first chapter does an excellent job explaining the basic math behind quantum mechanics .

u/SquirrelicideScience · 2 pointsr/math

Is it this one?

u/krypton86 · 2 pointsr/ECE

For vector calculus: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus

For complex variables/Laplace: Complex Variables and the Laplace Transform for Engineers - Caution! Dover book! Slightly obtuse at times!

For the finite difference stuff I would wait until you have a damn good reason to learn it, because there are a hundred books on it and none of them are that good. You're better off waiting for a problem to come along that really requires it and then getting half a dozen books on the subject from the library.

I can't help with the measurement text as I'm a physicist, not an engineer. Sorry. Hope the rest helps.

u/lewisje · 2 pointsr/learnmath

For vector calculus, you might enjoy the less formal British text Div, Grad, Curl, and All That by H. M. Schey; for group theory in brief, consider the free textbook Elements of Abstract and Linear Algebra by Edwin H. Connell.

Alternatives to Schey's book include the much more formal Calculus on Manifolds by Michael Spivak, which does have more exercises than Schey but uses most of them to develop the theory, rather than as the mindless drills that fill an ordinary textbook; Michael E. Corral's free textbook Vector Calculus isn't huge but is written closer to an ordinary textbook.

Haven't used it myself, but you might want to check out Div,Grad,Curl by Schey.

u/shitalwayshappens · 2 pointsr/math

For algebra, I'd recommend Mac Lane/Birkhoff. They may not be as comprehensive as some other texts but to me, they are more motivating, and will probably provide a better introduction to categorical thinking.

For linear algebra, I'm going to suggest something slightly unusual: Kreyszig's Introductory Functional analysis with applications. Functional analysis is essentially linear algebra on infinite dimensional spaces, and it generalizes a lot of the results in finite dimensions. Kreyszig does a good job motivating the reader. I can definitely sit down and read it for hours, much longer than I can for other books, and I definitely don't consider myself an analyst. However, it could be difficult if you are not familiar with basic topology and never seen linear algebra before.

u/nikofeyn · 2 pointsr/math

hey nerdinthearena,

i too find this area to be fascinating and wish i knew more on the upper end myself. i'm just going to list off a few resources. in my opinion, graduate school will concentrate a lot on progressing your technical knowledge, but will likely not give you a lot of time to hone your intuition (at least in the first few years). so, the more time you spend in undergraduate school doing so, the better.

# helpful for intuition and basic understanding

u/Yuushi · 2 pointsr/learnmath

For ODEs, I'd seriously suggest buying this. Lots and lots of exercises, and full solutions. Plus, at $15, it hopefully won't break the bank too badly. u/captainmeanyface · 2 pointsr/learnmath this one i used this book, the one that was required for the class sucked, this one is much better and it's super cheap. Also, answers and steps are included in the sections, so you can actually check if you're doing it correctly or not. u/SoTopological · 2 pointsr/learnmath I've never really used MIT OCW however I've used Paul's OMN a lot back when I was studying multivar calc. I do recommend books, though. I have books both on multivar calc and differential equations and they're both well, however, I've moved on from calculus (that is, I don't actively study it anymore) so I can't really say much more. The books I have: &gt; https://www.amazon.com/Multivariable-Calculus-Clark-Bray/dp/1482550741/ref=sr_1_3?s=books&amp;amp;ie=UTF8&amp;amp;qid=1500976188&amp;amp;sr=1-3&amp;amp;keywords=multivariable+calculus &gt; https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=sr_1_1?s=books&amp;amp;ie=UTF8&amp;amp;qid=1500976233&amp;amp;sr=1-1&amp;amp;keywords=differential+equations u/B-80 · 2 pointsr/math There seems to often be this sort of tragedy of the commons with the elementary courses in mathematics. Basically the issue is that the subject has too much utility. Be assured that it is very rich in mathematical aesthetic, but courses, specifically those aimed at teaching tools to people who are not in the field, tend to lose that charm. It is quite a shame that it's not taught with all the beautiful geometric interpretations that underlie the theory. As far as texts, if you like physics, I can not recommend highly enough this book by Lanczos. On the surface it's about classical mechanics(some physics background will be needed), but at its heart it's a course on dynamical systems, Diff EQs, and variational principles. The nice thing about the physics perspective is that you're almost always working with a physically interpretable picture in mind. That is, when you are trying to describe the motion of a physical system, you can always visualize that system in your mind's eye (at least in classical mechanics). I've also read through some of this book and found it to be very well written. It's highly regarded, and from what I read it did a very good job touching on the stuff that's normally brushed over. But it is a long read for sure. u/greatBigDot · 2 pointsr/math Ordinary Differential Equations by Tenenbaum and Pollard is a classic. I thought it explained things well and was more rigorous than some other treatments of subject that I've come across. u/jnethery · 2 pointsr/funny 15! Well then, you have plenty of time to figure this out. Well, a few years, in any case. I think what you should do is learn some programming as soon as possible (assuming you don't already). It's easy, trust me. Start with C, C++, Python or Java. Personally, I started with C, so I'll give you the tutorials I learned from: http://www.cprogramming.com/tutorial/c/lesson1.html You should also try out some electronics. There's too much theory for me to really explain here, but try and maybe get a starter's kit with a book of tutorials on basic electronics. Then, move onto some more complicated projects. It wouldn't hurt to look into some circuit theory. For mechanical, well... that one is kind of hard to get practical experience for on a budget, but you can still try and learn some of the theory behind it. Start with learning some dynamics and then move onto statics. Once you've got that down, try learning about the structure and property of materials and then go to solid mechanics and machine design. There's a lot more to mechanical engineering than that, but that's a good starting point. There's also, of course, chemical engineering, civil engineering, industrial engineering, aerospace engineering, etc, etc... but the main ones I know about are mechanical (what I'm currently studying), electrical and computer. Hope this helped. I wasn't trying to dissuade you from pursuing engineering, but instead I'm just forewarning you that a lot of people go into it with almost no actual engineering skills and well, they tend to do poorly. If you start picking up some skills now, years before college, you'll do great. EDIT: Also, try learning some math! It would help a lot to have some experience with linear algebra, calculus and differential equations. This book should help. u/Periflux · 2 pointsr/EngineeringStudents http://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=mt_paperback?_encoding=UTF8&amp;amp;me= Stay away from Youtube and Khan Academy unless you need reinforcement on a specific topic. Go through this book, page by page, learn the material, and do every problem. u/0xd4e · 2 pointsr/EngineeringStudents I've used Tenenbaum to teach myself ODEs. Got an A in my class. Arnold is cannon, but you need mathematical maturity so YMMV. u/solve-for-x · 2 pointsr/math With regards to your edit, if your friend is still incarcerated after reading his calculus text, send him Ordinary Differential Equations by Tenenbaum and Pollard. It contains zillions of worked problems showing how ODEs can be applied to physical problems. u/brickrickslick · 2 pointsr/EngineeringStudents The one and only , if you're willing to dedicate the time Ordinary Differential Equations (Dover Books on Mathematics) https://www.amazon.com/dp/0486649407/ u/shogun333 · 2 pointsr/math What are you majoring in? What you're describing could just be a personality issue that's unrelated to maths, that maths is just be an example of. That being said, I find the way people are taught maths to be a form of abuse. It's like the way someone who was molested as a child might have weird issues with sex, so do most people have issues with maths who have had to go through maths in high school. Just so that you know, what you think maths is, is actually almost not at all what maths really is. I would recommend, after you finish your exams and have nothing better to do, read this book about graph theory. It's$4 + shipping from amazon, or you may have it in the library wherever you're studying. It's kind of pointless, but there are a few nice bits about the philosophy of maths.

u/ur_mom415 · 2 pointsr/UBC

Read this: https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 and you're more than set for algebraic manipulation.

And if you're looking to get super fancy, then some of that: https://www.amazon.com/Method-Coordinates-Dover-Books-Mathematics/dp/0486425657/

And some of this for graphing practice: https://www.amazon.com/Functions-Graphs-Dover-Books-Mathematics/dp/0486425649/

And if you're looking to be a sage, these: https://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202/ + https://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210/

If you're uncomfortable with mental manipulation of geometric objects, then, before anything else, have a crack at this: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709/

u/c3534l · 2 pointsr/learnmath

From the ground up, I dunno. But I looked through my amazon order history for the past 10 years and I can say that I personally enjoyed reading the following math books:

An Introduction to Graph Theory

Introduction to Topology

Coding the Matrix: Linear Algebra through Applications to Computer Science

A Book of Abstract Algebra

An Introduction to Information Theory

u/Mayer-Vietoris · 2 pointsr/math

Yea John Green certainly isn't for everyone, particularly outside of the YA target audience. I wouldn't say it's his strongest book either, but it might be useful to check out.

In terms of mathematical directions you could go, graph theory is actually a pretty solid field to work in. It's basics are easy to grasp, the open problems are easy to understand and explain, and there are many obscure open ones that are easily within reach of a talented high schooler. In fact a lot of combinatorics is like that as well. I would recommend the book Introduction to Graph theory by Trudeau (which was originally titled Dot's and Lines). It's a great introduction to mathematical proof while leading the reader to the forefront of graph theory.

u/Sarcuss · 2 pointsr/learnmath

I personally think you should brush up on frequentist statistics as well as linear models before heading to Bayesian Statistics. A list of recommendations directed at your background:

u/urmyheartBeatStopR · 2 pointsr/rstats

&gt; I'd like to know, how did you learn to use R?

My batshit crazy lovable thesis advisor was teaching intro datascience in R.

He can't really lecture and he have high expectation. The class was for everybody including people that don't know how to program. The class book was advance R http://adv-r.had.co.nz/... (red flag).

We only survived this class because I had a cs undergrad background and I gave the class a crash course once. Our whole class was more about how to implement his version of random forest.

I learned R because we had to implement a version of Random forest with Rpart package and then create a package for it.

Before this a dabble in R for summer research. It was mostly cleaning data.

So my advice would be to have a project and use R.

&gt;how did you learn statistics?

Master program using the wackerly book and chegg/slader. (https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817)

It's a real grind. You need to learn probability first before even going into stat. Wackerly was the only real book that break down the 3 possible transformations (pdf,cdf, mgf).

u/sovietcableguy · 2 pointsr/learnmath

I learned from Wackerly which is decent, though I think Devore's presentation is better, but not as deep. Both have plenty of exercises to work with.

Casella and Berger is the modern classic, which is pretty much standard in most graduate stats programs, and I've heard good things about Stat Labs, which uses hands-on projects to illuminate the topics.

u/astrok0_0 · 2 pointsr/Physics

FYI, Jaynes actually wrote a whole probability textbook that essentially put together all his thoughts about probability theory. I haven't read it, but many people say it got some good stuff.

u/G-Brain · 2 pointsr/math

I'm really fond of Jaynes' Probability Theory: The Logic of Science and Rudin's Principles of Mathematical Analysis. Both are excellent, clearly written books in their own way.

u/bbsome · 2 pointsr/MachineLearning

Depends what your goal is. As you have a good background, I would not suggest any stats book or deep learning. First, read trough Probability theory - The logic of science and the go for Bishop's Pattern Recognition or Barbers's Bayesian Reasoning and ML. If you understand the first and one of the second books, I think you are ready for anything.

u/mrdevlar · 2 pointsr/statistics

If you want a math book with that perspective, I'd recommend E.T. Jaynes "Probability Theory: The Logic of Science" he devolves into quite a lot of discussions about that topic.

If you want a popular science book on the subject, try "The Theory That Would Not Die".

Bayesian statistics has, in my opinion, been the force that has attempted to reverse this particular historical trend. However, that viewpoint is unlikely to be shared by all in this area. So take my viewpoint with a grain of salt.

u/sleepingsquirrel · 2 pointsr/math
u/riraito · 2 pointsr/math

Probability Theory: The Logic of Science. This is an online pdf, possibly of an older version of the book. Science covers knowledge of the natural world, and mathematics and logic covers knowledge of formal systems.

u/dogdiarrhea · 2 pointsr/learnmath

I've heard good things about (but have not read) Probability, the logic of science.

A complete table of contents + the first 3 chapters are available here. This should tell you if it covers the appropriate material and if the explanations are to your satisfaction.

It sounds like you want some kind of regression, especially to answer 2. In a GLM, you are not claiming that the data by itself has a Normal/Poisson/Negative Binomial/Binomial distribution, only that it has such a distribution when conditioned on a number of factors.

In a nutshell: you model the mean of the distribution as a linear combination of the inputs. Then you can read the weighting factors on each input to learn about the relationship.

In other words, it doesn't need to be that your data is Poisson or NB in order to do a Poisson or NB regression. It only has to be that the error, that is, the difference between the expected based on the mean function and the actual, follows such a distribution. In fact, there may be some simple transformations (like taking the log of the outcome) that lets you use a standard linear model, where you can reasonably assume that the error is Normal, even if the outcome is anything but.

