Best study & teaching mathematics books according to redditors

First, you might want to start with /r/matheducation. They’re actually experts in this subject.

You can read work by hundreds of experts in child psychology/development, pedagogy, the philosophy of mathematics, the intuitive/psychological foundations of mathematics, etc. Personally I’m a fan of Piaget, Bruner, Papert, and like-minded thinkers, who advocate a child-centered “constructivist” approach to education. But there are certainly respectable educators and researchers who favor a more structured and top-down approach.

If you want to read concretely about the differences between typical US instruction and Chinese instruction in the 1990s, read Liping Ma’s book Knowing and Teaching Elementary Mathematics

Or watch this video from a few years ago discussing the TIMSS study and criticizing Khan Academy.

Or to see what a particular group of young children could learn with some expert guidance, check out Zvonkin’s book.

You might have read Lockhart’s Lament. He provides an alternative way of teaching high school mathematics in his book Measurement.

I like this concise theory of mathematical learning. YMMV. Here’s a short essay by Minksy about why mathematics is hard to learn.

If you want lesson plans and curriculum guidance, look to the American NCTM, who have been making detailed materials available for decades. Also look up math circles (both online materials and physical groups meeting in your area).

You might like this book by Van de Walle about general elementary teaching, or this book by Lenchner about problem solving.

Many people seem to like the Singapore math books. Read about Singapore’s curriculum.

If you ask homeschooling parents in your area, you can probably find strong opinions about curricula. Just searching around the web, many keywords about elementary math books etc. seem to lead to homeschooling sites. (This makes some sense: they have some free time, like to write about their experiences and form online communities, and do more personal evaluation of curricula than schoolteachers can necessarily have time/political power to do.)

There are hundreds of available books of mathematical puzzles and games, dozens of different types of physical manipulatives, and thousands of books, papers, essays, etc. about how to organize, order, and teach students of every imaginable age and background

If you have a particular age group / level of prior preparation / desired set of topics in mind, there might be some more specific materials people can point to. Are we talking about 4-year-olds? 10-year-olds? High school olympiad preparation? Are you interested in basic arithmetic? Geometry? Algebra? Do you have 1 advanced student to teach? 50 students of varying skill levels?

Only certain areas of programming require knowledge of maths - this doesn't mean you have to understand the maths, just know how it works (and how to use it) not necessarily why it works (obviously some areas will require more of an understanding).

A lot of people dislike maths because it's taught poorly, or if you fall behind you never catch up, there are a lot of resources for learning maths online which you can do at your own rate (https://www.khanacademy.org/ is really good), as well as books (http://www.amazon.co.uk/gp/product/0521017076/ is a pretty good book as an introduction - unlike most maths books its not aimed at mathematicians).

How to Study as a Mathematics Major by Lara Alcock
https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/ref=nodl_

This book was given to me my senior year of high school and it secured me as a mathematics major. I think it gives an excellent introduction to university mathematics and advice on how to think when approaching problems. Really I think this is exactly what you’re looking for.

You can graph the function and find where it equals zero.

Or learn some basic algrebra.

I think the TI-83 by design does not have an algebra solver. Most middle/high school math teachers wouldn't want them in the classroom if it did. The Ti-89 which is targeted towards engineers does.

If you want to learn the mathematics behind games of chance I would seriously look at brushing up on algebra.

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


> Anybody else feels like this?

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

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

• How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
  
  
• Thinking Mathematically
  
  
• How to Solve It: A New Aspect of Mathematical Method
  
  
• The Art of Problem Posing
  
  
• How to Study as a Mathematics Major
  
  
• How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Ist natürlich noch abhängig davon, was für eine Laufbahn und Verwendung du haben möchtest, je nach dem wird der Test schwerer oder die Fragen ändern sich etwas.
Zum lernen finde ich dieses Buch ganz hilfreich:
https://www.amazon.de/dp/3956240650/ref=cm_sw_r_cp_apa_i_4gCPDbG9WFW0N

Ah, you say something like "Algebra" on /r/askacademia people are going to assume you mean like graduate level pure math.

I think the first step for someone with your background is to just get comfortable with basic arithmetic and numbers again. At least I've found when trying to teach people without a strong math background that before you can get to things like algebra you have to instill a sort of "trust" in calculation. I think the best way to do that is probably repetition, repetition, repetition. Perhaps something like this:

http://www.amazon.com/Schaums-Outline-Elementary-Mathematics-Outlines/dp/007176254X/ref=sr_1_1?ie=UTF8&qid=1458739566&sr=8-1&keywords=schaum%27s+arithmetic

And do the shit out of the problems. That is absolutely crucial. Do them until they're second nature, move to the next section, then the next and then a couple weeks later COME BACK and always be mixing it up but pushing forward.

