(Part 2) 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 products ranked 21-40. You can also go back to the previous section.
26. Introduction to Probability (Chapman & Hall/CRC Texts in Statistical Science)
9 mentions
CRC Press
As of today, these books sell for:
At $274, this is probably the most expensive tofu presser I've ever seen.
When Trump supporters say this, they might as well wear a neon sign that says "I lack a 5th grade education in probability and statistics!"
Read this, if you can:
https://www.amazon.com/Probability-Dummies-Deborah-J-Rumsey/dp/0471751413
Yes. This is a classic question and the typical answer is
f(x) = x^2 sin(1/x) if x != 0
f(x) = 0 if x = 0
The proof that f is continuous, and f' exists but is not continuous is left as an exercise for the reader. :-)
The book Counterexamples in Analysis has this and more. Having this book handy will do wonders for you and your class and I highly recommend it. Thank god Dover got hold of the copyright and re-printed it, it is a great book and the original is hard to find.
I'm usually pretty optimistic for people when it comes to posts asking about "how do I get started in sabermetrics" because I was in that position once as well, and it's worked out okay for me, but I want to be a bit more realistic, because I think there is a big red flag that you should recognize in yourself in respect to this.
There are a couple ways to get jobs in fields that require sabermetrics, but you should be aware: there are very few, they are highly competitive, and they require a good amount of work.
The traditional progression for doing sabermetric work is usually something like:
Stage|Level of Sabermetric Experience|Work you're qualified to do|
--:|:--|:--|
1|You look up stats online to form arguments about baseball|Personal blogging, entry-level analytics writing (FanSided, SBN, other sites)|
2|You put stats into a spreadsheet to visualize data or calculate something new to form an argument about baseball|Personal blogging, entry-level analytics writing (FanSided, SBN, other sites), heavier stuff if you're very lucky and a good writer (bigger sites like FanGraphs, Baseball Prospectus), general baseball coverage that isn’t heavily analytical|
3|You use code with baseball stats to visualize data or calculate something new to form an argument about baseball|Heavier analytics writing (SBN, FanGraphs, Baseball Prospectus, The Athletic), entry-level baseball operations work|
4|You use code to create your own models, predictions, and projections about baseball.|Extremely heavy analytics writing, baseball operations/team analytics work|
From your post, it sounds like you're somewhere between #1 and #2 right now. However: "after trying [coding] out I did not like it." You have a very large barrier keeping you from making the jump to stage 3.
If you actually want to go into a sabermetric field as a career, you need to know how to code. Not with Javascript, mind you, but other languages (Python, R, SQL, etc.). I would advise that you try out Python or R (Analyzing Baseball Data with R is an excellent introduction and gives you a lot of practical skills) and see if those really suck you in - and believe me, they need to suck you in. If you really don't like it, don't force yourself to do it and find some other career path, because you won't be able to succeed if you can't enjoy the work that you do.
FanSided has very low barriers of entry and the compensation reflects that - you cannot make a career out of blogging for FanSided. Even if you get to where I am (stage 4), if you're lucky, you might land a contributing position at a site that pays decently for part-time work. There are extremely few people who are somewhere between #3 and #4 who can make a full-time living off of baseball work, and they do it because they like what they do - if you don't like coding and working with baseball data in that environment, you're not going to be able to beat out everybody else who's trying to get there.
Let's say that you work your rear end off, you get to stage three or stage four. What options are available to you? There's maybe a handful of people who work in the "public" sector - that is, writing for websites like FanGraphs, Baseball Prospectus, The Athletic - who make enough money to make sabermetrics their full-time job. It will take a hail fucking mary to land one of those jobs, regardless of how talented you are, and you'll basically need to work double-duty on both sabermetrics and whatever your main hustle is until one of those positions opens up, and even then, you're not guaranteed anything.
You could also work for a team! There are far more positions available, they pay better, you have more data to work with, better job security - this sounds great, right? Problem is, the market cap for analysts are at about 20 per team, so there's something like 600 analyst positions that could be available in the future (I can't promise that the MLB will ever have 600 analysts total at any given time, but that's an upper estimate). And almost half of those are already full! There's not a whole lot of brain drain from the industry, so it is still extremely hard to break in and you're still going to be competing with the absolute best people in the industry. You will have to love to code and do this work because everybody you're competing with already does, and everybody else is willing to work twice as hard for it.
My advice to you is this: try out R or Python with baseball data. See if it's enough to get you addicted. See if it starts to occupy every ounce of free time you have, and you feel comfortable with it, and you're willing to put yourself out there and advertise your own work. I'm a full time student and basically every ounce of my free time is put towards working with this stuff, like it's a second full-time job for the past three years, and I'm still a bit of a ways away from making a living off of this. If you can't learn to love it, your time and energy are best spent elsewhere.
The CRC Standard Mathematical Tables book was my bible in engineering, back before graphing calculators were a thing.
https://www.amazon.com/Standard-Mathematical-Formulae-Advances-Mathematics/dp/1439835489
I ended up with 2 copies, one in my car, one at home. Another good reference to have
There are definitely ways to visualize algebraic concepts and many algebraic concepts crop up in geometry. Unfortunately, many books and classes won't emphasize visual intuition. So algebra may be harder for you. In some ways, you get over it even if it isn't your cup of tea, but there are also resources for transfering visual/geometric intuition onto algebraic concepts.
After reading it for myself, I recommend the books visual group theory by Nathan Carter, and algebra, concrete and abstract by Frederick Goodman. The first focuses a lot on visual intuition for group theory, but a lot concepts in group theory generalize to abstract algebra in general. The second book is a more traditional book, less focus on visual intuition, uses symmetry of geometrical objects and linear algebra for many of the examples.
Analyzing Baseball with R is the best book, I believe:
https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229
I also would download PitchRX and Baseball on a Stick to round out your toolkit!
-Kyle
I highly recommend you read the relevant chapters of Nathan Carter’s book Visual Group Theory (site, amzn).
i have three categories of suggestions.
advanced calculus
these are essentially precursors to smooth manifold theory. you mention you have had calculus 3, but this is likely the modern multivariate calculus course.
out of these, if you were to choose one, i think the callahan book is probably your best bet to pull from. it is the most modern, in both approach and notation. it is a perfect setup for smooth manifolds (however, all of these books fit that bill). hubbard's book is very similar, but i don't particularly like its notation. however, it has some unique features and does attempt to unify the concepts, which is a nice approach. edwards book is just fantastic, albeit a bit nonstandard. at a minimum, i recommend reading the first three chapters and then the latter chapters and appendices, in particular chapter 8 on applications. the first three chapters cover the core material, where chapters 4-6 then go on to solidify the concepts presented in the first three chapters a bit more rigorously.
smooth manifolds
out of these books, i only have explicit experience with the first two. i learned the material in graduate school from john m. lee's book, which i later solidifed by reading tu's book. tu's book actually covers the same core material as lee's book, but what makes it more approachable is that it doesn't emphasize, and thus doesn't require a lot of background in, the topological aspects of manifolds. it also does a better job of showing examples and techniques, and is better written in general than john m. lee's book. although, john m. lee's book is rather good.
so out of these, i would no doubt choose tu's book. i mention the latter two only to mention them because i know about them. i don't have any experience with them.
conceptual books
these books should be helpful as side notes to this material.
i highly recommend all of these because they're all rather short and easy reads. the first two get at the visual concepts and intuition behind vectors, covectors, etc. they are actually the only two out of all of these books (if i remember right) that even talk about and mention twisted forms.
there are also a ton of books for physicists, applied differential geometry by william burke, gauge fields, knots and gravity by john baez and javier muniain (despite its title, it's very approachable), variational principles of mechanics by cornelius lanczos, etc. that would all help with understanding the intuition and applications of this material.
conclusion
if you're really wanting to get right to the smooth manifolds material, i would start with tu's book and then supplement as needed from the callahan and hubbard books to pick up things like the implicit and inverse function theorems. i highly recommend reading edwards' book regardless. if you're long-gaming it, then i'd probably start with callahan's book, then move to tu's book, all the while reading edwards' book. :)
i have been out of graduate school for a few years now, leaving before finishing my ph.d. i am actually going back through callahan's book (didn't know about it at the time and/or it wasn't released) for fun and its solid expositions and approach. edwards' book remains one of my favorite books (not just math) to just pick up and read.
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&qid=1510402907&sr=8-2&keywords=bayesian+statistics
https://www.amazon.com/Bayes-Rule-Tutorial-Introduction-Bayesian/dp/0956372848/ref=sr_1_6?ie=UTF8&qid=1510402907&sr=8-6&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&qid=1510402907&sr=8-1&keywords=bayesian+statistics
https://www.amazon.com/Introduction-Probability-Chapman-Statistical-Science/dp/1466575573/ref=sr_1_12?s=books&ie=UTF8&qid=1510403749&sr=1-12&keywords=probability
/u/another_user_name posted this list a while back. Actual aerospace textbooks are towards the bottom but you'll need a working knowledge of the prereqs first.