If your variance is not dependent on any of your inputs, that's a great sign, since heteroskedasticity is a great annoyance when trying to do regressions.

If you have time, the modern classic in this area is http://www.amazon.com/Analysis-Regression-Multilevel-Hierarchical-Models/dp/052168689X. It starts with a pretty gentle introduction to regression and works its way into the cutting edge by the end.

u/Here4TheCatPics · 2 pointsr/statistics

I've used a book by Gelman for self study. Great author, very good at using meaningful graphics -- which may be an effective way to convey ideas to students.

u/cokechan · 2 pointsr/rstats

https://www.amazon.com/Analysis-Regression-Multilevel-Hierarchical-Models/dp/052168689X is the definitive text on the subject. I highly recommend this book to understand the fundamentals of multilevel modeling.

u/geneusutwerk · 2 pointsr/sociology

So I am a political scientist (though my research crosses into sociology).

What I would recommend is starting by learning Generalized Linear Models (GLMs). Logistic regression is one type, but GLMs are just a way of approaching a bunch of other type of dependent variables.

Gelman and Hill's book is probably the best single text book that can cover it all. I think it provides examples in R so you could also work on picking up R. It covers GLMs and multi-level models which are also relatively common in sociology.

u/d_phase · 2 pointsr/ElectricalEngineering

I agree with brushing up on your math. EM requires good mathematical intuition as you need to visualize both electric and magnetic field lines. I strong understanding of vector calculus helps with this immensely.

That said: I've heard great things about A Student's Guide to Maxwell's Equations. Note you'll probably be learning things other than just Maxwell's Equations however, such as transmission lines.

http://www.amazon.co.uk/A-Students-Guide-Maxwells-Equations/dp/0521701473

This book is very short and explains it all from the bottom up. I'd definitely recommend if you're new to Electromagnetism and/or haven't really studied vector calculus.

u/navyjeff · 2 pointsr/ECE

Optics takes a fair amount of math. If you want to read something useful, I recommend:

u/mistatroll · 2 pointsr/math

Differential forms as they build up to the general Stokes theorem are extremely satisfying because they give you the full picture of multivariable integration generalized to arbitrary k-dimensional objects in n-dimensional spaces. They basically relieve you of that feeling you (maybe) had in calc 3 that there's got to be more to the story than greene's theorem and stokes theorem.

However, I don't know that they give you better intuition for vector calculus and maxwell's equations, eg stuff in R^3. The way I got intuition for those was by doing problems and going through the proofs of curl and divergence from their definitions as limits of integrals. Work through the proof that this is equivalent to the usual definition of curl, and you'll understand curl and stokes theorem. Do the same for divergence

For maxwell's equations, this is an excellent book for intuition.

&gt; the first half of my degree was heavy on theoretical statistics,

Really? Wow, I'm impressed. Actual coverage of even basic theoretical stats is extremely rare in psych programs. Usually it's a bunch of pronouncements from on high, stated without proof, along with lists of commandments to follow (many of dubious value) and a collection of bogus rules of thumb.

What book(s) did you use? Wasserman? Casella and Berger? Cox and Hinkley? or (since you say it was heavy on theory) something more theoretical than standard theory texts?

I'd note that reaction times (conditionally on the IVs) are unlikely to be close to normal (they'll be right skew), and likely heteroskedastic. I'd be inclined toward generalized linear models (perhaps a gamma model -probably with log-lnk if you have any continuous covariates- would suit reaction times?). And as COOLSerdash mentions, you may want a random effect on subject, which would then imply GLMMs

u/flight_club · 2 pointsr/math

http://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126
Is a fairly standard first year grad textbook with I quite enjoy. Gives you a mathematical statistics foundation.

http://www.amazon.com/All-Statistics-Concise-Statistical-Inference/dp/1441923225/ref=sr_1_1?ie=UTF8&amp;amp;s=books&amp;amp;qid=1278495200&amp;amp;sr=1-1
I've heard recommended as an approachable overview.

http://www.amazon.com/Modern-Applied-Statistics-W-Venables/dp/1441930086/ref=sr_1_1?ie=UTF8&amp;amp;s=books&amp;amp;qid=1278495315&amp;amp;sr=1-1
Is a standard 'advanced' applied statistics textbook.

http://www.amazon.com/Weighing-Odds-Course-Probability-Statistics/dp/052100618X
Is non-standard but as a mathematician turned probabilist turned statistician I really enjoyed it.

http://www.amazon.com/Statistical-Models-Practice-David-Freedman/dp/0521743850/ref=pd_sim_b_1
Is a book which covers classical statistical models. There's an emphasis on checking model assumptions and seeing what happens when they fail.

This book has a fairly good introduction to probability theory if you don't need it to be measure theoretic. Statistical Inference

u/gajeam · 2 pointsr/education

John Allen Paulos' Innumeracy goes into a similar subject. He says that logic puzzles, analytical and inductive skills, and more importantly probability and statistical analysis should be taught alongside regular mathematics.

It's a short read and the man is a genius.

u/jrandom · 2 pointsr/atheist

Argh. Numerology. It's like every logical fallacy for numbers rolled into one.

I highly recommend you pick up a copy of Innumeracy.

u/ltnately · 2 pointsr/math

Innumeracy by Paulos

A great read that deal in part with the general acceptability math incompetence has compared to other subjects. Also a fun book as a "math person" just in the way he speaks and confides in the reader.

http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Consequences-Vintage/dp/0679726012

u/Froost · 2 pointsr/programming

By the way, there's a book called Innumeracy which tackles the problem of the consequences of not knowing math, how come it became OK, or even fashionable to not know math in the society, places where you can apply the knowledge etc. You should give it a read, it's enjoyable and a short read. You can notice that most of the arguments you are making are similar to those that were against literacy ("I'm plantin' seeds all day and then weedin for some, what are books gonna do me for?")

How to Solve It by Polya is a great book about the use of critical thinking in the process of solving mathematics problems.

http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X

u/kirakun · 2 pointsr/math

I highly recommend Polya's How to Solve it too.

u/EdmundH · 2 pointsr/matheducation

The best advice to get better at solving these problems is to persist. You should have to try, to think, to fail slowly building a picture until you find the solution. Have patience with not knowing exactly what to do.

For more technical general advice Polya's lovely book How to Solve it is excellent.

u/foryouandforme · 2 pointsr/programming

how to solve it by g. polya

book wiki

book on amazon

George Pólya wiki

u/GBUS_TO_MTV · 2 pointsr/cscareerquestions
u/IAmVeryStupid · 2 pointsr/math

My favorite book on problem solving is Problem Solving Through Problems. There's an online copy, too. (I recommend you print it and get it bound at Kinkos if you intend to seriously work through it, though. This type of thing sucks on a screen.)

How To Solve It is another popular recommendation for that topic. Personally, I only read part of it. It's alright.

I can recommend other stuff if you tell me what level of math you're at, what you're interested in learning, etc.

u/farmerje · 2 pointsr/learnprogramming

Two good books:

u/ericineducation · 2 pointsr/Teachers
u/latam_gringo · 2 pointsr/EngineeringStudents

Check out "How to Solve It" It's a small book but well worth the price. It talks about how to think critically and creatively go about solving problems.

u/hodorhodor12 · 2 pointsr/IWantToLearn

I'm a former physicists The way I felt I got smarter over the years as an undergraduate and graduate student was by continuing to solve hard and harder math and physics problems. Throwing yourself at increasingly difficult problems forces you to think systematically (so that you aren't considering the same solution again and again) and creatively (bring in other concepts and apply them to new situations) and perhaps, most importantly, to not give up. I found myself just being able to solve technical problems in other areas faster. My brain naturally got faster just like how someone who continually runs a slightly greater distances or just a little bit faster everyday is going to just naturally develop the muscles to make that possible. Also having a repository of solved problems as reference helps you solve future problems.

&amp;#x200B;

I found this book useful for problem solving:

https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X

u/bluestrike2 · 2 pointsr/politics

Completely off-topic, but stick with it. I had the same problem. Then everything will start to fit together. In the meantime, might I suggest Adrian Banner's The Calculus Lifesaver as a really approachable second textbook/help guide/reference?

/tangent

u/cr3bits · 2 pointsr/math

You might also want to search for your question on MSE. One advice that I recall is to consider Gilbert Strang's book Introduction to Linear Algebra along with his videos on OCW. He has an offbeat style both in his book and in his videos that might be unappealing to some people but the reason is that he really tries to make his students understand rather than remember. Also note that his target audience is typically engineers so proofs are present in his book but not the emphasis of his course.

u/IjonTichy85 · 2 pointsr/compsci

I think before you start you should ask yourself what you want to learn. If you're into programming or want to become a sysadmin you can learn everything you need without taking classes.

If you're interested in the theory of cs, here are a few starting points:

Introduction to Automata Theory, Languages, and Computation

MIT: Introduction to Algorithms

Computer Architecture&lt;- The intro alone makes it worth watching!

Linear Algebra

The book you should buy &lt;-Only scratches on the surface but is a good starting point. Also it's extremely informal for a math book. The MIT-channel offers many more courses and are a great for autodidactic studying.

Everything I've posted requires no or only minimal previous education.
You should think of this as a starting point. Maybe you'll find lessons or books you'll prefer. That's fine! Make your own choices. If you've understood everything in these lessons, you just need to take a programming class (or just learn it by doing), a class on formal logic and some more advanced math classes and you will have developed a good understanding of the basics of cs. The materials I've posted roughly cover the first year of studying cs. I wish I could tell you were you can find some more math/logic books but I'm german and always used german books for math because they usually follow a more formal approach (which isn't necessarily a good thing).
I really recommend learning these thing BEFORE starting to learn the 'useful' parts of CS like sql,xml, design pattern etc.
Another great book that will broaden your understanding is this Bertrand Russell: Introduction to mathematical philosophy
If you've understood the theory, the rest will seam 'logical' and you'll know why some things are the way they are. Your working environment will keep changing and 20 years from now, we will be using different tools and different languages, but the theory won't change. If you've once made the effort to understand the basics, it will be a lot easier for you to switch to the next 'big thing' once you're required to do so.

One more thing: PLEASE, don't become one of those people who need to tell everyone how useless a university is and that they know everything they need just because they've been working with python for a year or two. Of course you won't need 95% of the basics unless you're planning on staying in academia and if you've worked instead of studying, you will have a head start, but if someone is proud of NOT having learned something, that always makes me want to leave this planet, you know...

EDIT: almost forgot about this: use Unix, use Unix, and I can't emphasize this enough: USE UNIX! Building your own linux from scratch is something every computerscientist should have done at least once in his life. It's the only way to really learn how a modern operating system works. Also try to avoid apple/microsoft products, since they're usually closed source and don't give you the chance to learn how they work.