Check out the book 101 Careers in Mathematics.

She's also written a few books to get kids intersted in math.

• Math Doesn't Suck - Middle school math
  
• Hot X: Algebra Exposed
  
• Kiss My Math - Pre-algebra
  
• Girls Get Curves - Geometry
  

Some good readings from the University of Cambridge Mathematical reading list and p11 from the Studying Mathematics at Oxford Booklet both aimed at undergraduate admissions.

I'd add:

Prime obsession by Derbyshire. (Excellent)

The unfinished game by Devlin.

Letters to a young mathematician by Stewart.

The code book by Singh

Imagining numbers by Mazur (so, so)

and a little off topic:

The annotated turing by Petzold (not so light reading, but excellent)

Complexity by Waldrop

I'm surprised Knowing and Teaching Elementary Mathematics by Liping Ma wasn't mentioned, as she did a pretty good job at documenting this.

See The Math Myth for an impassioned argument against using mathematics achievement as a requirement for various non-mathematical things. I'm not saying it isn't controversial - check out the various reviews on the book if you're curious.

One of the problems is that mathematics knowledge (depending on the context we could be talking about anything from algebra to calculus) is often used solely as a tool to filter people when it is not appropriate to do so. There is a belief that achievement in mathematics should be a proxy for intelligence, perseverance or "grit".

Mathematics for the Million contains some history, science, and personalities around the common math topics up thru calculus. I enjoyed it very much, mostly because it also contained much I hadn't seen before or considered how interesting some things could be.

I don't want to get very deep into this discussion because, fundamentally, it will turn into a battle of philosophy. Ian Stewart had a chapter dedicated to this very discussion in Letters to a Young Mathematican, wherein he posits that climate will have a very dramatic effect on how their mathematics formed. For example, on an extremely windy planet, the beings would have a stronger grapple on mathematical aerodynamics.

Check out Letters to a Young Mathematician by Ian Stewart. It is pretty short, and from one of the reviews: From Publishers Weekly "This new entry in the Art of Mentoring series takes the form of letters from a fictitious mathematician to his niece. The letters span a period of 20 years, from the time the niece is thinking about studying mathematics in high school through the early years of her academic career."

When do you realize that they are not learning? Is it when you get the test? Do you notice this earlier?

What is the structure of your class like? What techniques do you use to have the students doing more of the thinking and you doing less of it? Do the students collaborate or do they work independently?

Do you have manipulatives? Do you use pictures or models to help with their thinking to break up the thinking?

I teach at a much more priveledged school, but a class can be apathetic anywhere if the environment is off. There are plenty of teachers that don't have as much success as others because of their environment and their attitude in class. The major bits in that regard that I can offer is to structure the class around the student doing as much as possible and giving time for thinking, and time for sharing, and time for discussion, then with a quick follow up.

Whiteboarding is awesome. Look into a book called 5 Practices ... (long title) link here:

https://www.amazon.com/Practices-Orchestrating-Productive-Mathematics-Discussions/dp/0873536770

Focus on building up their ability to explain themselves by discussing how to explain how you know something using definitions or shared experiences / methods, and then implementing them relentlessly in class.

When it comes to technology, I prefer pencil and paper for most tasks and teacher led activities using electronics to prevent distraction and from them getting into pitfalls.

Also, some simple physics or probability stuff is always good to do in a lab setting to see how some math concepts show up in the real world (having 5 people measure someone's arm length as precisely as possible and averaging them, etc).

I'd also suggest this classic by Lancelot Hogben (who happens to have an awesome name):
http://www.amazon.com/Mathematics-Million-Master-Magic-Numbers/dp/039331071X

Read this book.

My friends and I really like this book. It goes in-depth with every skill needed on the ACT, with explanations and ample practice problems.

The NCTM has a lot of great resources that will give you some baseline of good strategies to use. For instance, they have a page full of "clips and briefs" about math education research. The briefs are short articles summarizing the research on a topic, and the clips are even shorter synopses of the briefs.

Edit: I just realized you have to be a member of the NCTM to access the briefs. I think there's a free trial you can get. It's worthwhile if you want to teach math.

This short book was a textbook in my mathematics education class. It gives a lot of examples of teachers doing things the authors like and dislike, and gives some good reasoning for why you should teach that way.