Non-core/Pre-reqs:
Mathematics:
Calculus.
1-4) Calculus, Stewart -- This is a very common book and I felt it was ok, but there's mixed opinions about it. Try to get a cheap, used copy.
1-4) Calculus, A New Horizon, Anton -- This is highly valued by many people, but I haven't read it.
1-4) Essential Calculus With Applications, Silverman -- Dover book.
More discussion in this reddit thread.
Linear Algebra
3) Linear Algebra and Its Applications,Lay -- I had this one in school. I think it was decent.
3) Linear Algebra, Shilov -- Dover book.
Differential Equations
4) An Introduction to Ordinary Differential Equations, Coddington -- Dover book, highly reviewed on Amazon.
G) Partial Differential Equations, Evans
G) Partial Differential Equations For Scientists and Engineers, Farlow
More discussion here.
Numerical Analysis
5) Numerical Analysis, Burden and Faires
Chemistry:
Physics:
2-4) Physics, Cutnel -- This was highly recommended, but I've not read it.
Programming:
Introductory Programming
Programming is becoming unavoidable as an engineering skill. I think Python is a strong introductory language that's got a lot of uses in industry.
Core Curriculum:
Introduction:
Aerodynamics:
Thermodynamics, Heat transfer and Propulsion:
Flight Mechanics, Stability and Control
5+) Flight Stability and Automatic Control, Nelson
5+)[Performance, Stability, Dynamics, and Control of Airplanes, Second Edition](http://www.amazon.com/Performance-Stability-Dynamics-Airplanes-Education/dp/1563475839/ref=sr_1_1?ie=UTF8&qid=1315534435&sr=8-1, Pamadi) -- I gather this is better than Nelson
Engineering Mechanics and Structures:
3-4) Engineering Mechanics: Statics and Dynamics, Hibbeler
6-8) Analysis and Design of Flight Vehicle Structures, Bruhn -- A good reference, never really used it as a text.
G) Introduction to the Mechanics of a Continuous Medium, Malvern
G) Fracture Mechanics, Anderson
G) Mechanics of Composite Materials, Jones
Electrical Engineering
Design and Optimization
Space Systems
Ordinary Differential Equations and Dynamical Systems by Gerald Teschl is a really good intro to ODE theory on the first-year graduate level. It also has the benefit of being freely available online. At the undergrad level, I haven't used this book personally but Differential Equations, Dynamical Systems, & and Introduction to Chaos by Hirsch, Smale, and Devaney seems to be a common choice.
For PDE, there are lots of standard texts that don't take the "toolbox" approach: at the undergrad level you have Walter Strauss, and at the begininning graduate level you've got Evans and Folland. For a slightly more advanced treatment, I like John Hunter's PDE notes, also free online.
Prerequisites: you should have a firm grasp of introductory analysis, say at the level of Baby Rudin, before diving into either of these subjects. You should also know your undergraduate linear algebra well.
CLRS for algorithms/CS.
Probability and random processes for statistics.
Biological Sequence Analysis by Richard Durbin for my subfield of bioinformatics.
Counterexamples in Analysis is a wonderful menagerie of mathematical oddities—it's full of pathological examples. It's the most fun math book I know of.
You mean the CRC Math Handbook?
https://www.amazon.com/Standard-Mathematical-Formulae-Advances-Mathematics/dp/1439835489
I got one in high school. Loved it!
Lee is still the easiest and best for self study. https://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1441979395/ref=sr_1_3?keywords=lee+manifolds&qid=1558265795&s=gateway&sr=8-3
followed by:
https://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/1441999817/ref=sr_1_2?keywords=lee+manifolds&qid=1558265795&s=gateway&sr=8-2
​
It's long, taking almost two volumes to get to Stokes theorem. If conciseness is important, you can just read Warner:
https://www.amazon.com/Foundations-Differentiable-Manifolds-Graduate-Mathematics/dp/0387908943/ref=sr_1_1?keywords=Warner+manifolds&qid=1558265966&s=gateway&sr=8-1
​
Tu looks good, but I haven't read it carefully.
I suggest you read John Kruschke's Doing Bayesian Data Analysis: http://www.amazon.com/Doing-Bayesian-Data-Analysis-Second/dp/0124058884
It's a very approachable read. I myself have very little math background, but you will learn all you need. It is a large book though.
Analyzing Baseball Data with R
https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229
​
Walks you through learning the program using baseball stats as the foundation.
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.
http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753 click to look inside.
Your professors really aren't expecting you to reinvent groundbreaking proofs from scratch, given some basic axioms. It's much more likely that you're missing "hints" - exercises often build off previous proofs done in class, for example.
I appreciated Laura Alcock's writings on this, in helping me overcome my fear of studying math in general:
https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/
https://www.amazon.com/dp/0198723539/ <-- even though you aren't in analysis, the way she writes about approaching math classes in general is helpful
If you really do struggle with the mechanics of proof, you should take some time to harden that skill on its own. I found this to be filled with helpful and gentle exercises, with answers: https://www.amazon.com/dp/0989472108/ref=rdr_ext_sb_ti_sims_2
And one more idea is that it can't hurt for you to supplement what you're learning in class with a more intuitive, chatty text. This book is filled with colorful examples that may help your leap into more abstract territory: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X
I don't have any good book recommendations for mechanical skills. I have a number of specialized ones but nothing really generic that I would recommend.
Anti-disclaimer: I do have personal experience with all the below books.
I really enjoyed Lee for Riemannian geometry, which is highly related to the Lorentzian geometry of GR. I've also heard good things about Do Carmo.
It might be advantageous to look at differential topology before differential geometry (though for your goal, it is probably not necessary). I really really liked Guillemin and Pollack. Another book by Lee is also very good.
If you really want to dig into the fundamentals, it might be worthwhile to look at a topology textbook too. Munkres is the standard. I also enjoyed Gamelin and Greene, a Dover book (cheap!). I though that the introduction to the topology of R^n in the beginning of Bartle was good to have gone through first.
I'm concerned that I don't see linear algebra in your course list. There's a saying "Linear algebra is what separates Mathematicians from everyone else" or something like that. Differential geometry is, in large part, about tensor fields on manifolds, and these are studied by looking at them as elements of a vector space, so I'd say that linear algebra is something you should get comfortable with before proceeding. (It's also great to study it before taking quantum.) I can't really recommend a great book from personal experience here; I learned from poor ones :( .
Also, there are physics GR books that contain semi-rigorous introductions to differential geometry, even if these sections are skipped over in the actual class. Carroll is such a book. If you read the introductory chapter and appendices, you'll know a lot. On the differential topology side of things, there's Schutz, which is a great book for breadth but is pretty material dense. Schwarz and Schwarz is a really good higher level intro to special relativity that introduces the mathematical machinery of GR, but sticks to flat spaces.
Finally, once you have reached the mountain top, there's Hawking and Ellis, the ultimate pinnacle of gravity textbooks. This one doesn't really fall under the anti-disclaimer from above; it sits on my shelf to impress people.
https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229
This book covers everything related to how to get the data (Retrosheet, Lahman's, pitchf/x IIRC) and then how to do a lot of different stuff with R. It's a good place to start. You could probably find it cheaper than that Amazon link though.
I'm going to guess this one based on high reviews and a description that mentions R.
If you have problems with probability take the MITx probability class on edX. That is as good as it can get as a EECS probability class. It teaches you tons of stuff but assumes nothing but multivariable calculus from you. If you have time, read Introduction to Probability by the class instructors.
Note the class alone is a huge time sink.
>what can I show her so she can be properly informed?
this
EDIT: or a bunch of leftist professors discussing it
http://freakonomics.com/2016/01/07/the-true-story-of-the-gender-pay-gap-a-new-freakonomics-radio-podcast/
> Probability states that either major party candidate had a 50% chance of winning (since there are two running,
Wow. Really? So all of probability theory is wrong then.
I recommend this book:
https://www.amazon.ca/Probability-Dummies-Deborah-J-Rumsey/dp/0471751413
This depends on your current level of knowledge and experience, generally you would start with multiple choice problems and then move on to International Maths Olympiad (IMO) type problems that require written solutions.
Most competitors at the IMO go through training and selection programs to make their national team. Many of the countries running these programs publish their material, for example South Africa : http://www.mth.uct.ac.za/imo/imopub.html.
Another great resource is http://www.artofproblemsolving.com/.