u/bobbyj_chard · 2 pointsr/MachineLearning

| $350 on amazon wat? the newest edition (2009) of his undergrad book is available for about 70 dollars, which is probably a steal. http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716/ref=sr_1_1?ie=UTF8&amp;amp;qid=1459450518&amp;amp;sr=8-1&amp;amp;keywords=gilbert+strang u/user0183849184 · 2 pointsr/gamedev I realized as I was writing this reply, I'm not sure if you're interested in a general linear algebra reference material recommendation, or more of a computer graphics math recommendation. My reply is all about general linear algebra, but I don't think matrix decompositions or eigensolvers are used in real-time computer graphics (but what do I know lol), so probably just focusing on the transformations chapter in Mathematics for 3D Game Programming and Computer Graphics would be good. If it feels like you're just memorizing stuff, I think that's normal, but keep rereading the material and do examples by hand! If you really understand how projection matrices work, then the transformations should make more sense and seem less like magic. I took Linear Algebra last semester and we used http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716, I would highly recommend it. Along with that book, I would recommend watching these video lectures, http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/, given by the author of the book. I've never watched MIT's video lectures until I watched these in preparation for an interview, because I always thought they would be dumb, but they're actually really great! I will say that I used the pause button furiously because the lectures are very dense and I had to think about what he was saying! In my opinion, the most important topics to focus on would be the definition of a vector space, the four fundamental subspaces, how the four fundamental subspaces relate to the fundamental theorem of linear algebra, all the matrix decompositions in that book, pivot variables and special solutions...I just realized I'm basically listing all of the chapters in the book, but I really do think they are all very important! The one thing you might not want to focus on is the chapter on incidence matrices. However, in my class, we went over PageRank in detail and I think it was very interesting! u/Second_Foundationeer · 2 pointsr/Physics I think the book I used was by Gilbert Strang. He also has some video lectures, apparently. However, I think most of my real understanding of linear algebra (after being introduced to the formalism) came from some combination of upper division classes (classical mechanics, mathematical methods, linear algebra in the math dept). Maybe quantum mechanics was when I just got used to it.. I think I'd suggest complex analysis if you've already been introduced to the basic formalism of linear algebra because you have to use linear algebra a shit ton in quantum mechanics so you'll get good at it just from sheer exposure, imo. u/DavidJayHarris · 2 pointsr/statistics This is very similar to the analysis featured on the cover of Bayesian Data Analysis (third edition). Here's a bigger picture of their decomposition into day-of-week effects, seasonal effects, long-term trends, holidays, etc. A bit more here, and lots more in the book. u/gatherinfer · 2 pointsr/statistics A lot of the recommendations in this thread are good, I'd like to add "Bayesian Data Analysis 3rd edition" by Gelman et al. Useful if you encounter Bayesian models, especially hierarchical/multilevel models. u/OrigamiDuck · 2 pointsr/artificial This may vary by school, but it's been my experience that there aren't a lot of classes explicitly labeled as "artificial intelligence" (especially at the undergraduate level). However, AI is a very broad and interdisciplinary field so one thing I would recommend is that you take courses from fields that form the foundation of AI. (Math, Statistics, Computer Science, Psychology, Philosophy, Neurobiology, etc.) In addition, take advantage of the resources you can find online! Self-study the topics you're interested in and try to get some hands on experience if possible: read blogs, read papers , browse subreddits, program a game-playing AI, etc. Given that you're specifically interested in reasoning: • (From the sidebar) AITopics has a page on reasoning with some recommendations on where to start. • I'm not an expert in this area but from what I've been exposed to I believe many of the state-of-the-art approaches to reasoning rely on bayesian statistics so I would look into learning more about it. I've heard good things about this book, the author also has some lectures available on youtube • From what I understand, whether or not we should look to the human mind for inspiration in AI reasoning is a pretty controversial topic. However you may find it interesting, and taking a brief survey of the psychology of reasoning may be a good way to understand the types of problems involved in AI reasoning, if you aren't very familiar with the topic. *As a disclaimer: I'm fairly new to this field of study myself. What I've shared with you is my best understanding, but given my lack of experience it may not be completely accurate. (Anyone, please feel free to correct me if I'm mistaken on any of these points) u/AllezCannes · 2 pointsr/statistics They're not free, but Doing Bayesian Data Analysis and Statistical Rethinking are worth their weight in gold. u/ST2K · 2 pointsr/IAmA &gt;I mean its to late now to enroll... Why wait? Pick up a few books on math and use your Google Fu to get yourself started. I really like this book. And instead of studying geometry (which I doubt you'd be using in college), study Logic instead. The way problems are constructed is similar to geometry. In geometry you have theorem and postulates, in logic you make proofs. You start out with two or three opening statements, and by using different combinations of OR, AND &amp; IF-THEN statements, you can prove the final statement. I'll give you this link about it but I'm hesitant to because it has lots of scary symbols and letters. Here. But save that for later. If you want to get started, take a look at truth tables . Logic is so much more interesting than geometry because it'll help your Google Fu get even better. You can make Boolean statements when you enter a Google query. It also gets you on the path to learning SQL (which your brother may also be able to help you with). SQL is all about sets - sets of records, and how you can join them and select those that have certain values, etc. You may even find this book a nice, gentle introduction to logic that doesn't require much math. Basically, what I'm saying to you is this: you live in the most incredible time to be alive ever. The Internet is a super-powerful tool you can use to educate yourself and you should make full use of it. I also want you to know that if you don't have a specialized skill, you're going to be treated like a virtual slave for the rest of your life. Working at WalMart is not a good career choice. That's just choosing a life of victimhood. Make full use of the Internet, and your lack of a car will seem less problematic. u/mrbarky · 2 pointsr/booksuggestions I've been working my way through the Humongous Book of Algebra Problems. It's about a thousand math problems with complete (and very good explanations). The only way to get good is to get out the paper and plow through problems. I supplement that with videos from Khan Academy (which has it's own math quiz system that is also excellent). I try to do every problem, even if I hate it (looking at you matrices!). And if I get it wrong, no matter the mistake, I re-do the whole problem. After I do that one, it's on to the Humongous book on Trig. Then calculus. All for the randy hell of it (I grew up with an interest in science and bad math teachers). u/Josharooski · 2 pointsr/learnmath http://www.amazon.com/The-Humongous-Book-Algebra-Problems/dp/1592577229 Maybe? I'm thinking about picking this up when I finish Khan academy algebra. u/PookaProtector · 2 pointsr/learnmath No worries. There's also a book called Humongous Book of Algebra Problems u/blakjesus · 1 pointr/AdviceAnimals We got told to buy this one, but after looking at the reviews and the price - I think i'll give it a miss... &gt;54 of 61 people found the following review helpful &gt;1.0 out of 5 stars Just awful. November 16, 2011 &gt;53 of 61 people found the following review helpful &gt;1.0 out of 5 stars Irresponsible Publishing! September 7, 2011 &gt;17 of 19 people found the following review helpful &gt;1.0 out of 5 stars Worst math textbook. Ever. February 11, 2012 u/roland23 · 1 pointr/compsci I've found Discrete Mathematics and Its Applications to be easily the most useful textbook I've owned throughout my CS degree. I highly recommend it. u/Ubermensch-1 · 1 pointr/math This was recommended by my very adept discrete math prof (don't worry, he's not the author). The excerpts I've used are good. The reviews make it seem pretty hit or miss, but textbooks tend to be that way on amazon. u/red-brick-dream · 1 pointr/learnmath I once took a first-year course in logic, starting with the propositional calculus. All these years later, I still regard it as the most important thing I ever did. Proof-writing became [almost] easy after that. It wasn't always easy to put the pieces together, but at least I had a blueprint. I knew that if I could clearly define a contrapositive, or understand how set identities like DeMorgan's Laws were constructed, I was on much firmer ground. I highly recommend Discrete Mathematics and Its Applications. It's such an enormous and comprehensive text, in so many subjects, that I found myself referring back to it, for something, in almost every class of my undergraduate. u/pmorrisonfl · 1 pointr/compsci I took a long, long break between undergrad and grad school (think decades). I found this GRE math prep book very helpful. (The GRE math section tests high school math knowledge), I'd take the sample tests, see where I fell short, and focus on understanding why. I also found Practical Algebra to be a good review-and-practice guide, for the fundamentals. I boned up on discrete math by buying an old copy of Rosen and the matching solutions guide. And, I watched a bunch of videos of this guy explaining various facets of the math you need for computer science. u/Wallblacksheep · 1 pointr/csbooks Looks like a good workbook, but fails as an instructional book according to the reviews. Still a good share! u/Caleb666 · 1 pointr/AskComputerScience Logic, Number theory, Graph Theory and Algebra are all too much for you to handle on your own without first learning the basics. In fact, most of those books will probably expect you to have some mathematical maturity (that is, reading and writing proofs). I don't know how theoretical your CS program is going to be, but I would recommend working on your discrete math, basic set theory and logic. This book will teach you how to write proofs, basic logic and set theory that you will need: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995 I can't really recommend a good Discrete Math textbook as most of them are "meh", and "How to Prove It" does contain a lot of the material usually taught in a Discrete Math course. The extra topics you will find in discrete maths books is: basic probability, some graph theory, some number theory and combinatorics, and in some books even some basic algebra and algorithm analysis. If I were you I would focus mostly on the combinatorics and probability. Anyway, here's a list of discrete math books. Pick the one you like the most judging from the reviews: u/Anirudh25 · 1 pointr/learnprogramming I found this book quite understandable u/jebuz23 · 1 pointr/actuary Superforecasting has been on my "get to soon" list since I got it last Christmas. It just got a nice nod in the latest CAS magazine. Along the probability/math lines, other books I've enjoyed are: u/JLHawkins · 1 pointr/explainlikeimfive Want to break your head? 0.999... = 1. 1. 1/3 is 0.333 repeating: 1/3 = 0.333... 2. Multiply both sides by 3 to get rid of the fraction: 1/3 * 3 = 0.333... * 3 3. 3/3 = 0.999... 4. 1 = 0.999... Want to get weirder? Try multiplying 0.999... by 10, which is just moving the decimal one spot to the right. 5. 10 * 0.999... = 9.999... 6. Now get rid of that annoying decimal by subtracting 0.999... from both sides: 10 * (0.999...) - 1 * (0.999...) = 9.999... - 0.999... 7. The left hand side of the equation is just 9 x (0.999...) because 10 times something minus that something is 9 times the aforementioned thing. And on the right hand side, we've canceled out the decimal. 8. 9 * (0.999...) = 9 9. If 9 times something is 9, that thing must be 1. Lots more fun stuff in the chapter, Straight Logically Curved Globally from the book How Not to Be Wrong: The Power of Mathematical Thinking, by Jordan Ellenberg. u/Clash_Tofar · 1 pointr/PoliticalOpinions Definitely not more qualified than you but do enjoy tackling tough questions like you proposed and thinking through some mental framework that would make the political environment we are in a little less overwhelming. Because the system you proposed would likely be based on (for the most part) universal values, it's probably in your best interest to do some light reading that will help you feel more grounded in your choices. If someone asked you why you believe wealth inequality was a bad thing, you might be able to form a more streamlined and coherent thought (outside of something simple like "it's just the right thing to do" or "because that's how I was raised" etc) a couple of good books I've enjoyed and don't require advanced degrees in psychology / philosophy are: The Island of Knowledge How not to be Wrong While enticing to set up a simple acronym or mantra around your political decision making, I've always felt it's better to dig in a bit and then in turn use what you've learned to organize your values etc. Thoughts? u/fulgoray · 1 pointr/math Try out Jordan Ellenberg's How Not to Be Wrong: The Power of Mathematical Thinking. http://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535 u/Capermis · 1 pointr/explainlikeimfive That doesn't sound right. There is a simple mathematical explanation of insurance and risk in this book:https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535 I'll try to give my two cents from memory. The point of any insurance is to spread the risk across more than one person. I don't have the liquidity to pay the huge cost associated with an accident/serious health issue. So, in the unlikely event this happens, I'm screwed and would bankrupt. In contrast, rich people don't need insurance as they can pay up when the event does happen. They should keep on to their money as long as possible. However, barring the margins taken by the insurer, on average the uninsured rich person and the insured poor person are expected to pay equal amounts (assuming for simplicity that both have the same probability of an event occurring). So, I think that if you work out the math even an insurance company covering only two people would make sense as it reduces the probility of an insurmountable cost occurring (by a little bit). So, rationally, I think the only stable point is for everybody to be insured that is either not rich enough to be able to take a hit (essentially these people can act as their own insurer) or too poor to pay the monthly fees (these are the people crossing their fingers no cataclysmic event pushes them over the edges). u/penndotsucks · 1 pointr/CFBOffTopic If you're actually interested in why we don't have a tiered voting system, I'd encourage you to read more about the mathematics of voting; in particular, the chapter titled "There Is No Such Thing As Public Opinion" from the book How Not To Be Wrong. Won't necessarily answer all of your questions but basically the answer is that a dictatorship is the only pure "election" system. u/kentnl · 1 pointr/INTP Read ( or listen to ) the book "How not to be wrong" by Jordan Ellenberg It covers not just the stupid "do this" of math, but talks more high level abstract concepts, and discusses real world problems with mathematical implications, and talks about how Math is not some arcane magic, but is in fact a product of human intelligence, and that Math is mostly a formalised version of human natural understanding and rationalisation. It also covers statistical reasoning, something INTPs typically don't do to well at, because we get distracted by focusing on the details, not realising we don't need the details to draw a good enough conclusion, failing to realise spending too much time on details may actually hinder, not help, the decision making process. ( Because ultimately, you any detail you think is sufficient can be subdivided into details that you don't understand at some level, and you can get side tracked working out how quantum particles work in the process of deciding whether or not you want chicken for dinner, so you need to stop at some depth ) IME, INTJs beat us at math because their statistical reasoning is more naturally adapted, and so they're more likely to follow a Mathematical Discipline than we are. u/thang1thang2 · 1 pointr/learnmath Honestly, I highly recommend this book, and pretty much anything else by Arthur Benjamin. He's the real deal when it comes to mental math. Take it seriously, and do tons of practice problems. Feel free to go "fast" through the book the first time through, but go super slow the second time through and get everything super solid. After completing the book you'll be able to do squares, multiplication, division, addition, subtraction pretty damn fast up to around 3-4 digits. With more practice you can eventually get as good as Prof. Benjamin (he doesn't leave anything out! Tells you the entire technique). By more, I mean years more, but hey, at least it's possible u/IIGrudge · 1 pointr/howto Wow thanks. Also read Secrets of Mental Math. It provides lots of helpful tricks. u/eipi1is0 · 1 pointr/math Aside from Khan, The Secrets of Mental Math was extremely helpful in this endeavor. u/eitauisunity · 1 pointr/math I used to be just like you, then really became fascinated by physics, which was very difficult given my deficiencies in math. I figured I would start with flash cards and what not, so I started browsing amazon and came across this. This guy is a genius, and teaches you a lot of tricks to do math quickly in your head. The next thing I did was checked out Khan Academy. I can not over-exaggerate how utterly fucking awesome this site is. Not only does he have like 2300+ videos on every topic, but he has something like 125 math modules that allow you to practice. It's completely free and all you need is a facebook or gmail account to log in... u/Spoogly · 1 pointr/math I would enumerate on the various techniques I've used over the years, which drove my early math teachers somewhat mad, but, well, those little tricks and more are readily available in the book The Secrets Of Mental Math. I never finished the book, but it's got quite a few very useful tips, just in the opening couple of chapters, and it builds on them to add other neat things. u/hurrayfortimemachine · 1 pointr/AskReddit Benjamin Arthur is great at this. He wrote a book that may interest you. u/CuttlefishQuincunx · 1 pointr/math I read this book in high school when it was originally published as "Mathemagics." https://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=pd_lpo_sbs_14_t_2?_encoding=UTF8&amp;psc=1&amp;refRID=WQYSFNW9WRJY77M30PZG Its a collection of tips and shortcuts to make mental math easier. I really enjoyed it and found it very useful. u/watertap · 1 pointr/IWantToLearn Asked myself the same question this morning. I found this book is supposed to be a good start. http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401 u/muff1nz · 1 pointr/math Read the book by Arthur Benjamin. He's one of my role models. :D The book has the most amazing mental math tricks ever, and I can square 2, 3, and even 4 digit numbers in my head. Getting to 5 digits soon. There are a lot of other cool tricks in there as well. u/looselyspeaking · 1 pointr/math Here's another one that's pretty good u/APPARENTLY_HITLER · 1 pointr/AskReddit Little mental trick you can do to show off to some people: any number * 11 is easy. Even in the 2 digits. Let's do 32 again. *32 11 Separate 32 into two digits, add them, and then put that number between those two digits. For example: 3 + 2 = 5 place between the two original digits: 352 ----- This works with three digits as well (but I have to go figure out how to do that one again). There is a book on the Apple Store that is an awesome read if you're into it. All of the things I am showing you are possible to do mentally. I can currently square 4 digit numbers in my head sorta reliably, and can square 3 and 2 digit numbers without fail. It is really fun and I enjoy doing it. ----- EDIT: PLEASE PLEASE PLEASE support this guy and do not download a pdf of the book. He is absolutely incredible with what he can do and is sharing it with people so they can do it too. Give him credit! Book on Amazon Book on iBooks ----- Youtube video of this guy u/arktor314 · 1 pointr/videos This is one of the methods suggested in this book: https://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401 It’s a really nice read for doing mental math. The author, Arthur Benjamin, has some really impressive videos on YouTube IIRC u/thisisnotjr · 1 pointr/math I'm premed, the most I know is just 2 semesters of calculus. However I am reading [Mental Math tricks] (http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401). I don't know what good that'll do me other than make look more of a nerd than I do now. I am also learning how to program and work with computer. I'm starting small with PyScript and trying to get A+ certified. u/noahpoah · 1 pointr/suggestmeabook If you liked Consider the Lobster, then you will also very probably like A Supposedly Fun Thing I'll Never Do Again and Both Flesh and Not. Edited to add that Everything and More is also very good, though it's not a collection of essays. u/RuttyRut · 1 pointr/INTP It sounds like you would enjoy Everything and More: A Compact History of Infinity, also by DFW. Fascinating read, non-fiction, both somewhat technical and easily readable. "The task Wallace has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining." https://www.amazon.com/Everything-More-Compact-History-Infinity/dp/0393339289 u/racketship · 1 pointr/davidfosterwallace I would be interested in Everything and More: A Compact History of Infinity Is that a possibility? u/threepoint14ApplePi · 1 pointr/332e313431353932 Of note, DFW also wrote this. u/Oldkingcole225 · 1 pointr/technicallythetruth This is the basis of calculus. An infinitesimal (1/Infinity) can both = 0 and &gt; 0. When calculus was first presented to the math community, they saw this and called it a bunch of liberal hippie bullshit. It took ~100-150 years for calculus to be fully formalized and accepted within the math community, but it was immediately accepted in the engineering community because it worked. If you’re interested, I highly recommend Everything and More: A Compact History of Infinity by David Foster Wallace u/CentralNervousPiston · 1 pointr/philosophy I am a Strange Loop is about the theorem Another book I recommend is David Foster-Wallace's Everything and More. It's a creative book all about infinity, which is a very important philosophical concept and relates to mind and machines, and even God. Infinity exists within all integers and within all points in space. Another thing the human mind can't empirically experience but yet bears axiomatic, essential reality. How does the big bang give rise to such ordered structure? Is math invented or discovered? Well, if math doesn't change across time and culture, then it has essential existence in reality itself, and thus is discovered, and is not a construct of the human mind. Again, how does logic come out of the big bang? How does such order and beauty emerge in a system of pure flux and chaos? In my view, logic itself presupposes the existence of God. A metaphysical analysis of reality seems to require that base reality is mind, and our ability to perceive and understand the world requires that base reality be the omniscient, omnipresent mind of God. Anyway these books are both accessible. Maybe at some point you'd want to dive into Godel himself. It's best to listen to talks or read books about deep philosophical concepts first. Jay Dyer does a great job on that https://www.youtube.com/watch?v=c-L9EOTsb1c&amp;amp;t=11s u/dagbrown · 1 pointr/ContagiousLaughter I invite you to read a couple of books, both of which I really enjoyed. One, Two, Three...Infinity by George Gamow (that link is almost certainly an act of piracy, but I doubt the author would mind because he dedicated his life to spreading knowledge), and Everything and More by David Foster Wallace. That's a publication which is so recent that if you want to read it, you'll have to cough up money. Go ahead and do it: it's so interesting that it's worth the eight bucks for the e-book easily. Don't worry, it's not an affiliate link, I stand to gain nothing from your purchase. Both of those books talk about the mind-blowing idea that there are multiplie levels of infinity, with some infinities being much bigger than other infinities. The state of the art in thinking about infinities is so brain-hurting that David Foster Wallace's book was published 40 years after George Gamow's book, and includes a relatively small number of concepts that weren't in the older book (which isn't to say that they're insignificant--they're ideas about infinity so by necessity they're huge). One of the things I liked about David Foster Wallace's book is that it actually has a formula for quantifying how much bigger a higher-level infinity is than a lower-level infinity. Nobody in Gamow's day had come up with anything like that yet, they were just waving their arms talking about "huge" and "huger". u/wonkybadank · 1 pointr/math Calc 3 was series for us, 4 was multivariable. We were quarters with summer quarter being optional so it was really trimesters for most people. Vector calc was basically taught from the book Div, Grad, Curl and All That. So it was useful prior to going into electrodynamics, which was also 4th year. &amp;#x200B; EDIT: Added link. u/Arienna · 1 pointr/EngineeringStudents There's a book called Div, Grad, Curl and All That, here is an Amazon link. It's an informal approach to vector mathematics for scientists and engineers and it's pretty readable. If you're struggling with the math, this is for you :) All their examples are EM too. It's also a good idea to get a study group together. The blind leading the blind actually do get somewhere. :) u/Thoonixx · 1 pointr/math http://www.amazon.com/dp/0471725692/ref=wl_it_dp_o_pd_S_ttl?_encoding=UTF8&amp;amp;colid=2UCFQZHNW5VVF&amp;amp;coliid=I1RPWVCSMOOV09 is one good suggestion, I've seen around here. It's on my wishlist and the book that I intend to work from. Now I always struggled with vector calculus and its motivations. So I have this one waiting for me as well http://www.amazon.com/dp/0393925161/ref=wl_it_dp_o_pC_nS_ttl?_encoding=UTF8&amp;amp;colid=2UCFQZHNW5VVF&amp;amp;coliid=I20JETA4TTSTJY since I think it covers a lot of the concepts that I had the most trouble with in calc 3 u/_11_ · 1 pointr/EngineeringStudents Div, Grad, Curl, and All That is a good way to shore up your knowledge of vector calc. u/runs_on_command · 1 pointr/ECE When I took EM in addition to Cheng the professor suggested getting Div, Grad, Curl and all of that. I found that to be alot of help in solidifying the math and intuition needed. u/RRuruurrr · 1 pointr/CasualConversation No worries for the timeliness! For Measure and Integration Theory I recommend Elements of Integration and Measure by Bartle. For Functional Analysis I recommend Introductory Functional Analysis with Applications by Kreyszig. And for Topology, I think it depends on what flavor you're looking for. For General Topology, I recommend Munkres. For Algebraic Topology, I suggest Hatcher. Most of these are free pdf's, but expensive ([;\approx \$200;]) to buy a physical copy. There are some good Dover books that work the same. Some good ones are this, this, and this.