If you intend to teach in the US eventually, you should probably become familiar with the Common Core Standards, particularly the practice standards.

You might also be interested in /r/matheducation. They're not as active as here, but there always seems to be somebody helpful hanging out there, so if you have any specific issues you need help with, an experienced math teacher will be able to give you some tips.

Honestly the only resources I can recommend are the official ACT and SAT study guides. Our training is done in-house and most of the techniques that I use were developed by tutors working for the company. If I shared some of the other study materials I have I would be breaking my contract :-/

edit Actually, there is one book that I'd recommend for people that are already quite good (600+) on the math section and want to ace it. That's Dr. John Chung's SAT Math. Great guide for understanding how the questions work and the concepts behind them.

If you are talking about this book, this book, or this book, they contain all the same tests.

If you want more exams, get the subject specific Official Guides in Math 1, 2, Bio, Chem, Physics, WH, etc.

If the exams you're preparing for don't have specific Official Guides and you want 1 more real exam, you'd need to get this book.

https://www.amazon.com/Official-Study-Guide-Subject-Tests/dp/0874477565 It's $18.77 US dollars online from Amazon. There are disappointingly few other resources available, and I have read a number of comments critical of Barron's and Princeton Review resources for those tests. Use the official tests wisely - there are not many for each subject. They are an evaluation tool for once you have prepared elsewhere, not a teaching tool.

Yes. There is an organized attack on America happening right now. It MUST be stopped.

I have had arguments in op-ed pieces with these folks, and man...are they fucking stupid.

I have a large math background, and can argue with these fakers. There used to be a guy called Dembski that got a graduate degree in math and then used a bizarre area of game theory to argue for creationism. He lost. Even his professors have denounced his work as "meaningless" and "dishonest". He'll usually simply put up some equations that appear "mathy" and nobody argues with him. But I'll give him a run for his money with my own equations.

Long ago, a famous mathematician (Euler) cited an equation as proof for God's existence. His work was pure bullshit. Even a gifted mathematician fucks up when trying to prove god.

Have a good one, man.

However, I cannot recommend math highly enough. There's some real wisdom there. Did you know that some numbers have biographies? If you're interested (and most people aren't), you could start (and I already know you're probably not interested), here's some books that make math sexy and fun:

By Danica McKellar

Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail

Kiss My Math: Showing Pre-Algebra Who's Boss

Girls Get Curves: Geometry Takes Shape

Hot X: Algebra Exposed!

Good luck.

idk about past exams, but you could always try collegeboard books which have 2 practice exams for each test.
Math (for both level 1 and 2) : https://www.amazon.com/Official-Subject-Tests-Mathematics-Levels/dp/0874477727

PHysics: https://www.amazon.com/Official-Subject-Physics-Study-College/dp/1457309211/ref=sr_1_1?s=books&ie=UTF8&qid=1502221552&sr=1-1&keywords=official+physics+sat

Alright, since you're not going for any electronic resources, I'll list a couple of books. Your main problem seems to be English in general. While the books might help you, I recommend reading a lot. Try historical and scientific articles online or even in a book. Read a couple of classics by Charles Dickens or Victor Hugo.


1- Kaplan https://www.amazon.com/SAT-Prep-Plus-2018-Strategies/dp/1506221300
This book has exceptional EBRW practice and thorough explanation with multiple methods of approaches. The math section is alright, but I feel that it is a little easier than the actual test.


2- Dr. John Chung's SAT math book. https://www.amazon.com/Dr-John-Chungs-SAT-Math/dp/1481959794
A phenomenal book. It has challenging question in the math section that will over prepare you. If you can get a 700 on his tests, you're set up on getting an 800 for the math section.


3- Barron's New SAT 28th edition https://www.amazon.com/Barrons-NEW-SAT-28th-Sat/dp/1438006497
Great book for learning the entirety of standard English convention and reading strategies. The EBRW questions might be a little easier than the actual thing, but the information it provides is meritorious. The math section also has some challenging problems that will over prepare you.

The official SAT study guide (alias blue book.) https://www.amazon.com/Official-SAT-Study-Guide-2018/dp/1457309289
This is the best book to test all you've practiced for. After you complete all other books, take all 8 practice tests. This will prepare you well.


Now for some tips:
1- Focus on your writing section more at the begining. Getting 44/44 in this section while missing 10 on the reading puts your score at 740-760. It weighs more.

2-Write some essays and have someone check them. It'll help you spot mistakes easier.

3-Calm down, you can always take it again.


Good luck!

I recommend this book, https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316. Cambridge University has a well-known math program, and they have made several resources on how to study math public. Ideally, you'd want to get various ideas and test them out.