There are a lot of books as well, a small sample :
http://books.google.co.za/books/about/In_P%C3%B3lya_s_Footsteps.html?id=Z3p_MToD32MC&amp;redir_esc=y
http://www.amazon.com/Mathematical-Olympiad-Handbook-Introduction-Publications/dp/0198501056/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1375034070&amp;sr=1-1&amp;keywords=lets+solve+some+math+problems
http://www.amazon.com/Erd%25f6s-Kiev-Problems-Mathematical-Expositions/dp/0883853248/ref=sr_1_2?s=books&amp;ie=UTF8&amp;qid=1375033538&amp;sr=1-2
http://www.amazon.com/dp/0883856190
Our site www.examify.net will email you multiple choice 'math competition' papers that the site will mark and send you worked solutions, most of the content is at a very introductory level at the moment.
Get a copy (or as you're at university might as well take it out of the library on long loan if they've got it) of Engineering Mathematics by K.A Stroud. Amazon link
I found it really helpful in the 1st + 2nd year for the basics, non patronising and it doesn't assume much, if any, prior maths knowledge.
In all seriousness, the applications of analysis to geometry can be really interesting and insightful, but to get to them you would have to first have background in differential topology, which it seems you lack. That might be a good subject to start with. A good book would be John Lee's An Introduction to Smooth Manifolds.
A very user-friendly treatment that hits every criterion you mention is John Kruschke's Doing Bayesian Data Analysis, Second Edition.
Unfortunately for you, 251 learning is mostly from lecture and recitation lessons, for which there is not an official textbook (student informally use the Concepts of Mathematics Textbook, which is quite decent).
This is the public course website: https://colormygraph.ugrad.cs.cmu.edu/15251-s12/
Course materials are located in the calendar tab and many of them are public.
You will have a tough time learning anything of consequence without something like videos of the lectures, etc. (Which even students don't have access to)
These were the most enlightening for me on their subjects:
There is an excellent series of Counterexamples in ... books which might be relevant to this thread:
counterexamples in...
Or just run a search on amazon for "Counterexamples in".
If you weren't satisfied with geometry in your school, then I can suggest this wonderful text: http://www.amazon.com/gp/product/0883856190/
Lewin's book is... interesting. It's a rare kind of music theory book which involves some actual math (with absolutely abhorrent typesetting). But it's actually quite straightforward if you know some basic group theory.
So I recommend to take a look at Visual Group Theory lectures on youtube: https://www.youtube.com/watch?v=UwTQdOop-nU&amp;list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv. By the way, there's also a book with the same name.
https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X
I'm not much of a visual person so I didn't learn much from skimming it, but many people stand by it and it's a beautiful exposition (of a topic I also think is beautiful) indeed!
Hi there,
For all intents and purposes, for someone your level the following will be enough material to stick your teeth into for a while.
Mathematics: Its Content, Methods and Meaning https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163
This is a monster book written by Kolmogorov, a famous probabilist and educator in maths. It will take you from very basic maths all the way to Topology, Analysis and Group Theory. It is however intended as an overview rather than an exhaustive textbook on all of the theorems, proofs and definitions you need to get to higher math.
For relearning foundations so that they're super strong I can only recommend:
Engineering Mathematics
https://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1403942463
Engineering Mathematics is full of problems and each one is explained in detail. For getting your foundational, mechanical tools perfect, I'd recommend doing every problem in this book.
For low level problem solving I'd recommend going through the ENTIRE Art of Problem Solving curriculum (starting from Prealgebra).
https://www.artofproblemsolving.com/store/list/aops-curriculum
You might learn a thing or two about thinking about mathematical objects in new ways (as an example. When Prealgebra teaches you to think about inverses it forces you to consider 1/x as an object in its own right rather than 1 divided by x and to prove things. Same thing with -x. This was eye opening for me when I was making the transition from mechanical to more proof based maths.)
If you just want to know about what's going on in higher math then you can make do with:
The Princeton Companion to Mathematics
https://www.amazon.co.uk/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809
I've never read it but as far as I understand it's a wonderful book that cherry picks the coolest ideas from higher maths and presents them in a readable form. May require some base level of math to understand
EDIT: Further down the Napkin Project by Evan Chen was recommended by /u/banksyb00mb00m (http://www.mit.edu/~evanchen/napkin.html) which I think is awesome (it is an introduction to lots of areas of advanced maths for International Mathematics Olympiad competitors or just High School kids that are really interested in maths) but should really be approached post getting a strong foundation.
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.
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;psc=1&amp;refRID=58357AYY9N1EZRG0WAMY) also seems to be another beginner friendly book.
No the drop isn't broken. Here, this should help.
I've got just the thing for you. The Shape of Space by Weeks.
https://www.amazon.com/Shape-Space-Chapman-Applied-Mathematics/dp/0824707095
Have you ever realized that the Asteroids gaming screen is actually the surface of a torus? You go left and you come back from right, you go down and you come back from the top. What would happen if WE lived in such universe? You could tap on your own shoulder (if you can stretch your arm enough).
Consider a sphere (like the surface of the Earth) and start drawing larger and larger circles with center at the north pole. As the radius gets bigger, so does the area and circumference. But once you pass the equator, the circumference will actually start getting smaller while the area will continue to grow larger. Can you imagine the 3D analogy? It would mean that inside the Earth could be another planet (or realm) which is actually larger than our planet. This is how Dante pictured his inferno.
The book is about this kind of stuff. The actual mathematics (differential geometry and differential topology) goes WAY beyond linear algebra, but the book is readable for anyone with enough imagination.
> I'm hoping for something like what Div, Grad, Curl and All That does for Vector Calculus.
Is that a math text? I am not really familiar with it, but from what I heard it sounds more like a physics/engineering text. Does it have any formal proofs in it?
You won't be able to get too far with a proofless(?) Abstract Algebra text if there exists one to begin with. Even Charles Pinter's A Book of Abstract Algebra presupposes some degree of mathematical maturity.
Anyway, try these and see if you like them:
Visual Group Theory by Nathan Carter
Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem by Al Cuoco, Joseph J. Rotman
I’d recommend Blitzstein’s Into to Probability book- it’s the book used for Harvard’s Stat110 which has free lectures online as well.
https://www.amazon.com/Introduction-Probability-Chapman-Statistical-Science/dp/1466575573
This is a fan favorite if you can read proofs, but i can't personally testify to it: https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X
This seems to be lecture notes corresponding to the book: https://www.google.com/url?sa=t&amp;source=web&amp;rct=j&amp;url=http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf&amp;ved=0ahUKEwi0tPaYhfXVAhVJro8KHQVuB9sQFghnMAo&amp;usg=AFQjCNHg2bvy0qIa4qilsIT9qVtC3xX8VQ
Also, this StackOverflow answer to your question is highly-rated: https://math.stackexchange.com/q/31838/200344
Shankar's book teaches almost everything you need: calculus, vectors, series, complex variables, ODE, linear algebra in only ~300pag.
http://www.amazon.com/Basic-Training-Mathematics-Fitness-Students/dp/0306450364
For more advanced topics check out Arfken.
Both JAGS and BUGS use the same language and can perform very similar operations. JAGS is more portable across operating systems, so for that reason, I would suggest JAGS (BUGS is generally limited to Windows). However, documentation/blog posts/forum posts (which exist in abundance!) for both languages will generally work for either tool. If you are looking for a textbook, Doing Bayesian Data Analysis provides a nice introduction to both bayesian statistics as well as JAGS.
Outside of JAGS/BUGS, there exists another similar language for performing Bayesian statistics called Stan (also described in the above book). Stan is newer, and often times will "run faster" than JAGS, however it does not directly support as many types of analyses.
My advice would be to learn JAGS while simultaneously learning the basics of Bayesian methods. Once you understand the basics of JAGS, try exploring Stan!
For proofs in general, I like D'Angelo and West's Mathematical Thinking. http://www.amazon.com/Mathematical-Thinking-Problem-Solving-Proofs-Edition/dp/0130144126
For discrete math, especially combinatorics, I loved Miklos Bona's A Walk Through Combinatorics. http://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9814335231/
For induction proofs, you check your base case, assume the induction hypothesis (true for k), and then check k+1.
You should be able to manipulate the k+1 term into something involving the k term, and that will then lead to the k+1 conclusion.
Example For all n >= 4, 2^(n) < n!
Base case: n = 4. 2^(4) = 16 < 24 = 4!
IH: Assume true for some k >= 4.
Then 2^(k+1) = 2*2^(k)
2*2^(k) < 2*k! (Induction Hypothesis used here)
2*k! < (k+1)k! (k > 3, so k+1 > 2)
(k+1)k! = (k+1)! (definition of factorial)
Uhm. Do you mean this one?
https://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198572220
At the elementary level, Braun is good.
At the intermediate level, Arnold is the best.
You're question is kind of vague, i.e. there are a lot of way's to interpret 'the basics'. Do you mean addition/substraction, etc. or possibly the content of a calculus or linear algebra course? If it's the latter (i.e. the basics of integration, ODE's, PDE's, vectorspaces, ...) I would suggest picking up a mathematics for engineers kind of book ( http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364/ref=sr_1_4?ie=UTF8&amp;qid=1406991103&amp;sr=8-4&amp;keywords=engineering+mathematics or something). Those will have loads of excercises, and mainly go on about intuition instead of proofs (again it could be that by basics you also mean the proofs of basic theorems etc. ...).