u/CD_Johanna · 1 pointr/math

I hate to disappoint you OP, but here are some books just in my wish list on Amazon that outdo that:

This has 14, 5 star reviews.

This has 20, 5 star reviews, and 1, 4 star review.

u/manualcrank · 1 pointr/math

Kreyszig is the best first book on functional analysis IMO. For measure theory I liked Royden, specifically the 3rd edition.

u/brational · 1 pointr/math

If you're coming from a more applied background (or physics / engineering) https://www.amazon.com/Introductory-Functional-Analysis-Applications-Kreyszig/dp/0471504599 is pretty easy to follow. Obviously it goes into the infinite dim too but it covers all the finite stuff first.

u/jevonbiggums2 · 1 pointr/math

I have a variety of books to recommend.
http://www.amazon.com/Beginning-Functional-Analysis-Karen-Saxe/dp/0387952241
If you get this from your library or browse inside of it and it seems easy there are then three books to look at:

1. http://www.amazon.com/Functional-Analysis-Introduction-Princeton-Lectures/dp/0691113874/ref=sr_1_4?s=books&amp;amp;ie=UTF8&amp;amp;qid=1368475848&amp;amp;sr=1-4&amp;amp;keywords=functional+analysis challenging exercises for sure.
2. http://www.amazon.com/Introductory-Functional-Analysis-Applications-Kreyszig/dp/0471504599/ref=sr_1_2?s=books&amp;amp;ie=UTF8&amp;amp;qid=1368475848&amp;amp;sr=1-2&amp;amp;keywords=functional+analysis (A great expositor)
3. Rudin's Functional Analysis (A challenging book for sure)

(An awesome book with exercise solutions that will really get you thinking)

Working on this book and Rudin's (which has many exercise solutions available online is very helpful) would be a very strong advanced treatment before you go into the more specialized topics.

The key to learning this sort of subject is to not delude yourself into thinking you understand things that you really don't. Leave your pride at the door and accept that the SUMS book may be the best starting point. Also remember to use the library at your institution, don't just buy all these books.
u/ndat · 1 pointr/webdev