This is an applied field. The books above wont help you. In fact they will do the exact opposite. I assume your math education probably stopped at the differential equations. I would recommend as refresher to start building from calculus (avoid the ones in the picture, try something from your past, it would go faster) then go directly to an engineering focused math book like this book If this transition is too sharp you can try other more basic engineering math books. These books are more focused on what works for practicing engineers but you need a strong foundation in Calculus.
For signal processing, I highly recommend a tiny book on Fourier Transformation. Antenna theory is difficult since it varies depends on what level your school covers it at, like device or EM theory or even operational. Anyway start with Calculus and avoid all the books in the picture. Read them for fun but not for study.
I dove into this stuff almost two years ago with very little preparation or background. Now I'm in an MS program for Applied Statistics, and doing quite well. Here are some tips that worked for me:
Good luck.
They are probably a bit advanced but should at least help you understand something about those fancy numbers.
https://www.amazon.com/Probability-Dummies-Deborah-J-Rumsey/dp/0471751413
https://www.amazon.com/Statistics-Dummies-Lifestyle-Deborah-Rumsey/dp/1119293529
I wouldn't call it a "branch" exactly, but pathological functions are pretty much the definition of "weird." Things like Weierstrass functions, the Cantor function, the Conway base 13 function. There's a good book with a lot of this stuff in it called Counterexamples in Analysis. There's another one on topology I haven't read yet.
Here are some suggestions :
https://www.coursera.org/course/maththink
https://www.coursera.org/course/intrologic
Also, this is a great book :
http://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X/ref=sr_1_5?ie=UTF8&amp;qid=1346855198&amp;sr=8-5&amp;keywords=history+of+mathematics
It covers everything from number theory to calculus in sort of brief sections, and not just the history. Its pretty accessible from what I've read of it so far.
EDIT : I read what you are taking and my recommendations are a bit lower level for you probably. The history of math book is still pretty good, as it gives you an idea what people were thinking when they discovered/invented certain things.
For you, I would suggest :
http://www.amazon.com/Principles-Mathematical-Analysis-Third-Edition/dp/007054235X/ref=sr_1_1?ie=UTF8&amp;qid=1346860077&amp;sr=8-1&amp;keywords=rudin
http://www.amazon.com/Invitation-Linear-Operators-Matrices-Bounded/dp/0415267994/ref=sr_1_4?ie=UTF8&amp;qid=1346860052&amp;sr=8-4&amp;keywords=from+matrix+to+bounded+linear+operators
http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753/ref=sr_1_5?ie=UTF8&amp;qid=1346860077&amp;sr=8-5&amp;keywords=rudin
http://www.amazon.com/DIV-Grad-Curl-All-That/dp/0393969975
http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536/ref=sr_1_2?s=books&amp;ie=UTF8&amp;qid=1346860356&amp;sr=1-2&amp;keywords=chaos+and+dynamics
http://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0534392008/ref=sr_1_5?s=books&amp;ie=UTF8&amp;qid=1346860179&amp;sr=1-5&amp;keywords=numerical+analysis
This is from my background. I don't have a strong grasp of topology and haven't done much with abstract algebra (or algebraic _____) so I would probably recommend listening to someone else there. My background is mostly in graduate numerical analysis / functional analysis. The Furata book is expensive, but a worthy read to bridge the link between linear algebra and functional analysis. You may want to read a real analysis book first however.
One thing to note is that topology is used in some real analysis proofs. After going through a real analysis book you may also want to read some measure theory, but I don't have an excellent recommendation there as the books I've used were all hard to understand for me.
In order to understand the modern approach to PDEs in full generality you must have a minimum background of ODEs, basic topology, complex analysis, and basic differential geometry.
Many of the foundational theorems for these fields are directly applicable to the study of PDEs and it would be fruitless to try to study PDEs in full generality without that basic understanding. That being said, Evans ( http://www.amazon.com/Partial-Differential-Equations-Graduate-Mathematics/dp/0821849743 ) is an excellent well-rounded introduction to the general theory.
If this is too difficult for you to tackle at the moment, you will need to work your way through the above topics first. PDEs, studied in full generality instead of in particular cases, is not a light topic.
If you're looking for the "bible" of PDE - Evans is typically considered the standard at the graduate level. For an undergraduate exposition of differential equations (ODE), then my professor liked to use Zill for ODE and Haberman for PDE.
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If you're a little more specific I might be able to direct you to better sources - hope you enjoy the above, I have them all and really like them.
Case 5 is definitely a Klein bottle. You will have to allow self-intersections for it, but that's no big deal.
Case 6 is some form of the real projective plane, although depending on how you construct that, you can make it have either one or two "sides".
You can read more about this and related topics in The Shape of Space by Jeffrey R. Weeks.
Mathematical Literature is a genre I don't think many people are aware of, I'm glad you're interested.
The Mathematical Experience is a great survey of mathematical ideas. This book toes the line perfectly - someone not knowledgable of advanced mathematics can follow easily yet the book does not dumb down complicated ideas. This is my top recommendation for anyone thinking about studying mathematics.
If you love geometry, then check out Geometry Revisited by H.S.M Coxeter. Coxeter is one of the greatest mathematicians of his time - he single handedly brought geometry back into vogue as a serious study.
Maybe for lighter reading, Ian Stewart has a bunch of good Mathematical survey books for the "layman" - I'd recommend if you have minimal mathematic knowledge.
There's a yearly collection of mathematical writings that you might like too. I've only bought and read the 2010 edition, but I assume the followups have been great. The essays collected vary from finance, game theory, geometry, social sciences, literature, etc. with connections to mathematics.
Hope you have a fun time with math, good luck!
FWIW I had no fun with mathematics in school and didn't start studying it til I was in my thirties. I'm no genius, but I now teach the subject and still self-study it. You don't need any mysterious talent to get very competent at university-level maths, just to be interested enough in it to put the hours in.
Self-study is hard and frustrating. Be prepared for that. Reading one page can take a day. You can stare at a definition or theorem for hours and not understand it. Looking things up in multiple books can really help with that -- there are some good resources online as well. Also, some things just take a while to "cook" in the brain; keep at it. Take lots and lots of notes, preferably with pictures. Do plenty of exercises. When you're really stumped, post here.
I'll echo what others have said: add to Spivak a couple of other books so you can change it up. A book on group theory and one on linear algebra would be a nice combination -- maybe one on discrete maths, probability or something similar as well if that interests you. For group theory I think this book is fantastic, though it's expensive.
If you really want to make it through Spivak, make a plan. Break the book down into, say, 50-page chunks and make 50 pages your target for each week (I have no idea whether this is too ambitious for you -- try it and see). Track your progress. Celebrate when you hit milestones.
Good luck!
[EDIT: Also, be aware that maths books aren't really designed to be read like novels. Skim a chapter first looking for the highlights and general ideas, then drill into some of the details. Skip things that seem difficult and see if they become important later, then go back (with more motivation) etc.]
http://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1403942463
Study what you find the most interesting!
Does your linear algebra include the spectral theorem or Jordan canonical form? IMHO, a pure math subject that is relatively the easiest to learn and is useful no matter what you do is linear algebra.
Group theory (representation theory) has also served me well so far.
If you want to learn GR and Hamiltonian mechanics in-depth, learning smooth manifolds would be a must. Smooth manifolds are basically spaces that locally look like Euclidean spaces and we can do calculus on. GR is on a pseudo-Riemannian manifold with changing metric (because of massive stuffs). Hamiltonian mechanics is on a cotangent bundle, which is a symplectic manifold (whereas Lagrangian mechanics is on a tangent bundle.) John Lee's book is a gentle starting point.
Edit: If you feel like the review of topology in the appendix is not enough, Lee also wrote a book on topological manifolds.
Here you go! It's very helpful and has a wide range of topics so you can learn whatever you want. It uses Retrosheet, Lahman and Pitch Fx
https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229/ref=sr_1_1?ie=UTF8&amp;qid=1494296330&amp;sr=8-1&amp;keywords=analyzing+baseball+data+with+r
Sure! I'll just assume knowledge of the more common stuff like OPS. I'll try to break it into learning resources v. interesting work to be read. Think my suggestions to OP might be structured a bit differently. I'll try to keep it moderately short.
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Learning
The Book: Playing the Percentages in Baseball set the foundation for a lot of stuff seen today. Win expectancy, lineup optimization, "clutch" hitting, matchups, etc. A lot of it is common knowledge today, but probably because of this work. It's great to see them work through it.
This is a bit of a glossary to many of the more important stats, with links for further reading.
As well, not quite the same, but Analyzing Baseball Data With R is also a great introduction to learning R, which is probably preferable to Python for a lot of baseball-specific work (not to make a general statement on the two, at all).
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Reading
A lot of good work is, somewhat annoyingly, scattered through the internet on blogs. I don't have time to dig up too much right now but I'll shamelessly plug some work a couple of friends did a few years ago that was rather successful. These are mostly just examples of the what these projects tend to look like.
Much of the more current work will probably be found on FanGraphs' community submissions section, which I honestly haven't up with recently. I imagine a lot of focus is on using all the new Statcast data.
There's also the MIT Sloan Sports Analytics Conference, where a lot of really cool work comes from. The awesome part about Sloan is that there seems to be a strong emphasis on sharing; I looked for the data/code for two papers I was interested in and ended up getting it for three! My favourite work might be (batter|pitcher)2vec. This is more machine-learning oriented, which I think is a good direction.
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That's all I have time for rn, hope that helps!
https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229/
It's an introduction to baseball data, statistical analysis, and the R programming language.
http://www.amazon.com/Introduction-Probability-Edition-Dimitri-Bertsekas/dp/188652923X/ref=sr_1_1?ie=UTF8&amp;qid=1394424420&amp;sr=8-1&amp;keywords=bertsekas+probability
You can find the video lectures from http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ or taking the course on edX https://www.edx.org/course/mitx/mitx-6-041x-introduction-probability-1296
*Solutions to the book exercises can be found on the book's website. Perfect for self-taught learner.
For math you're going to need to know calculus, differential equations (partial and ordinary), and linear algebra.
For calculus, you're going to start with learning about differentiating and limits and whatnot. Then you're going to learn about integrating and series. Series is going to seem a little useless at first, but make sure you don't just skim it, because it becomes very important for physics. Once you learn integration, and integration techniques, you're going to want to go learn multi-variable calculus and vector calculus. Personally, this was the hardest thing for me to learn and I still have problems with it.
While you're learning calculus you can do some lower level physics. I personally liked Halliday, Resnik, and Walker, but I've also heard Giancoli is good. These will give you the basic, idealized world physics understandings, and not too much calculus is involved. You will go through mechanics, electromagnetism, thermodynamics, and "modern physics". You're going to go through these subjects again, but don't skip this part of the process, as you will need the grounding for later.
So, now you have the first two years of a physics degree done, it's time for the big boy stuff (that is the thing that separates the physicists from the engineers). You could get a differential equations and linear algebra books, and I highly suggest you do, but you could skip that and learn it from a physics reference book. Boaz will teach you the linear and the diffe q's you will need to know, along with almost every other post-calculus class math concept you will need for physics. I've also heard that Arfken, Weber, and Harris is a good reference book, but I have personally never used it, and I dont' know if it teaches linear and diffe q's. These are pretty much must-haves though, as they go through things like fourier series and calculus of variations (and a lot of other techniques), which are extremely important to know for what is about to come to you in the next paragraph.
Now that you have a solid mathematical basis, you can get deeper into what you learned in Halliday, Resnik, and Walker, or Giancoli, or whatever you used to get you basis down. You're going to do mechanics, E&M, Thermodynamis/Statistical Analysis, and quantum mechanics again! (yippee). These books will go way deeper into theses subjects, and need a lot more rigorous math. They take that you already know the lower-division stuff for granted, so they don't really teach those all that much. They're tough, very tough. Obvioulsy there are other texts you can go to, but these are the one I am most familiar with.
A few notes. These are just the core classes, anybody going through a physics program will also do labs, research, programming, astro, chemistry, biology, engineering, advanced math, and/or a variety of different things to supplement their degree. There a very few physicists that I know who took the exact same route/class.
These books all have practice problems. Do them. You don't learn physics by reading, you learn by doing. You don't have to do every problem, but you should do a fair amount. This means the theory questions and the math heavy questions. Your theory means nothing without the math to back it up.
Lastly, physics is very demanding. In my experience, most physics students have to pretty much dedicate almost all their time to the craft. This is with instructors, ta's, and tutors helping us along the way. When I say all their time, I mean up until at least midnight (often later) studying/doing work. I commend you on wanting to self-teach yourself, but if you want to learn physics, get into a classroom at your local junior college and start there (I think you'll need a half year of calculus though before you can start doing physics). Some of the concepts are hard (very hard) to understand properly, and the internet stops being very useful very quickly. Having an expert to guide you helps a lot.
Good luck on your journey!
Rather than list various courses, I'll say this. If you can use all the techniques in this book:
http://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Edition/dp/0123846544/ref=dp_ob_title_bk/185-3957242-1103639
and understand the content of this book:
http://www.amazon.com/Mathematical-Physics-Sadri-Hassani/dp/0387985794/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1335192374&amp;sr=1-1
then you will almost certainly know all they math you'll ever need for advanced undergraduate and general graduate courses. In fact, you'll almost certainly know much more than you'll need.
That's not to say that you should simply study those books - the second one is a gem, but the first is.... polarizing - but they're useful guides of what you ought to know.
Interdisciplinary connections spring up from generality. You'd be hard pressed to find a spontaneous connection between something like particle phenomenology and an unrelated field.
To illustrate this idea of generality, consider the methods of statistical mechanics, which are so general that they can be used to describe everything from black holes to ferromagnets. However, the methods have also been used to model neural networks and social dynamics (the latter being accurate enough to successfully recreate historical events.)
What makes statistical mechanics more general than other branches? Probably the fact that it's almost more mathematics than physics, specifically a branch of probability theory regarding highly correlated random variables.
With this in mind, perhaps you'd benefit from focusing your attention on the mathematical ideas that drive physics rather than physics itself. Take the calculus of variations which, whilst developed for problems in classical mechanics, has found applications in mathematical optimisation. Another example being brownian motion, the mathematics of which have been generalised to higher dimensions and applied to finance. The mathematics behind relativity is differential geometry, which has been applied to too many fields to list.
I'd recommend having a look at Mathematical Methods for Physicists by Arfken, Weber and Harris for a broad overview of the methods.
An intermediate resource between the Downey book and the Gelman book is Doing Bayesian Analysis. It's a bit more grounded in mathematics and theory than the Downey, but a little less mathy than the Gelman.
The absolute best book I've found for someone with a frequentist background and undergraduate-level math skills is Doing Bayesian Data Analysis by John Kruschke. It's a fantastic book that goes into mathematical depth only when it needs to while also building your intuition.
The second edition is new and I'd recommend it over the first because of its improved code. It uses JAGS and STAN instead of Bugs, which is Windows-only now.
I used Mathematical Thinking: Problem-Solving and Proofs by D’Angelo and West, and I remember it being quite a good book as an introduction to proofs. We didn’t use the book extensively in that course, but when we did need it I had no complaints.
These are some good books:
Mathematical Thinking: Problem-Solving and Proofs
(DJVU)
Mathematical Puzzles: A Connoisseur's Collection
(PDF)
(DJVU)
The first is a good introduction to proofs. The second has a bunch of puzzles that are reasonably challenging and don't require advanced mathematics but do require an understanding of mathematical proofs.
If you're looking for a thorough and rigorous introduction into probability theory, I'd recommend going with Introduction to Probability Theory and Its Applications Vol.1 and 2 by Feller. Another well recommended book is Probability and Random Processes by Grimmett and Stirzaker (this starts from the get-go with measure theory).
If you're looking for general statistics, then you may want to look at All of Statistics by Wasserman and perhaps Bayesian Data Analysis by Gelman, et al.
Finally, since you're a physicist, you'll probably want to take a look at Monte Carlo methods in particular, such as with Monte Carlo Statistical Methods by Robert and Casella.
Try this.
Grimmett and Stirzaker.
Probability and Random Processes is a wonderful book in probability; but focused on probability to the point that major statistical distributions (chi-squared, T) are merely asides.
Oh sorry, I forgot to reply to you. There's two textbooks I typically reference for ODEs that will be more than sufficient by the sounds of it.
There is Braun - Differential Equations and their Applications. The author tries to motivate each problem by going to some interesting applications. I think he fails in this as the applications are quite standard at the end of the day, he just goes into more detail to give the context. But the book is overall great and quite well explained.
The other one is kind of tough to track down as it seems to be out of print now Differential Equations with applications and historical notes by Simmons. Again the book has a bit of a gimmick where it puts each of the big contributors, and methods, in historical context. It's an excellent resource I find, it gets pretty in depth on Laplace transforms.
It's really your call which one you go with, if you have some extra time once you make it through your course content I would recommend taking a look at the sections on qualitative theory, systems of ODEs, and numerical methods. Those topics are both fascinating and I think tend to have more active work associated with them.
I'm in engineering, and back when I took DE I mainly used Braun for applications I think. I remember liking it quite a bit. http://www.amazon.com/Differential-Equations-Their-Applications-Introduction/dp/0387978941/
Edit: also IIRC, Churchill (Complex Variables and Applications) had a section about applications of DE in Laplace transforms.