I just bought this for $10. Not all textbook companies are jokes. Just most. u/wowSuchPotato · 1 pointr/getdisciplined General Advice • Try to put in a consistent amount of work daily. • Make sure you're doing exercises (not just reading watching videos) Specific Advice • Videos/Course: MIT Calculus Course. Watch the videos, supplement with notes if you need to. Do the assignments and check your solutions. Work towards getting passing grades in the exams. It's not important to get this done before college, just work on it and you will be more prepared. • ODE Textbook: Love this book, working my way through it now, not sure if a better ODE book exists. It's also fairly simple but you might want to do some work on the MIT course first. It's not legally free, but... u/ThroughTheForests · 1 pointr/math u/Chade_Fallstar · 1 pointr/learnmath Tenenbaum and Pollard's book is fine. It is cheap too (published by Dover methinks) https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407 u/lordpie314 · 1 pointr/NoStupidQuestions That helps a little. I'm not too familiar with that world (I'm a physics major), but I took a look at a sample civil engineering course curriculum. If you like learning but the material in high school is boring, you could try self-teaching yourself basic physics, basic applied mathematics, or some chemistry, that way you could focus more on engineering in college. I don't know much about engineering literature, but this book is good for learning ODE methods (I own it) and this book is good for introductory classical mechanics (I bought and looked over it for a family member). The last one will definitely challenge you. Linear Algebra is also incredibly useful knowledge, in case you want to do virtually anything. Considering you like engineering, a book less focused on proofs and more focused on applications would be better for you. I looked around on Amazon, and I found this book that focuses on applications in computer science, and I found this book focusing on applications in general. I don't own any of those books, but they seem to be fine. You should do your own personal vetting though. Considering you are in high school, most of those books should be relatively affordable. I would personally go for the ODE or classical mechanics book first. They should both be very accessible to you. Reading through them and doing exercises that you find interesting would definitely give you an edge over other people in your class. I don't know if this applies to engineering, but using LaTeX is an essential skill for physicists and mathematicians. I don't feel confident in recommending any engineering texts, since I could easily send you down the wrong road due to my lack of knowledge. If you look at an engineering stack exchange, they could help you with that. &amp;#x200B; You may also want to invest some time into learning a computer language. Doing some casual googling, I arrived at the conclusion that programming is useful in civil engineering today. There are a multitude of ways to go about learning programming. You can try to teach yourself, or you can try and find a class outside of school. I learned to program in such a class that my parents thankfully paid for. If you are fortunate enough to be in a similar situation, that might be a fun use of your time as well. To save you the trouble, any of these languages would be suitable: Python, C#, or VB.NET. Learning C# first will give you a more rigorous understanding of programming as compared to learning Python, but Python might be easier. I chose these three candidates based off of quick application potential rather than furthering knowledge in programming. This is its own separate topic, but my personal two cents are you will spend more time deliberating between programming languages rather than programming if you don't choose one quickly. &amp;#x200B; What might be the best option is contacting a professor at the college you will be attending and asking for advice. You could email said professor with something along the lines of, "Hi Professor X! I'm a recently accepted student to Y college, and I'm really excited to study engineering. I want to do some rigorous learning about Z subject, but I don't know where to start. Could you help me?" Your message would be more formal than that, but I suspect you get the gist. Being known by your professors in college is especially good, and starting in high school is even better. These are the people who will write you recommendations for a job, write you recommendations for graduate school (if you plan on it), put you in contact with potential employers, help you in office hours, or end up as a friend. At my school at least, we are on a first name basis with professors, and I have had dinner with a few of mine. If your professors like you, that's excellent. Don't stress it though; it's not a game you have to psychopathically play. A lot of these relationships will develop naturally. &amp;#x200B; That more or less covers educational things. If your laziness stems from material boredom, everything related to engineering I can advise on should be covered up there. Your laziness may also just originate from general apathy due to high school not having much impact on your life anymore. You've submitted college applications, and provided you don't fail your classes, your second semester will probably not have much bearing on your life. This general line of thought is what develops classic second semester senioritis. The common response is to blow off school, hang out with your friends, go to parties, and in general waste your time. I'm not saying don't go to parties, hang out with friends, etc., but what I am saying is you will feel regret eventually about doing only frivolous and passing things. This could be material to guilt trip yourself back into caring. &amp;#x200B; For something more positive, try to think about some of your fun days at school before this semester. What made those days enjoyable? You could try to reproduce those underlying conditions. You could also go to school with the thought "today I'm going to accomplish X goal, and X goal will make me happy because of Y and Z." It always feels good to accomplish goals. If you think about it, second semester senioritis tends to make school boring because there are no more goals to accomplish. As an analogy, think about your favorite video game. If you have already completed the story, acquired the best items, played the interesting types of characters/party combinations, then why play the game? That's a deep question I won't fully unpack, but the simple answer is not playing the game because all of the goals have been completed. In a way, this is a lot like second semester of senior year. In the case of real life, you can think of second semester high school as the waiting period between the release of the first title and its sequel. Just because you are waiting doesn't mean you do nothing. You play another game, and in this case it's up to you to decide exactly what game you play. &amp;#x200B; Alternatively, you could just skip the more elegant analysis from the last few paragraphs and tell yourself, "If I am not studying, then someone else is." This type of thinking is very risky, and most likely, it will make you unhappy, but it is a possibility. Fair warning, you will be miserable in college and misuse your 4 years if the only thing you do is study. I guarantee that you will have excellent grades, but I don't think the price you pay is worth it. u/freyrs3 · 1 pointr/math For DEs try: Ordinary Differential Equations by Tennenbaum Its a great book with a TON of worked examples and solutions to all the exercises. This text was my holy book during my undergrad engineering courses. u/kem3 · 1 pointr/EngineeringStudents I had a hard time getting through dif eq also, because the book was unreadable (to me). I also hate reading anything by Hibbler. The Munson fluid mechanics book is... barely tolerable. When that happens, I tend to look, with more vigor than usual, for other sources. Dif eq: I was lucky, and our tutoring center has dif eq tutors. Fluids: I found a wonderful lecture series done by UC Irvine OpenCourseWare. Hibbler... well, I've been S.O.L. on that so far. Generally, I also try to find a solutions manual. If I'm having a terrible time with a problem, I work through it and check myself each step of the way. I often try to find a different book, too. The only reason you need the required book is so you know what to look for in your chosen book. I recently discovered there is a very highly-rated dif eq book available used on Amazon for about$13, so I ordered it in the hopes that it will be readable, as I now need to brush up on dif eq and can't stand the book we used in class.

u/anvaka · 1 pointr/math

I know this is removed, so I can recommend my tool which builds a graph of products that are often bought together at Amazon.

http://www.yasiv.com/#/Search?q=graph%20theory&amp;amp;category=Books&amp;amp;lang=US - this is a network of books related to graph theory. Finding the most connected product usually yields a good recommendation. In this case it recommends to take a deeper look at https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709

u/iHateTheStuffYouLike · 1 pointr/politics

&gt;I like how you came here to make a distinction without a difference

That you think these sets are equivalent is the problem with "STEM" in this country. I'm not blaming you, it's not your fault. For whatever reason, set theory is barely discussed. Even in multivariate calculus, the most you care about sets is with domain and range, just like in algebra. Here are a few topics that are mathematics, and not arithmetic:

-Set Theory

-Topology (Better than Munkres)

-Graph Theory

-Abstract Algebra (Groups/Rings/Fields)

Basic quantifiers pop up first in set theory, which as far as I can tell is only recommended after integral calculus. Things like ∀, and ∃ have a particular meaning, and their orders and quantities are very specific.

If you would like to know more about the difference between mathematics and arithmetic (which is a subset), then start with set theory. You'll need that to do anything else. I can try to answer any other questions you may have.

If anyone is interested in learning more about graph theory, this is a great (and brief) book that requires very little mathematical background. I highly recommend it.

u/TonySu · 1 pointr/learnmath

Probability and Random Processes by Grimmett is a good introduction to probability.

Mathematical Statistics by Wackerly is a comprehensive introduction to basic statistics.

Probability and Statistical Inference by Nitis goes into the statistical theory from heavier probability background.

The first two are fairly basic and the last is more involved but probably contains very few applied techniques.

u/Jimmy_Goose · 1 pointr/math

If that is the case: The most widely used undergrad book is Wackerly et al. I also taught out of Devore before and it is not bad.

Wackerly covers more topics, but does so in a much more terse manner. Devore covers things better, but covers less things (some of which are pretty important).

Grad: Casella and Berger. People might have their qualms with this book but there is really no better book out there.

u/kenderpl · 1 pointr/learnmath

If you want to do statistics in a rigorous way you should start with calculus and linear algebra.

For calculus I recommend Paul's notes -&gt; http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
They are really clearly written with good examples and provide good intuition.
As supplement go through 3blue1borwn Essence of calculus. I think it's an excellent resource for providing the right intuition.

For linear algebra - linear algebra - Linear algebra done right as already recommended. Additionally, again 3blue1brown series on linear algebra are top notch addition for providing visual intuition and understanding for what is going on and what it's all about.

Finally, for statistics - I would recommend starting with probability calculus - that way you'll be able to do mathematical statistics and will have a solid understanding of what is going on. Mathematical statistics with applications is self-contained with probability calculus included. https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

u/LoKx · 1 pointr/actuary

Sadly the only university in my city lost their accreditation since they couldn't pay a competitive salary.

I lucked out because my Statistics professor is insanely qualified. (Ph.D in Mathematics and Ph.D in Statistics) So our Stats course covers MGFs and the derivations of all the theorems. Pretty much every question in this book: http://www.amazon.ca/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

Thanks a lot for the response. The thought of taking on something of this magnitude with no real life mentor-ship is really daunting.

u/crossingtheabyss · 1 pointr/math

Just completed Probability this semester, and moving on to Statistical Inference next semester. Calc. B is a prerequisite, and wound up seeing plenty of it along with a little Calc C (just double integrals). I'm an Applied Mathematics undergrad major btw and former Physics major from some years ago. I wound up enjoying it despite my bad attitude in the beginning. I keep hearing from fellow math majors that Statistical Inference is really difficult. Funny thing is I heard the same about Linear Algebra and didn't find it overwhelming. I'll shall soon find out. We used Wackerly's Mathematical Statistics with Applications. I liked the book more than most in my class. Some thought it was overly complicated and didn't explain the content well. Seems I'm always hearing some kind of complaint about textbooks every semester. Good luck.

This was mine.

This book comes to mind.

u/pgoetz · 1 pointr/statistics

I would try Mathematical Statistics and Data Analysis by Rice. The standard intro text for Mathematical Statistics (this is where you get the proofs) is Wackerly, Mendenhall, and Schaeffer but I find this book to be a bit too dry and theoretical (and I'm in math). Calculus is less important than a thorough understanding of how random variables work. Rice has a couple of pretty good chapters on this, but it will require some mathematical maturity to read this book. Good luck!

I enjoyed

Introduction to Probability Theory, Hoel et. al

Also,

Probability Theory, Jaynes

is essential. For probabilistic programming I would also look into

Bayesian Methods for Hackers

u/whitewhim · 1 pointr/Physics

I really love Probability Theory: The Logic of Science by Jaynes. While it is not a physics book, it was written by one. It is very well written, and is filled with common sense (which is a good thing). I really enjoy how probability theory is built up within it. It is also very interesting if you have read some of Jaynes' more famous works on applying maximum entropy to Statistical Mechanics.

u/qtMITTENS · 1 pointr/math
u/Kijanoo · 1 pointr/technology

&gt; Honestly, both of our arguments have become circular. This is because, as I have stressed, there is not enough data for it to be otherwise. Science is similar to law in that the burden of proof lies with the accuser. In this case there is no proof, only conjecture.

((Just in case it is relevant: Which two arguments do you mean exactly, because the circularity isn't obvious to me?))

In my opinion you can argue convincingly about future events where you are missing important data and where no definitive proof was given (like in the AI example) and I want to try to convince you :)

I want to base my argument on subjective probabilities. Here is a nice book about it. It is the only book of advanced math that I worked through \^\^ (pdf).

My argument consists of multiple examples. I don't know where we will disagree, so I will start with a more agreeable one.

Let's say there is a coin and you know that it may be biased. You have to guess the (subjective) probability that the first toss is head . You are missing very important data: The direction the coin is biased to, how much it is biased, the material .... . But you can argue the following way: "I have some hypotheses about how the coin behaves and the resulting probabilities and how plausible these hypotheses are. But each hypothesis that claims a bias in favour of head is matched with an equally plausible hypothesis that points in the tail direction. Therefore the subjective probability that the first toss is head is 50%"

What exactly does "the subjective probability is 50%" mean? It means if I have to bet money where head wins 50 cent and tail wins 50 cent, I could not prefer any side. (I'm using small monetary values in all examples, so that human biases like risk aversion and diminishing returns can be ignored).

If someone (that doesn't know more than me) claims the probability is 70% in favour of heads, then I will bet against him: We would always agree on any odds between 50:50 and 70:30. Let's say we agree on 60:40, which means I get 60 cent from him if the coin shows tail and he gets 40 cent from me if the coin shows head. Each of us agrees to it because each one claims to have a positive expected value.

This is more or less what happened when I bet against the brexit with my roommate some days ago. I regularly bet with my friends. It is second nature for me. Why do I do it? I want to be better at quantifying how much I believe something. In the next examples I want to show you how I can use these quantifications.

What happens when I really don't know something. Let's say I have to guess my subjective probability that the Riemann hypothesis is true. So I read the Wikipedia article for the first time and didn't understand the details ^^. All I can use is my gut feeling. There seem to be some more arguments in favour of it being true, so I set it to 70%. I thought about using a higher value but some arguments might be biased by arguing in favour to what some mathematicians want to be true (instead of what is true).

So would I bet against someone who has odds that are different from mine (70:30) and doesn't know much more about that topic? Of course!

Now let's say in a hypothetic scenario an alien, a god, or anyone that I would take serious and have no power over him appears in front of me, chooses randomly a mathematical conjecture (here: it chooses the Rieman hypotheses) and speaks the following threat: "Tomorrow You will take a fair coin from your wallet and throw it. If the coin lands head you will be killed. But as an alternative scenario you may plant a tree. If you do this, your death will not be decided by a coin, but you will not be killed if and only if the Riemann hypothesis is true"

Or in other words: If the subjective probability that the Riemann hypothesis is true is &gt;50% then I will prefer to plant a tree; otherwise, I will not.

This example shows that you can compare probabilities that are more or less objective (e.g. from a coin) with subjective probabilities and that you should even act on that result.

The comforting thing with subjective probabilities is that you can use all the known rules from "normal" probabilities. This means that sometimes you can really try to calculate them from assumptions that are much more basic than a gut feeling. When I wrote this post I asked myself what the probability is that the Riemann hypothesis will be proven/disproven within the next 10 years. (I just wanted to show you this, because the result was so simple, which made me happy, but you can skip that).