If you'd like some alternatives, I personally like Braun and I heard Arnold is good.
These are my personal favourites for introductory books on ODEs - [Simmons & Krantz's Differential equations: theory, techniques and practice](https://www.amazon.com/Differential-Equations-Steven-Krantz-Simmons/dp/0070616094) is a great book with examples from physics and engineering along with lots of historic notes.
[Braun's differential equations and their applications](https://www.amazon.com/Differential-Equations-Their-Applications-Introduction/dp/0387978941/ref=sr\_1\_1?crid=35EOUTZZ32HDA&amp;keywords=braun+differential+equations&amp;qid=1556968795&amp;s=books&amp;sprefix=braun+Differenz%2Cstripbooks-intl-ship%2C215&amp;sr=1-1) is another applications oriented differential equations book that is a bit more involved than Simmon's but has a much broader perspective with introductions to bifurcation theory and applications in mathematical biology.
&#x200B;
If you're not planning to do research in ODE theory, but want to learn the basic theory more rigorously, then [Hurewicz's Lectures](https://www.amazon.com/Lectures-Ordinary-Differential-Equations-Hurewicz/dp/1258814889/ref=sr\_1\_1?crid=341Z3D48AUTBU&amp;keywords=hurewicz+differential&amp;qid=1556969136&amp;s=gateway&amp;sprefix=hurewicz+%2Cstripbooks-intl-ship%2C216&amp;sr=8-1) is a perfect short book that covers the basic theorems for existence and uniqueness of solutions of ODEs.
I have never argued that draw is good for the game. If you read my posts around this subreddit, I have critized mojang for not putting in the proper way to the hand limit and have argued that it makes the game less tactical on several occasions. As for the rest, try this:
http://www.amazon.co.uk/Statistics-For-Dummies-Deborah-Rumsey/dp/0470911085
Honestly, if you're wanting an understanding of statistics, I'd recommend Statistics for Dummies. Don't be deceived by the title, you'll still have to do some real thinking on your own to grasp the ideas discussed. You might consider using textbooks or other online resources as secondary supports to your study.
I can also give you a basic breakdown of the topics you'd want to develop an understanding of in beginning to study statistics.
Descriptive Statistics
Descriptive statistics is all about just describing your sample. Major ideas in being able to describe the sample are measures of center (e.g., mean, median, mode), measures of variation (e.g., standard deviation, variance, range, interquartile range), and distributions (e.g., uniform, bell-curve/normally distributed, skewed left/right).
Inferential Statistics
There is a TON of stuff related to this. However, I would first recommend beginning with making sure you have some basic understanding of probability (e.g., events, independence, mutual exclusivity) and then study sampling distributions. Because anything you make an inference about will depending upon the measures in your sample, you need to have a sense of what kinds of samples are possible (and most likely) when you gather data to form one. One of the most fundamental ideas of inferential statistics is based upon these ideas, The Central Limit Theorem. You'll want to make sure you understand what it means before progressing to making inferences.
With that background, you'll be ready to start studying different inferences (e.g., independent/dependent sample t-tests). Again, there are a lot of different kinds of inference tests out there, but I think the most important thing to emphasize with them is the importance of their assumptions. Various technologies will do all of the number crunching for you, but you have to be the one to determine if you're violating any assumptions of the test, as well as interpret what the results mean.
As a whole, I would encourage you to focus on understanding the big ideas. There is a lot of computation involved with statistics, but thanks to modern technology, you don't have to get bogged down in it. As a whole, keep pushing towards understanding the ideas and not getting bogged down in the fine-grained details and processes first, and it will help you develop a firm grasp of much of the statistics out there.
Pm me i'll order this for you
https://www.amazon.com/Probability-Dummies-Deborah-J-Rumsey/dp/0471751413
Take your pick from this book: https://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753
Counterexamples in topology
Counterexamples in analysis
Depending on your level, i have used PDEs by Evans which is very well written, and the most recommended book i know of on the subject. It is pretty advanced though.
the shape of space by jeffrey weeks is the cutest folk history book that manages to explain some extremely delicious topology along the way.
Here are some great books that I believe you may find helpful :)
and last but definitely not least:
Later on:
You might like Geometry Revisited by Coxeter and Greitzer.
http://www.amazon.com/Geometry-Revisited-Mathematical-Association-Textbooks/dp/0883856190
Geometry Revisited by Coxeter and Greitzer
http://www.amazon.com/Geometry-Revisited-New-Mathematical-Library/dp/0883856190/
Coxeter, maybe?
Here is an actual blog post that conveys the width of the text box better. Here is a Tufte-inspired LaTeX package that is nice for writing papers and displaying side-notes; it is not necessary for now but will be useful later on. To use it, create a tex file and type the following:
\documentclass{article}
\usepackage{tufte-latex}
\begin{document}
blah blah blah
\end{document}
But don't worry about it too much; for now, just look at the Sample handout to get a sense for what good design looks like.
I mention AoPS because they have good problem-solving books and will deepen your understanding of the material, plus there is an emphasis on proof-writing when solving USA(J)MO and harder problems. Their community and resources tabs have many useful things, including a LaTeX tutorial.
Free intro to proofs books/course notes are a google search away and videos on youtube/etc too. You can also get a free library membership as a community member at a nearby university to check out books. Consider Aluffi's notes, Chartrand, Smith et al, etc.
You can also look into Analysis with intro to proof, a student-friendly approach to abstract algebra, an illustrated theory of numbers, visual group theory, and visual complex analysis to get some motivation. It is difficult to learn math on your own, but it is fulfilling once you get it. Read a proof, try to break it down into your own words, then connect it with what you already know.
Feel free to PM me v2 of your proof :)
You need an appropriate level of knowledge to engage in fruitful discourse
Engineering Mathematics. This monster got me through half of my first year.
Engineering Mathematics https://www.amazon.co.uk/dp/1403942463/ref=cm_sw_r_wa_apa_i_AtIwCbD4VEH94
Frequently... No.
The reality is that I use it infrequently enough that I keep a copy of Stroud on the bookcase in my office, so I can refresh my maths as required. In case I start exploring a seemingly simple problem, black out and suddenly come to covered in symbolic notation, knee deep in integrals, clutching the beating heart of a laplace transform and screaming "Leibniiiiiiiiiiiiiiiiiiiiz!" at the top of my voice!.
So yeah... when I need it, I need it.
I was in a similar situation as you, last year. If you are willing to spend any money on this, I definitely suggest this book.
Link
Mostly because I wanted to analyze baseball stats, and at the time (4-5 years ago) that was mostly done in R. If the last industry conference I went to is any indication, it still is, many of the presentations features plots that were clearly ggplot2. There are also books like this one floating around: https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229/ref=nodl_.
I'm in a similar boat as you. I'm a biologist by trade, but want to delve deeper into statistical analysis with R programming to add a new skill to my career. I'm also a huge baseball fan, especially love it for the stats.
A friend of mine gave me this book for a birthday gift and I've been working way my through it, albeit very slowly. So far (I'm only at Chapter 3), it's been easy to follow and a nice to guide through R. I'd suggest it.
The edx course, that /u/sin7 suggested sounds interesting as well.
At least re: random variables, events, PDF, and CDF, I like the diagrams from Prof. Joe Blitzstein's textbook:
http://i.imgur.com/aBkgHGC.jpg
Blitzstein and one of his students published a probability textbook
Although I am not a statistician myself and given your background, some of my recommendations would be:
This should probably be enough for now but if you need more recommendations just say so :)
Regarding the time series question, it's not my area of expertise but since time series analysis ends up employing many statistical methods, I think it can be considered an area of statistics (Statisticians around here correct me if I am wrong :P)
The Nature of Computation
(I don't care for people who say this is computer science, not real math. It's math. And it's the greatest textbook ever written at that.)
Concrete Mathematics
Understanding Analysis
An Introduction to Statistical Learning
Numerical Linear Algebra
Introduction to Probability
I have very few universal recommendations. Think the only one that actually comes to mind is "Introduction to Probability" by Blitzstein and Hwang. It is probably the best book on probability that I've found for a broad audience. It also has a corresponding video lecture series.
If you want any more, please answer this:
Maybe I can see what I have laying around that meets your criteria.
https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X/ref=sr_1_1?ie=UTF8&amp;qid=1523289228&amp;sr=8-1&amp;keywords=bertsekas
No busques mas porque explica todo de 10. Si todos los textos fuesen asi...
This is the book I used when I was studying statistics and probability. https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X
"Math isn't a spectator sport", but you shouldn't make yourself hate math by doing hundreds of problems. Study what you find interesting.
It's pretty basic stuff, but the first three chapters of this book was a game-changer for me
https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X
My mind was blown when I finally understood the connection between random variables and the "basic" probability theory with events and sample spaces. For me they had always been two seperate things.