• assumption 1: Given a single arbitrary mathematical statement I know nothing about. And lets say I consider only those with a given difficulty, which means it is either easy to solve or difficult to solve from an objective point of view. Now I use the approximation that if it wasn't solved for n days, then the probability that it will be solved within the next day is like throwing a dice - it is independent of n. This behaviour is described by an exponential function "exp(-r t)", where the result is the probability that it remains unsolved after t years and a given difficulty parameter r. You could use better models of course, but given I know nothing about that statement, it is OK for me to expect a distribution which looks like an exponential function.
• assumption 2: Most mathematical problems and subproblems are solved rather fast/instantly, because they are simple. The outstanding problems are the difficult ones. This can be described by a difficulty parameter probability distribution where each possible parameter value has the same subjective probability. This is only one way to describe the observation of course, but I also get this probability distribution if I use the principle of indifference, according to which the problem should be invariant with respect to the timescale (= nothing changes if I change the units from months to decades).
• result: Ok I don't know how difficult the Riemann hypothesis is to prove, but integrating over all possible difficulties and weighting them by their subjective probability (=assumption 2) and the plausibility of not being solved for past years "p", I can calculate the odds that it will be solved within the next years "t". The solution = "t:p". So given, that it wasn't solved for 100 years the odds are very small (10:100).

And this result is useful for me. Would I bet on that ratio? Of course! Would I plant a tree in a similar alien example? No I wouldn't, because the probability is &lt;50%. Again, it is possible to use subjective probabilities to find out what to do.

And here is the best part, about using subjective probabilities. You said "Science is similar to law in that the burden of proof lies with the accuser. In this case there is no proof, only conjecture." But this rule is no longer needed. You can come to the conclusion that the probability is too low to be relevant for whatever argument and move on. The classic example of Bertrand Russel's teapot can be solved that way.

Another example: You can calculate which types of supernatural gods are more or less probable. One just needs to collect all pro and contra arguments and translate them to likelihood ratios . I want to give you an example with one type of Christian god hypothesis vs. pure scientific reasoning:

• Evidence "The species on planet earth can be organized by their genes in a tree shape.": evolution predicts this (therefore p=1) and Christian-god-intelligent-design-hypothesis says "maybe yes maybe something else" (p= 1/2 at most). Therefore the likelihood ratio is 1:2 in favour of pure scientific reasoning.
• more arguments, contra: problem of evil, lawful universe and things that follow from that, ...
• more arguments, pro: Fine-tuned Universe problem, existence of consciousness, ...

In the end you just multiply all ratios of all arguments and then you know which hypothesis of these two to prefer. The derived mathematical formula is a bit more complicated, because it takes into account that the arguments might depend on each other and that there is an additional factor (the prior) which is used to indicate how much you privilege any of these two hypotheses over all the other hypotheses (e.g. because the hypothesis is the most simple one).

I wanted to show you that you can construct useful arguments using subjective probabilities, come to a conclusion and then act on the result. It is not necessary to have a definitive proof (or to argue about which side has the burden of proof).

I can imagine two ways were my argument is flawed.

• Maybe there will be too much to worry/ things to do, if one uses that method consequently. But all extreme examples I can think of either have too low probability (e.g. Pascal's Wager), or there is not much that can be done today (most asteroids are detected too late), or it is much easier to solve the problem when it arrives instead of today.
• Subjective probabilities are formalized and can be used consistently for environmental uncertainty. But there are problems if you try to reason under logical uncertainty. This is not yet formalized. Assuming it will never be, then my argument cannot be used.
u/mryanbell · 1 pointr/probabilitytheory

Jaynes' Probability Theory is fantastic.

u/leoc · 1 pointr/programming

All gone now. (05:30 UMT 10 August) LiSP and Probability Theory: The Logic of Science are still in the top two slots, but amazon.ca appears to have sold out of new copies.

u/Bromskloss · 1 pointr/statistics

&gt; There are some philosophical reasons and some practical reasons that being a "pure" Bayesian isn't really a thing as much as it used to be. But to get there, you first have to understand what a "pure" Bayesian is: you develop reasonable prior information based on your current state of knowledge about a parameter / research question. You codify that in terms of probability, and then you proceed with your analysis based on the data. When you look at the posterior distributions (or posterior predictive distribution), it should then correctly correspond to the rational "new" state of information about a problem because you've coded your prior information and the data, right?

Sounds good. I'm with you here.

&gt; However, suppose you define a "prior" whereby a parameter must be greater than zero, but it turns out that your state of knowledge is wrong?

Isn't that prior then just an error like any other, like assuming that 2 + 2 = 5 and making calculations based on that?

&gt; What if you cannot codify your state of knowledge as a prior?

Do you mean a state of knowledge that is impossible to encode as a prior, or one that we just don't know how to encode?

&gt; What if your state of knowledge is correctly codified but makes up an "improper" prior distribution so that your posterior isn't defined?

Good question. Is it settled how one should construct the strictly correct priors? Do we know that the correct procedure ever leads to improper distributions? Personally, I'm not sure I know how to create priors for any problem other than the one the prior is spread evenly over a finite set of indistinguishable hypotheses.

The thing about trying different priors, to see if it makes much of a difference, seems like a legitimate approximation technique that needn't shake any philosophical underpinnings. As far as I can see, it's akin to plugging in different values of an unknown parameter in a formula, to see if one needs to figure out the unknown parameter, or if the formula produces approximately the same result anyway.

&gt; read this book. I promise it will only try to brainwash you a LITTLE.

I read it and I loved it so much for its uncompromising attitude. Jaynes made me a militant radical. ;-)

I have an uncomfortable feeling that Gelman sometimes strays from the straight and narrow. Nevertheless, I looked forward to reading the page about Prior Choice Recommendations that he links to in one of the posts you mention. In it, though, I find the puzzling "Some principles we don't like: invariance, Jeffreys, entropy". Do you know why they write that?

This one? Damn, it's £40-ish. Any highlights or is it just a case of this book is the highlight?

It's on my wishlist anyway. Thanks.

u/fyl999 · 1 pointr/Christianity

&gt;All I'm saying is that the origin of a claim contains zero evidence as to that claim's truth.

I had a look back though your other posts and found this, which explains a lot, for me anyway. Most people would put some more options in there - yes, no, im pretty sure, its extremely unlikely etc..

Heres what I think is the problem, and why I think you need to change the way you are thinking - Your whole concept of what is "logical" or what is "using reason" seems to be constrained to what is formally known as deductive logic. You seem to have a really thorough understanding of this type of logic and have really latched on to it. Deductive logic is just a subset of logic. There is more to it than that.

I was searching for something to show you on other forms of logic and came across this book - "Probability Theory - The Logic of Science" Which looks awesome, Im going to read it myself, it gets great reviews. Ive only skimmed the first chapter... but that seems to be a good summary of how science works- why it does not use just deductive logic. Science draws most of its conclusions from probability, deductive logic is only appropriate in specific cases.

Conclusions based on probability - "Im pretty sure", "This is likely/unlikely" are extremely valid - and rational. Your forcing yourself to use deductive logic, and only deductive logic, where its inappropriate.

&gt;You have no way of knowing, and finding out that this person regularly hallucinates them tells you nothing about their actual existence.

Yeah I think with the info you've said we have it would be to little to draw a conclusion or even start to draw one. Agreed. It wouldnt take much more info for us to start having a conversation about probabilities though - Say we had another person from the planet and he says its actually the red striped jagerwappas that are actually taking over - and that these two creatures are fundamentally incompatible. ie. if x exists y can't and vice-versa.

u/bayen · 1 pointr/RPI

I'd suggest MATP 4600, Probability Theory &amp; Applications. Only prerequisite is Calc if I remember right.

Or if you're confident in your time management, maybe read this textbook on your own; it's pretty accessible: https://www.amazon.com/gp/aw/d/0521592712/

(Neither of these will teach you a bunch of statistical tests, but those are easy to abuse if you don't understand the fundamentals ... and very easy to look up if you do understand the fundamentals.)

u/chrispine · 1 pointr/atheism

&gt; For one, you need a categorical definition by which to justify your "probability" with. What, does each time you tell a god to speak deduct 1%? That's absurdly vague, stupid, and unheard of, so no wonder I never thought you'd actually be arguing this.

I don't happen to know the appropriate decibel-values to assign to E and not-E in this case. But I know the fucking SIGNS of the values.

No, I don't know how many times god needs to appear for me to believe that I wasn't drugged or dreaming or just going crazy. But god appearing is evidence for the existence of god, and him not appearing is evidence against.

Does it really matter if we are talking intervals of 5-seconds versus lifetimes?

3 pages, and you don't even have to go to a library! Check it out:

Click on "First Pages" to get to the front.

You can lead a horse to water...

u/llama-lime · 1 pointr/reddit.com

"Bayesian" is a very very vague term, and this article isn't talking about Bayesian networks (I prefer the more general term graphical models), or Bayesian spam filtering, but rather a mode of "logic" that people use in everyday thinking. Thus the better comparison would be not to neural nets, but to propositional logic, which I think we can agree doesn't happen very often in people unless they've had lots of training. My favorite text on Bayesian reasoning is the Jaynes book..

Still, I'm less than convinced by the representation of the data in this article. Secondly, the article isn't even published yet to allow anyone to review it. Thirdly, I'm suspicious of any researcher that talks to the press before their data is published. So in short, the Economist really shouldn't have published this, and should have waited. Yet another example of atrocious science reporting.

u/mark_bellhorn · 1 pointr/statistics
u/PM_ME_YOUR_WOMBATS · 1 pointr/statistics

Somewhat facetiously, I'd say the probability that an individual who has voted in X/12 of the last elections will vote in the next election is (X+1)/14. That would be my guess if I had no other information.

As the proverb goes: it's difficult to make predictions, especially about the future. We don't have any votes from the next election to try to discern what relationship those votes have to any of the data at hand. Of course that isn't going to stop people who need to make decisions. I'm not well-versed in predictive modeling (being more acquainted with the "make inference about the population from the sample" sort of statistics) but I wonder what would happen if you did logistic regression with the most recent election results as the response and all the other information you have as predictors. See how well you can predict the recent past using the further past, and suppose those patterns will carry forward into the future. Perhaps someone else can propose a more sophisticated solution.

I'm not sure how this data was collected, but keep in mind that a list of people who have voted before is not a complete list of people who might vote now, since there are some first-time voters in every election.

If you want to get serious about data modeling in social science, you might check out this book by statistician/political scientist Andrew Gelman.

u/Farion · 1 pointr/math

No, I am not familiar with vector calculus. Do I need a lot of background before I can try to learn that or is it okay to jump right in? I know there are a lot of gradients and that is something I hadn't seen before.

I was also looking at getting this.

u/efox29 · 1 pointr/ECE

I didn't full understand the material that well when I was in school but I wanted to learn it better after school. I, like you, tried to find something to supplement my existing texting books. I came across the A student's guide to maxwell equations and I began to understand more. It's a small book and what the author does is break down what the equation means. One chapter might be just on what does the surface integral mean.. Or another chapter might be on just the E vector. I found breaking it down to be more understandable than trying to take the entire equation(s) in together.

u/kerrijay · 1 pointr/EngineeringStudents

Ah but did your tour have a guide?

u/Sticky_Bandit · 1 pointr/EngineeringStudents

For when you get into Electricity and Magnetism - This

I will second this. I used this book for my year of undergrad foundations of probably and stats.
I also really like Casella and Berger's 'Statistical Inference.'

https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

Since you are still in college, why not take a statistics class? Perhaps it can count as an elective for your major. You might also want to consider a statistics minor if you really enjoy it. If these are not options, then how about asking the professor if you can sit in on the lectures?

It sounds like you will be able to grasp programming in R, may I suggest trying out SAS? This book by Ron Cody is a good introduction to statistics with SAS programming examples. It does not emphasize theory though. For theory, I would recommend Casella &amp; Berger, many consider this book to be a foundation for statisticians and is usually taught at a grad level.

Good luck!

u/mathwanker · 1 pointr/math

For probability I'd recommend Introduction to Probability Theory by Hoel, Port &amp; Stone. It has the best explanations of any probability book I've seen, great examples, and answers to most of the problems are in the back (making it well-suited for self-study). I think it's still the best introductory book on the subject, despite its age. Amazon has used copies for cheap.

For statistics, you have to be more precise as to what you mean by an "average undergraduate statistics" course. There's a difference between the typical "elementary statistics" course and the typical "mathematical statistics" course. The former requires no calculus, but goes into more detail about various statistical procedures and tests for practical uses, while the latter requires calculus and deals more with theory than practice. Learning both wouldn't be a bad idea. For elementary stats there are lots of badly written books, but there is one jewel: Statistics by Freedman, Pisani &amp; Purves. For mathematical statistics, Introduction to Mathematical Statistics by Hogg &amp; Craig is decent, though a bit dry. I don't think that Statistical Inference by Casella &amp; Berger is really any better. Those are the two most-used textbooks on the subject.

u/gabbriel · 1 pointr/math

Maybe "too applied", depending on your fields, but there's always Casella and Berger, especially if you're in Economics.

u/El-Dopa · 1 pointr/statistics

If you are looking for something very calculus-based, this is the book I am familiar with that is most grounded in that. Though, you will need some serious probability knowledge, as well.