The notation is also really nice.
Having solid fundamentals makes it much easier to study advanced topics, so I would start here.
There's also a great EDX course which is based on the book, but it's a complement and not a substitute. Get the book.
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.
I can recommend a very good book, I am using it and it is beautiful.
I looked at similar (WA resident also) but there's only a few community college classes that are interesting (linear algebra, probability, ODE) so then you're looking at UW/WSU tuition. There's a couple applied tracks you could consider: machine learning and financial math:
https://metacademy.org/roadmaps/
http://www.deeplearningweekly.com/pages/open_source_deep_learning_curriculum
https://www.quantstart.com/articles/Quantitative-Finance-Reading-List
-----------
Self study: math for physics texts like Arfken/Harris/Weber, Boas, Riley/Hobson, Thomas Garrity
http://www.goldbart.gatech.edu/PostScript/MS_PG_book/bookmaster.pdf
https://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Comprehensive/dp/0123846544
For math there isn't much better undergraduate/beginning graduate review than Arfken, Weber, Harris. This will cover most mathematics you'll encounter in your first and maybe second years of graduate studies. Personally I'm not a huge fan of the complex contour integration sections you'll encounter in that book - I much prefer Ahlfors or Rudin for something more on the pure side or Churchill for something more on the applied side of complex analysis. The other sections are, in my opinion, stellar - although I have only the third edition in my possession.
Personally I make a distinction between scripting and programming that doesn't really exist but highlights the differences I guess. I consider myself to be scripting if I am connecting programs together by manipulating input and output data. There is lots of regular expression pain and trial-and-error involved in this and I have hated it since my first day of research when I had to write a perl script to extract the energies from thousands of gaussian runs. I appreciate it, but I despise it in equal measure. Programming I love, and I consider this to be implementing a solution to a physical problem in a stricter language and trying to optimise the solution. I've done a lot of this in fortran and java (I much prefer java after a steep learning curve from procedural to OOP). I love the initial math and understanding, the planning, the implementing and seeing the results. Debugging is as much of a pain as scripting, but I've found the more code I write the less stupid mistakes I make and I know what to look for given certain error messages. If I could just do scientific programming I would, but sadly that's not realistic. When you get to do it it's great though.
The maths for comp chem is very similar to the maths used by all the physical sciences and engineering. My go to reference is Arfken but there are others out there. The table of contents at least will give you a good idea of appropriate topics. Your university library will definitely have a selection of lower-level books with more detail that you can build from. I find for learning maths it's best to get every book available and decide which one suits you best. It can be very personal and when you find a book by someone who thinks about the concepts similarly to you it is so much easier.
For learning programming, there are usually tutorials online that will suffice. I have used O'Reilly books with good results. I'd recommend that you follow the tutorials as if you need all of the functionality, even when you know you won't. Otherwise you get holes in your knowledge that can be hard to close later on. It is good supplementary exercise to find a method in a comp chem book, then try to implement it (using google when you get stuck). My favourite algorithms book is Numerical Recipes - there are older fortran versions out there too. It contains a huge amount of detailed practical information and is geared directly at computational science. It has good explanations of math concepts too.
For the actual chemistry, I learned a lot from Jensen's book and Leach's book. I have heard good things about this one too, but I think it's more advanced. For Quantum, there is always Szabo & Ostlund which has code you can refer to, as well as Levine. I am slightly divorced from the QM side of things so I don't have many other recommendations in that area. For statistical mechanics it starts and ends with McQuarrie for me. I have not had to understand much of it in my career so far though. I can also recommend the Oxford Primers series. They're cheap and make solid introductions/refreshers. I saw in another comment you are interested potentially in enzymology. If so, you could try Warshel's book which has more code and implementation exercises but is as difficult as the man himself.
Jensen comes closest to a detailed, general introduction from the books I've spent time with. Maybe focus on that first. I could go on for pages and pages about how I'd approach learning if I was back at undergrad so feel free to ask if you have any more questions.
Out of curiosity, is it DLPOLY that's irritating you so much?
For applied Bayesian statistics, Kruschke's Doing Bayesian Data Analysis is fantastic. It's a fantastic intro book that goes into only as much technical detail as you need to grasp what's going on.
The pymc3 documentation is a good place to start if you enjoy reading through mini-tutorials: pymc3 docs
Also these books are pretty good, the first is a nice soft introduction to programming with pymc & bayesian methods, and the second is quite nice too, albeit targeted at R/STAN.
We are using Mathematical Thinking: Problem Solving & Proofs 2nd Edition. We get lectures notes because the text book is difficult to understand, but they dont really help..
EDIT: I realize now its the same book! Great! Any help?
Ah yes, traditionally math learning is a fairly linear progression and is bottlenecked up until you take your first proof/analysis class, after which your path can branch out. Seeing as how you already have a link there, a textbook is listed for that class and that one happens to be popular so maybe you can buy that one. Me personally, I used this one when I went through the fundamentals
> The set/subset relation could be considered an inverse relation as well.
Let A = {1, 2} be a set. Then B = {1} is a subset of A. Let's define a relation between them, f: A -> B given by f(1) = 1 and f(2) = 1. f is, actually, a function. But this function f doesn't have an inverse. Why? Find out from Mathematical Thinking: Problem-Solving and Proofs by D'Angelo and West.
Therefore
> Then that would also make the infinite/finite relation an inverse relation.
doesn't follow.
> My problem is that I have never really been introduced to sets or other things,
How did that happen? I know that at my alma mater, you're supposed to have some kind of proofs-oriented course before you take intro abstract algebra (either "abstract linear algebra", which is a proofs-heavy intro to linear algebra, or "fundamental mathematics" or "theory of computation"). Does this course not have appropriate prereqs, or did you disregard them?
Edit: the text that the fundamental mathematics class there uses is Mathematical Thinking: Problem-Solving and Proofs. It's written by a couple of the professors from the university. I don't know much about West, but I had D'Angelo for real analysis, and he was both meticulous and clear in lecture; I'd be surprised if any book that he put his name on was not.
I'd start with a discrete math course (often offered for intro computer-science, but make sure the curriculum doesn't consist of any coding). Then move on to real analysis.
I really like this book as an intro.
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.
An oldie but good is Introductory Probability and Statistical Applications by Meyer! I've used newer, more fashionable textbooks (Ross, Miller & Miller) but this one is my favorite for the introductory level. It feels a bit dated at times (e.g. "although we cannot expect all readers to own a personal computer"), but the relevant math hasn't changed much in the passed few decades. It is very clear with more exposition than I've found in the newer books I mentioned.
As for an advanced text, I've heard good things about Probability and Random Processes by Grimmet and Stirzaker. My friends used it in a graduate course on basic probability, and compare it favorably to their undergraduate experiences with probability.
This is the best one I have used.
LIST OF APPLICATIONS IN MY DIFF EQ PLAYLIST
Have you seen the first video in my series on differential equations?
I'm still working on the playlist, but the first video lists a bunch of applications that you might not have seen before. My goal was to provide a sample of the diversity of applications outside of mathematics, and I chose fairly concrete examples that include applications in engineering.
I don't go into any depth at all regarding any of the particular applications (it's just a short introductory video), but you might find the brief introduction to be helpful.
If you find any one of the applications interesting, then a Google search will reveal more detailed resources.
A COUPLE OF FREE OR INEXPENSIVE BOOKS
Also, off the top of my head, the books below have quite a few applications that you might not see in the more standard textbooks.
I think you can find other legal PDFs of Braun's third edition, too. Pollard and Tenenbaum is an inexpensive paperback from Dover, and I actually found a copy at my local library.
ENGINEERING BOOKS
Of course, the books I listed are strictly devoted to differential equations, but you can find other applications if you look for books in engineering. For example, I used differential equations in a course on signals and systems that I tutored last semester (applications included electrical circuits and mass-spring-damper systems).
NEAT VIDEO (SOFT BODY MODELING)
By the way, here's a cool video of various soft body simulations based on mass-spring-damper systems modeled by differential equations.
Here's a Wikipedia article on soft body dynamics. This belongs to the field of computer graphics, so I'm not sure if you're interested, but mass-spring-damper systems come up a fair amount in engineering courses, and this is an application of those ideas that might open your mind a bit to other possible applications.
Edit: typo
> 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.
> 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.
Advanced Engineering Mathematics by Kreyzsig. Fuck, the size of that book fills me with awe.
Ha that's why I hate non-Euclidian geometry. I'm not good at figuring out the curvatures. ;) But maybe you'll find it interesting?
You said you were interested in math. What got you interested? What is it about math that you like? Or what would you like to do if you had a degree in math? You can start there to figure out something you might be interested in. I would suggest a basic calculus book to learn. Really any one would do. If you find that interesting, and want to continue on advanced mathematics, then Advanced Engineering Mathematics by Kreyszig is a fantastic book.