If you are looking for something somewhat less theoretical but still mathematical, I have to suggest my favorite. Statistics by William L. Hays is great. Look at the top couple of reviews on Amazon; they characterize it well. (And yes, the price is heavy for both books.... I think that is the cost of admission for such things. However, considering the comparable cost of much more vapid texts, it might be worth springing for it.)

u/whyilaugh · 1 pointr/math

We use Casella and Berger. It glosses over the measure theory somewhat but it appropriately develops the concept of "a probability". If you haven't had much background in proper math stats, then this is a good place to start (even if you've done the more applied courses).

u/lrnz13 · 1 pointr/statistics

I’m finishing up my stats degree this summer. For math, I took 5 courses: single variable calculus , multi variable calculus, and linear algebra.

My stat courses are divided into three blocks.

First block, intro to probability, mathematical stats, and linear models.

Second block, computational stats with R, computation &amp; optimization with R, and Monte Carlo Methods.

Third block, intro to regression analysis, design and analysis of experiments, and regression and data mining.

And two electives of my choice: survey sampling &amp; statistical models in finance.

Here’s a book for intro to probability. There’s also lectures available on YouTube: search MIT intro to probability.

For a first course in calculus search on YouTube: UCLA Math 31A. You should also search for Berkeley’s calculus lectures; the professor is so good. Here’s the calc book I used.

For linear algebra, search MIT linear algebra. Here’s the book.

The probability book I listed covers two courses in probability. You’ll also want to check out this book.

If you want to go deeper into stats, for example, measure theory, you’re going to have to take real analysis &amp; a more advanced course on linear algebra.

u/determinot · 1 pointr/math

Since you're an applied math PhD, maybe the following are good. They are not applied though.

This is the book for first year statistics grad students at OSU.
http://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126/ref=sr_1_1?ie=UTF8&amp;amp;qid=1368662972&amp;amp;sr=8-1&amp;amp;keywords=casella+berger

But, I like Hogg/Craig much more.
http://www.amazon.com/Introduction-Mathematical-Statistics-7th-Edition/dp/0321795431/ref=pd_sim_b_2

I believe each can be found in international editions, and for download on the interwebs.

Only tangentially relevant, but a really good read!

Innumeracy

u/cruise02 · 1 pointr/math

Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos, and its sequel Beyond Numeracy are two of my favorites.

u/santino314 · 1 pointr/math

Well is not exactly statistics, rather a bunch of anecdote on common mistakes and misconception about mathematics, but there is this book:

"Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen
(http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Consequences-Vintage/dp/0679726012)

and it's topic is vaguely related to OP's concern.

I haven't read it all but so far it was quite fun. Again is more anecdotal than scientific and the author might be a little condescending, but is worth reading.

u/rottedtree · 1 pointr/science

Some great stuff here.

First, for a good introduction to numbers, read:
Innumeracy
http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Consequences-Vintage/dp/0679726012

It explains how numbers work very, very well, in a non-technical fashion.

The Structure of Scientific Revolutions by Thomas Kuhn
This excellent, excellent easy to read book is simply THE BEST EXPLANATION OF HOW SCIENCE WORKS.

Next, The Way Things Work by David Macaulay. It is not a 'science' book, per se, more of an engineering book, but it is brilliantly written and beautifully illustrated.

Then, dive into Asimov. "Please Explain" is fantastic. Though dated, so is his Guide to Science.

The great thing about these books is that they are all very short and aimed at people who are not technically educated. From there I am sure you will be able to start conquering more material.

Honestly, Innumeracy and The Structure of Scientific Revolutions, alone, will fundamentally change the way you look at absolutely everything around you. Genuinely eye opening.

u/BeornPlush · 1 pointr/IWantToLearn

Practice, practice, practice, practice. Getting good at maths is 90% equal to the practice you put in. People who seem "naturally" good at maths, most of the time, are just used to trying everything in their head and thus get more practice. Also, they may have done more in the past, and gotten used to using the smaller concepts they need to solve a bigger problem.

2 good books about learning: Waitzkin, The Art of Learning and Polya, How to Solve It.

u/gtani · 1 pointr/math

Putnam comp http://www.math.rutgers.edu/~saks/PUTNAM/

Also look at "Customers Also Bought" for books by Devlin, Mason etc

http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X/

u/BrainFameGame · 1 pointr/learnprogramming

Www.lpthw.org

Www.hackerrank.com

And when he's not in front of a computer he should be reading

http://www.amazon.com/How-Solve-It-Mathematical-Princeton/dp/069111966X (don't let the math scare him away if that's not his thing...at its core it's a book about how to solve any type of problem)

u/tophology · 1 pointr/math

You might want a book like How to Solve It which will give you a general toolkit of problem solving techniques. It's not a textbook per se, but if you're struggling with how to even approach math problems then it might be a good first step.

u/jdigittl · 1 pointr/math

Azcel wrote a good book on Fermat's Last Theorem and Wiles' solution. Amazon

Simon Singh's book on the same subject is also good, but Amazon has it at $10.17 whereas Azcel's is$0.71 better at $10.88. Either way you get an enjoyable read of one man's dedication to solve a notoriously tricky problem and just enough of the mathematical landscape to get a sense of what was involved. Another fun &amp; light holiday read is Polya's 'How To Solve it' - read the glowing reviews over at Amazon u/Ranalysis · 1 pointr/learnprogramming I recommend maybe doing more math instead. Or pick up a book called how to solve it . Alot of the things are easily translatable to programming and computer science really is mathematics as well. They're both related. u/jpredmann · 1 pointr/math This is just my perspective, but . . . I think there are two separate concerns here: 1) the "process" of mathematics, or mathematical thinking; and 2) specific mathematical systems which are fundamental and help frame much of the world of mathematics. &amp;#x200B; Abstract algebra is one of those specific mathematical systems, and is very important to understand in order to really understand things like analysis (e.g. the real numbers are a field), linear algebra (e.g. vector spaces), topology (e.g. the fundamental group), etc. &amp;#x200B; I'd recommend these books, which are for the most part short and easy to read, on mathematical thinking: &amp;#x200B; How to Solve It, Polya ( https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X ) covers basic strategies for problem solving in mathematics Mathematics and Plausible Reasoning Vol 1 &amp; 2, Polya ( https://www.amazon.com/Mathematics-Plausible-Reasoning-Induction-Analogy/dp/0691025096 ) does a great job of teaching you how to find/frame good mathematical conjectures that you can then attempt to prove or disprove. Mathematical Proof, Chartrand ( https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094 ) does a good job of teaching how to prove mathematical conjectures. &amp;#x200B; As for really understanding the foundations of modern mathematics, I would start with Concepts of Modern Mathematics by Ian Steward ( https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247 ) . It will help conceptually relate the major branches of modern mathematics and build the motivation and intuition of the ideas behind these branches. &amp;#x200B; Abstract algebra and analysis are very fundamental to mathematics. There are books on each that I found gave a good conceptual introduction as well as still provided rigor (sometimes at the expense of full coverage of the topics). They are: &amp;#x200B; A Book of Abstract Algebra, Pinter ( https://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178 ) &amp;#x200B; Understanding Analysis, Abbott ( https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116 ). &amp;#x200B; If you read through these books in the order listed here, it might provide you with that level of understanding of mathematics you talked about. u/doc_samson · 1 pointr/learnmath Do you understand what unknown variables are and why you are solving for them? Do you know why you are asked to move variables from one side to another? Regarding problem solving... If you are dead serious and really want to learn problem solving as a general skill, and are willing to read something that has a few examples a bit over your head but is extremely helpful in general, then may I suggest George Polya's How to Solve It. It is written at probably a high school geometry level but many of his discussions are generic enough that they should give you some insight into the problem solving process. Essentially Polya wrote a book (maybe the book) on problem solving patterns i.e. when faced with a problem ask this set of questions and try strategy A or B, etc. He has I think 12 core questions to always ask. I found it very helpful myself. The first third or so of the book is a narrative of him showing how an ideal teacher would apply his teaching methods to guide students to discover concepts on their own. A PDF of his original 1945 edition is available here: https://notendur.hi.is/hei2/teaching/Polya_HowToSolveIt.pdf But a new edition paperback is on Amazon for$14, I have it and have made tons of pencil notes in the margins.

BTW if you do try to read it, you only need to know a few things to have the first part make sense. A "rectangular parallelipiped" (horrible name) is just a rectangular prism, so imagine it is your classroom's four walls floor and ceiling, etc. If you know how to find the diagonal length of a square or rectangle (the length of a line between two opposite corners) you probably know enough to basically follow along since that is the core of his example. If not, here's the trick, just divide the square (or rectangle) into two triangles and apply the pythagorean theorem. A huge part of his problem solving method revolves around asking yourself if you know of a similar problem with a similar pattern that you can adapt to solve your current problem. It's like being asked to find the area of a half circle, you don't know the formula, but you know the formula for the area of a circle, so you can use that as a base and adapt it to the problem of the half circle.

BTW 2: Math is hard. For everybody. People who are good at math paid for it in blood sweat and tears.

u/juicyfizz · 1 pointr/learnmath

I took both precalc and calc 1 back to back (and we used Stewart's calc book for calc 1-3). To be honest, concepts like limits and continuity aren't even covered in precalculus, so it isn't like you've missed something huge by skipping precalc. My precalc class was a lot of higher level college algebra review and then lots and lots and lots of trig.

I honestly don't see how you'd need much else aside from PatricJMT and lots of example problems. It may be worthwhile for you to pick up "The Calculus Lifesaver" by Adrian Banner. It's a really great book that breaks down the calc 1 concepts pretty well. Master limits because soon you'll move onto differentiation and then everything builds from that.

Precalc was my trig review that I was thankful for when I got to calc 2, however, so if you find yourself needing calculus 2, please review as much trig as you can. If you need some resources for trig review, PM me. I tutored college algebra, precalc, and calc for 3 years.

Good luck!

u/truckbot101 · 1 pointr/math

Hello!

It's been a while since I last suggested a resource for calculus - so far, I've been finding the following two books extremely helpful and thought it would be good to share them:

1. The Calculus Lifesaver
http://www.amazon.com/The-Calculus-Lifesaver-Tools-Princeton/dp/0691130884/ref=sr_1_1?ie=UTF8&amp;amp;qid=1398747841&amp;amp;sr=8-1&amp;amp;keywords=the+calculus+lifesaver

I have mostly been using this as my main source of calculus lessons. You can find the corresponding lectures on youtube - the ones on his site do not work for whatever reason. The material is quite good, but still slightly challenging to ingest (though still much better than other courses out there!).

2. How to Ace Calculus: The Street-Wise Guide

When I first saw this book, I thought it was going to be dumb, but I've been finding it extremely helpful. This is the book I'm using to understand some of the concepts in Calculus that are taken for granted (but that I need explained more in detail). It actually is somewhat entertaining while doing an excellent job of teaching calculus.

The previous website I recommended to you is quite good at giving you an alternative perspective of calculus, but is not enough to actually teach you how to derive or integrate functions on your own. Hope your journey in math is going well!

u/maxximillian · 1 pointr/EngineeringStudents

These are the two things that saved my ass in calc 2:

this book, the calculus lifesaver
and this guy, Mr. McKeague from MathTV

Well the good news is that we have more resources available now than even 5 years ago. :) I'm in calc 1 right now, and was having trouble putting the pieces together into a whole that made sense. A few of my resources are classroom specific but many would be great for anyone not currently in a class.

Free:

free video lectures and practice problems on all manner of topics, starting with elementary algebra. You can start at the beginning and work your way through, or just start wherever.

http://ocw.mit.edu/index.htm

free online courses and lessons from MIT (!!) where you can watch lectures on a subject, do practice problems, etc. Use just for review or treat it like a course, it's up to you.

Cheap 

http://www.amazon.com/How-Ace-Calculus-Streetwise-Guide/dp/0716731606/ref=sr_1_1?ie=UTF8&amp;amp;qid=1331675661&amp;amp;sr=8-1

$10ish shipped for a book that translates calculus from math-professor to plain english, and is funny too. http://www.amazon.com/Calculus-Lifesaver-Tools-Excel-Princeton/dp/0691130884/ref=pd_cp_b_1$15 for a book that is 2-3x as thick as the previous one, a bit drier, but still very readable. And it covers Calc 1-3.

u/legogirl · 1 pointr/learnmath

This book and his videos: https://www.amazon.com/Calculus-Lifesaver-Tools-Princeton-Guides/dp/0691130884

I was good at calculus, but this book made anything I struggled to fully understand much easier. He does a good job of looking back at how previous work supports and and talks about how this relates to future topics.

u/jctapp · 1 pointr/learnmath

The best way to learn is take the class and find your deficiencies. Khan Academy is also great to get a base line of where you are. If you need help with calc. And precal, calculus lifesaver book is good.
lifesaver calculus amazon

u/Natsfan3754 · 1 pointr/learnmath

I don't, but I'm in the minority of the field. It definitely required a lot of catch-up in my first couple years. If you want to try and break in I can make some suggestions for self-teaching.

Linear Algebra is the backbone of all numerical modeling. I can make two suggestions to start with:

• I was very impressed with Jim Hefferon's book. It's part of an open courseware project so is available for free here (along with full solutions) but for $13 used I'd rather just have the book. • The Gilbert Strang course on MIT Open Courseware is very good as well. I didn't like his book as well, but the video lectures are excellent as supplemental material for when I had questions from Hefferon. As for the actual FEA/CFD implementations: • Numerical Heat Transfer and Fluid Flow ($22, used) seems to the standard reference for fluid flow. I'm relatively new to CFD so can't comment on it, but it seems to pop up constantly in any discussion of models or development.

• Finite Element Procedures, (\$28, used) and the associated Open Courseware site. The solid mechanics (FEA) is very well done, again, haven't looked much at the fluids side.

• 12 steps to Navier Stokes. If you're interested in Fluids, start here. It's an excellent introduction and you can have a basic 2D Navier Stokes solver implemented in 48 hours.

Note that none of these will actually teach you the the software side, but most commercial packages have very good tutorials available. These all teach the math behind what the solver is doing. You don't need to be an expert in it but should have a basic idea of what is going on.

Also, OpenFoam is a surprisingly good open source CFD package with a strong community. I'd try and use it to supplement your existing work if possible, which will give you experience and make future positions easier. Play with this while you're learning the theory, don't approach it as "read books for two years, then try and run a simulation".
u/roninsysop · 1 pointr/learnmath

I find Gilbert Strang's Introduction to Linear Algebra quite accessible, and seems to be aimed towards the practical (numerical) side of things. His video lectures are also quite good, IMHO.

u/ekg123 · 1 pointr/learnmath

&gt; To be honest, I do still think that step 2 is a bit suspect. The inverse of [;AA;]is [;(AA)^{-1};] . Saying that it's [;A^{-1}A^{-1};] seems to be skipping over something.

I realized how right you are when you say this after I reread the chapter on Inverse Matrices in my book. I am using Introduction to Linear Algebra by Gilbert Strang btw. I'm following his course on MIT OCW.

The book saids: If [;A;] and [;B;] are invertible then so is [;AB;]. The inverse of a product [;AB;] is [;(AB)^{-1}=B^{-1}A^{-1};].

So, before I went through with step two, I would have to have proved that [;A;] is indeed invertible.

&gt;Their proof is basically complete. You could add the step from A2B to (AA)B which is equivalent to A(AB) due to the associativity from matrix multiplication and then refer to the definition of invertibility to say that A(AB) = I means that AB is the inverse of A. So you can make it a bit more wordy (and perhaps more clear), but the basic ingredients are all there.

I will write up the new proof right here, in its entirety. Please let me know what you think and what I need to fix and/or add.

Theorem: if [;B;] is the inverse of [;A^2;], then [;AB;] is the inverse of A.

Proof: Assume [;B;] is the inverse of [;A^2;]

1. Since [;B;] is the inverse of [;A^2;], we can say that [;A^2B=I;]

2. We can write [;A^2B=I;] as [;(AA)B=I;]

3. We can rewrite [;(AA)B=I;] as [;A(AB)=I;] because of the associative property of matrix multiplication.

4. Therefore, by the definition of matrix invertibility, since [;A(AB)=I;], [;AB;]is indeed the inverse of [;A;].

Q.E.D.

Do I have to include anything about the proof being correct for a right-inverse and a left-inverse?

&gt; That's a great initiative! Probably means you're already ahead of the curve. Even if you get a step (arguably) wrong, you're still practicing with writing up proofs, which is good. Your write-up looks good to me, except for the questionability of step 2. In step 3 (and possibly others) you might also want to mention what you are doing exactly. You say "therefore", but it might be slightly clearer if you explicitly mention that you're using your assumption. You can also number everything (including the assumption), and then put "combining statement 0 and 2" to the right (where you can also go into a bit more detail: e.g. "using associativity of multiplication on statement 4").

I haven't began my studies at university yet, but I sure am glad that I exposed myself to proofs before taking an actual discrete math class. I think that very few people get exposed to proof writing in the U.S. public school system. I've completed all of the Khan Academy math courses, and the MIT OCW Math for CS course is still very difficult. I basically want to develop a very strong foundation in proof writing, and all the core courses I will take as a CS major now, and then I will hopefully have an easier time with my schoolwork once I begin in the fall. Hopefully this prior knowledge will keep my GPA high too. I really appreciate all the constructive criticism about my proof. I will try to make them as detailed as possible from now on.
u/GhostOfDonar · 1 pointr/math

I recommmend the math video lectures at the MIT [1]. Single variable calculus is 39 lectures at about 50 minutes each [2]. Go through the first ones and you'll have not only a refresher but also a head start. While you are about it, don't miss out Prof. Gilbert Strang's video lectures on Linear Algebra [3], that man is phenomenal (he teaches based on one of his own books [4].)

Resources:
1,
2,
3,
4.

u/ProceduralDeath · 1 pointr/mathbooks

Strang's book looks nice, and I noticed he has accompanying lectures which is good. I found this version, which is more or less in my price range but appears a bit outdated. https://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716

u/skytomorrownow · 1 pointr/compsci

I think for a rigorous treatment of linear algebra you'd want something like Strang's class book:

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716

For me, what was great about this book was that it approached linear algebra via practical applications, and those applications were more relevant to computer science than pure mathematics, or electrical engineering like you find in older books. It's more about modern applications of LA. It's great for after you've studied the topic at a basic level. It's a great synthesis of the material.

It's a little loose, so if you have some basic chops, it's fantastic.

u/BallsJunior · 1 pointr/learnmath

To piggy back off of danielsmw's answer...

&gt; Fourier analysis is used in pretty much every single branch of physics ever, seriously.

I would phrase this as, "partial differential equations (PDE) are used in pretty much every single branch of physics," and Fourier analysis helps solve and analyze PDEs. For instance, it explains how the heat equation works by damping higher frequencies more quickly than the lower frequencies in the temperature profile. In fact Fourier invented his techniques for exactly this reason. It also explains the uncertainty principle in quantum mechanics. I would say that the subject is most developed in this area (but maybe that's because I know most about this area). Any basic PDE book will describe how to use Fourier analysis to solve linear constant coefficient problems on the real line or an interval. In fact many calculus textbooks have a chapter on this topic. Or you could Google "fourier analysis PDE". An undergraduate level PDE course may use Strauss' textbook whereas for an introductory graduate course I used Folland's book which covers Sobolev spaces.

If you wanted to study Fourier analysis without applying it to PDEs, I would suggest Stein and Shakarchi or Grafakos' two volume set. Stein's book is approachable, though you may want to read his real analysis text simultaneously. The second book is more heavy-duty. Stein shows a lot of the connections to complex analysis, i.e. the Paley-Wiener theorems.

A field not covered by danielsmw is that of electrical engineering/signal processing. Whereas in PDEs we're attempting to solve an equation using Fourier analysis, here the focus is on modifying a signal. Think about the equalizer on a stereo. How does your computer take the stream of numbers representing the sound and remove or dampen high frequencies? Digital signal processing tells us how to decompose the sound using Fourier analysis, modify the frequencies and re-synthesize the result. These techniques can be applied to images or, with a change of perspective, can be used in data analysis. We're on a computer so we want to do things quickly which leads to the Fast Fourier Transform. You can understand this topic without knowing any calculus/analysis but simply through linear algebra. You can find an approachable treatment in Strang's textbook.

If you know some abstract algebra, topology and analysis, you can study Pontryagin duality as danielsmw notes. Sometimes this field is called abstract harmonic analysis, where the word abstract means we're no longer discussing the real line or an interval but any locally compact abelian group. An introductory reference here would be Katznelson. If you drop the word abelian, this leads to representation theory. To understand this, you really need to learn your abstract/linear algebra.

u/dp01n0m1903 · 1 pointr/math

Yes, -5/9 is a typo, just as you say.

By the way, the lecturer in the MIT video is Gilbert Strang, and his textbook, Introduction to Linear Algebra is the text that he uses for the course. I'm not really familiar with that book, but I believe that it has a pretty good reputation. See for example, this recent reddit thread, where Strang is mentioned several times.

u/crowsmen · 1 pointr/learnmath

&gt; don't think that there is a logical progression to approaching mathematics

Well, this might be true of the field as a whole, but def not true when it comes to learning basic undergrad level math after calc 1, as the OP asked about. There are optimized paths to gaining mathematical maturity and sufficient background knowledge to read papers and more advanced texts.

&gt; Go to the mathematics section of a library, yank any book off the shelf, and go to town.

I would definitely NOT do this, unless you have a lot of time to kill. I would, based on recommendations, pick good texts on linear algebra and differential equations and focus on those. I mean focus because it is easy in mathematics to gloss over difficulties.

My recommendation, since you are self-studying, is to pick up Gil Strang's linear algebra book (go for an older edition) and look up his video lectures on linear algebra. That's a solid place to start. I'd say that course could be done, with hard work, in a summer. For a differential equations book, I'm not exactly sure. I would seek out something with some solid applications in it, like maybe this: http://amzn.com/0387978941

That is more than a summer's worth of work.

Sorry, agelobear, to be such a contrarian.

u/josquindesprez · 1 pointr/statistics

If you want an extremely practical book to complement BDA3, try Statistical Rethinking.

It's got some of the clearest writing I've seen in a stats book, and there are some good R and STAN code examples.

u/lickorish_twist · 1 pointr/learnmath

This may be good for example:
http://www.amazon.com/The-Humongous-Book-Algebra-Problems/dp/1592577229/ref=pd_sim_b_5?ie=UTF8&amp;amp;refRID=0H1GD8HDQZB58PWTY0F5
You could take a look and see if it suits you.

But don't trust me on this. Others on /r/learnmath or /r/matheducation may be more knowledgeable than me about good algebra workbooks.

u/GOD_Over_Djinn · 1 pointr/math

I'm late to this party, but as a lot of other people have said, missing a negative sign somewhere is not an indication that you're bad at math. What is important in math is understanding why things are the way that they are. If you can look at the spot where you missed a negative sign and understand exactly why there should have been a negative sign there then you're doing fine. Being good at math isn't so much about performing the calculations—I mean, computers can find the roots of a quadratic function polynomial pretty reliably, so probably no one's going to hire you to do that by hand—but it's following the chain of reasoning that takes you from problem to solution and understanding it completely.

That said, there are things you can do to make yourself better at performing the calculations. Go back to basics, and I mean wayyyy back to like grade 5. A lot of students are seriously lacking skills that they should have mastered in around grade 5, and that will really screw up your ability to do algebra well. For instance, know your times tables. Know, and I mean really know and understand, how arithmetic involving fractions works: how and why and when do we put two fractions over a common denominator, what does it mean to multiply and divide by a fraction, and so on. It's elementary stuff but if you can't do it with numbers then you'll have an even harder time doing it with x's and y's. Make sure you understand the rules of exponents: Do you know how to simplify (a^(2)b^(3))^(2)? How about (a^(3)b)/(ab^(5)) How about √(3^(4))? What does it mean to raise a number to a negative power? What about a fractional power? These things need to be drilled into you so that you don't even think twice about them, and the only way to make it that way is to go through some examples really carefully and then do as many problems as you can. Try to prove the things to yourself: why do exponents behave the way that they do? Go out and get yourself something like this and just work through it and make sure you understand exactly why everything is the way that it is.

Feel free to PM me if you are stuck on specific stuff.

u/senseofdecay · 1 pointr/math

this is one of the best for self teaching. the examples are very clear so you don't get tripped up on them jumping steps. You will need to get more problems from somewhere like a more formal textbook, but this will help you get the idea of what to do instead of fuming at an impasse.

http://www.amazon.com/The-Humongous-Book-Calculus-Problems/dp/1592575129

there's also trig and precalc versions if he needs the review.

http://www.amazon.com/The-Humongous-Book-Algebra-Problems/dp/1592577229/ref=pd_bxgy_b_text_z

http://www.amazon.com/The-Humongous-Book-Trigonometry-Problems/dp/1615641823/ref=pd_bxgy_b_text_y

u/bryanrabbit · 1 pointr/learnmath

It's a lot of work but with this book I lost my math anxiety and actually started to enjoy math. The author's philosophy is the only way to get better at algebra is to just do a lot of algebra, it starts out with the most basic fundamentals you need to know too, like if you have trouble with negative numbers or fractions (as I did). It's possible you just need a recap on the foundational stuff you forgot in grade school + more practice. By the end of the book you'll be working with functions and logarithms and you'll understand it.

Try this.

But really it comes with practice, the more you use it, the better you get at reading it and comfortable with it. In my case at least.

u/INTEGRVL · 0 pointsr/matheducation

Introduction to Linear Algebra by Serge Lang.

http://www.amazon.com/Introduction-Linear-Algebra-Serge-Lang/dp/3540780602

Or Introduction to Linear Algebra by Gilbert Strang

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edition/dp/0980232716

I have not used the Strang book, but I here it is all right for non-mathematicians.