I like algebra and statistics. That's the part of math that I work in; dealing with using statistics to better understand biology. The reason I like algebra is because, honestly, there's only one answer. There's one right answer and it's a puzzle for me to figure out. I like working with numbers. Numbers are always the same and they always follow the same rules. However, I know some people who hate algebra and love geometry. Want to figure out what curvature you should make your satellite in to receive the best signal? Or at what angle you need to point your telescope at? That's geometry. It's more pictorial whereas algebra is more numeric. That's at least a very basic start.
Well, I appreciate your interest in engineering. You will love your college i am sure. Engineering College are like Hogwarts, there is lots of magic happening on daily basis. You need not to worry about maths. I followed this book in my college years. It is very good book.
Trigonometry is not that important as Calculus. So i would say first complete the Calculus. If you are going to Electrical Engineering, Complex Analysis is must. I hope that helps. Any doubts please ask me.
Are there any significant differences b/w Advanced Engineering Mathematics 9th and 10th editions?
When I took a course on PDE's I watched a bunch of this guys videos.
My class used Strauss's book.
My brother learnt from Kreszig's book, no idea if it's any good though.
Wathever courses that requires this book.
Only if you are too dumb to know how to use it. Knowing a median is actually quite useful when making future predictions.
I would encourage you to read up on statistics, so you can focus on things that matter, rather than on the odds that Urban Meyer wins a game when there is snow within 100 miles and he is wearing khakis.
http://www.amazon.com/Statistics-Dummies-Deborah-J-Rumsey/dp/0470911085
IQ tests are calibrated to return an average of 100. Absent any evidence to the contrary, we assume the null hypothesis and place all subgroups at the global average. Here's a good starting point if you're interested in learning more.
Educational barriers for African Americans are well documented and muddy the relationship between intelligence and education. You'll note that the educational data I provided earlier was solely for whites, where the relationship is clear cut. I'm unaware of any reliable data for blacks.
Now, since you're presumably white, and we do have that data, would you mind telling the audience a little about your education, and we'll see what inferences we can draw?
Asking every single person is definitely not the only way to get accurate numbers. For starters you could give this read:
http://www.amazon.com/Statistics-For-Dummies-Deborah-Rumsey/dp/0470911085/ref=sr_1_5?ie=UTF8&amp;qid=1412872846&amp;sr=8-5&amp;keywords=intro+to+statistics
But you're right about this little piece of click bait. I'm not sure why more people aren't commenting on the NBC/Survey Monkey Ad they were just tricked into reading.
[citation needed]
http://www.amazon.ca/Statistics-For-Dummies-Deborah-Rumsey/dp/0470911085
Here is the lowest end dumbed down version.
Should be perfect.
for you because you seem upset
Sorry, I went on vacation and totally blanked about posting these for you!
Anyway, here are some books
Linear Algebra Done Right (Undergraduate Texts in Mathematics) https://www.amazon.com/dp/3319110799/ref=cm_sw_r_cp_api_1L8Byb5M5W9D3
This one is actually for analysis but depending on your appetite, it might help greatly with the proof side of your class. You can buy it here: Counterexamples in Analysis (Dover Books on Mathematics) https://www.amazon.com/dp/0486428753/ref=cm_sw_r_cp_api_GS8BybQWYBFXX
But there's also a PDF hosted here: http://www.kryakin.org/am2/_Olmsted.pdf
As an undergrad physics major, I would recommend this as well. If you're going to continue and do graduate PDE work, I would just jump into Evans after that.
Graduate or undergraduate level?
If graduate, this is THE book to get.
This is much more applied.
I am no expert (undergrad applied maths), but from what I have heard, Evans is the go to text. I have also heard good things about Salsa as a general overview/ course on PDEs.
YES!!!
http://www.amazon.com/Shape-Space-Chapman-Applied-Mathematics/dp/0824707095
phenomenal book, incredibly approachable
Side note: Jeff Weeks (the mathematician quoted in the article) is a really nice guy who gives public lectures to non-mathematicians and even children in which he explains these ideas. A lot of it summarized in his book "The Shape of Space" (http://www.amazon.com/Shape-Space-Chapman-Applied-Mathematics/dp/0824707095) which I highly recommend if you can get your hands on a copy. But another good place to start (if you haven't already) would be "Flatland" by Edwin Abbott. Weeks' book expands on the Flatland story a bit.
Edit: Jeff also has a website with free downloads of computer games he designed: http://www.geometrygames.org/ In the game "Curved Spaces", you can take a test flight around the dodecahedral space they describe in the article.
http://amzn.com/082477437X or (2nd ed) http://amzn.com/0824707095 - The Shape of Space by Jeffrey R. Weeks.
This book is just an absolute pleasure to delve into without needing prior knowledge of topology. With a lot of pictures, it manages to go quite deep while being very clear and accessible.
Eh. Not every abstract algebra/group theory textbook even tries to link its topics to the intuitive modes of thinking that evolution had to work with.
https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X
This book might be worth a shot?
..You're probably beyond this level though.
Answer here
If you think that sample size is enough, you really need this.
Like I said, you are clueless about statistics...and just fyi, my username's from a damn scifi show you dimwit.
As for Munich, I used to live there so get the fuck out with your nonsense :D
chapter 13: https://lesacreduprintemps19.files.wordpress.com/2012/11/the-bell-curve.pdf
also, you should invest in this: https://www.amazon.com/Statistics-Dummies-Math-Science/dp/1119293529
>Ça tombe bien puisque l’expérience a été reproduite 10 fois.
lol à ce niveau là de stupidité je peux rien faire pour toi désolé
EDIT : nan allez, en vrai je vais t'aider un peu, va lire ça : https://www.amazon.com/Statistics-Dummies-Math-Science/dp/1119293529
Here is some recommended reading. It's absurd to attempt to make a 1-1 comparison when whites are between 62% and 77% (depending on if you count Hispanics as white) of the total population of the US. It makes much more sense to make a per capita compairsion so total mass shootings per 100000.
Seek out engineering math books, seriously.
The two tomes by K.A.Stroud are astoundingly simple to follow.
The only issue would be that they don't cover everything you need :(
The CRC book of math tables and formulae could be helpful.
And likewise the CRC Handbook of Chemistry And Physics.
Keep this under your pillow, bought because of a recommendation from a PhD candidate and it hasn't left my side since as I work:
CRC Standard Mathematical Tables and Formulae 32nd Ed.
Wonder no more. These things were as common as scientific calculators are now.
new 2011 32nd ed. $65
http://www.amazon.com/Standard-Mathematical-Formulae-Mathematics-Applications/dp/1439835489
used 27th ed. $2
http://www.amazon.com/Standard-Mathematical-Formulae-Mathematics-Applications/dp/0849306272
Lots of editions available, at basically every major bookseller, including amazon.
I suggest either Tu or (easy) Lee.
This book might be a helpful start: https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229
https://www.amazon.com/Analyzing-Baseball-Data-Chapman-Hall/dp/1466570229
I found Prof. Joseph Blitzstein's course, at Harvard, on statistics engaging. First I watched his lectures and worked through the problem sets. This was extemely rewarding, so I went on to work through his book on probability. According to me, what separates him from other Profs is that he takes a lot of effort to build intuition about statistical concepts.
Stat110 is the course website. You can find his book here.
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Computer Science Grad School Reading List
Video Game Development Reading List
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 & 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 & 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 & a more advanced course on linear algebra.
A lot of people on this thread could do with
Statistics For Dummies, 2E https://www.amazon.co.uk/dp/0470911085/ref=cm_sw_r_cp_apa_w4xUAbNGYEP37
> The same way that buying a lotto ticket this week doesn't increase my odds of winning next weeks draw if I don't win.
no, but buying multiple tickets this week increses your chance to win this week
> You would be correct if you could use multiple keys on one box to increase your odds of getting a ship, but thats not how it work.
yes, i am also correct if i can use multiple keys on multiple boxes
> You only get to buy 1 ticket to this weeks lotto, one for next weeks etc etc
not really, you can buy as many tickets as you can afford
i suggest https://www.amazon.com/Probability-Dummies-Deborah-J-Rumsey/dp/0471751413/ unless you want to make fool out of yourself some more...
That's a start. Now read this to refresh your memory.
https://www.amazon.com/Statistics-Dummies-Math-Science/dp/1119293529
http://www.amazon.com/Standard-Mathematical-Formulae-Mathematics-Applications/dp/1439835489
CRC Tables is a must for anyone that may use math in their job. Also good for students. It has just about any formula or table you'd ever encounter in your math career.
Try this.
https://www.amazon.com/Statistics-Dummies-Deborah-J-Rumsey/dp/1119293529
https://www.amazon.com/Statistics-Dummies-Math-Science/dp/1119293529