• Knowing and Teaching Elementary Mathematics, by Liping Ma. Compares how a group of math teachers from China and a group of math teachers from the US think about concepts and teaching. This book really demonstrates how deeply you can think about even the most elementary mathematical topic.
  
  
• The Teaching Gap, by Stigler and Hiebert. Compares and contrasts teaching practices and teaching philosophies in the US, Germany, and Japan.

If you have a 600+ in math, I suggest getting this book:
https://www.amazon.com/Math-Lessons-Improve-Score-Month/dp/1519617372/ref=pd_lpo_sbs_14_t_0/134-8109725-5809825?_encoding=UTF8&psc=1&refRID=WN2TSZPQRMJ94F2NAAHD

This is the book I used to prepare, and it helped a lot. He has three books, for beginners, intermediate, and advanced.

Good luck on the SAT!

No problem! I'm very happy to pass this stuff on to those at your stage, given how much these and similar books helped me. There is another I should mention too: Letters to a Young Mathematician - Stewart. I doesn't cover any mathematical topics, but it does give a window in to what mathematics is like in higher levels. It helped me when deciding to apply for mathematics at Uni.

I don't have digital copies, and I don't know of anywhere that does. If you're in the US, the official book is only $12 from amazon, and it's well worth it:

http://amzn.com/0874477727

Find a copy of 101 Careers in Mathematics and look through it.

You may also be interested that a math major is among the best for taking the MCAT and LSAT (for medical school and law school, respectively).

Specific to your situation, I would concur with the other posters that say that upper-division mathematics is quite different from lower-division, and this difference scares some people away. You should try some courses and see for yourself!

I used Liping Ma's Knowing and Teaching Elementary Mathematics when I homeschooled my kids and still refer to it in planning remediation activities as a high school math teacher in an alternative school now.

These are the study materials I ordered:

• CliffsNotes Math Review for Standardized Tests
  
  
• Cracking the New GRE with DVD by Princeton Review
  
  
• 30 Days to a More Powerful Vocabulary by Wilfred Funk, Norman Lewis
  
  
• New GRE 2011-2012 Premier with CD by Kaplan
  
  
• Barron's New GRE, 19th Edition
  
  
  

Like Ptolemy you've probably heard there aren't any secret study hacks or Royal road, see how much help your department advisor is, poke around mathSE soft-question tags and focus on what you can learn in the next hour: https://math.stackexchange.com/questions/tagged/self-learning?sort=votes&pageSize=15

-------

books on how to study math: Kevin Houston, Keith Devlin etc https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/ and https://www.maths.cam.ac.uk/undergrad/studyskills/studyskills.pdf

Maybe this helps http://calnewport.com/blog/2012/10/26/mastering-linear-algebra-in-10-days-astounding-experiments-in-ultra-learning/

Read this book: http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/ref=asap_bc?ie=UTF8

And work through this book in its entirety: http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_1?s=books&ie=UTF8&qid=1463201632&sr=1-1

I recommend this

one of his theories is that asians do better in math because they had to plant rice paddies in the past. Yes, that is the actual argument. No, i'm not taking it out of context. Yes, he ignores advanced horticulture in all other regions of the world to make this argument. No, the authors of the study he used to make the claim that asians are better at math don't believe that rice paddies are the reason for the achievement gap between countries. In fact, the principle investigators of the TIMS study wrote a book on the results of their study and make the case that professional teacher development plays a pivotal role in the achievement gap.

And shit like that is rampant in gladwell's books. Established and renowned researchers and experts in the fields he mishandles are regularly at odds with what he writes.

OK, confession time. I hated math from first grade on. I had a first grade teacher who took a dislike to me and stuck me out in the hall because I didn't understand how to add above ten. The humiliation was horrible and I suppose that set the pattern for the rest of my years in school, that I "wasn't good at math." As a sophomore in high school I was put in a remedial class, dropped out of chemistry (I was fairly good at science in general, but the math stopped me cold).

I didn't really have anything else to do with learning math until I was in my forties and took some real estate and property management classes at a technical college. It turned out that math is used in real estate all the time, from calculating mortgages, square footage of properties, figuring out taxes, and so on, and though I decided not to go into it as a profession I learned that I was actually pretty good at doing the math after all since I was motivated to learn the subjects.

Flash forward to the present. I'm just finishing the school year home schooling my eight year old daughter. My wife had been doing it but I took over in 3rd grade. We started the year using the Saxon math course for 3rd grade, but my wife had had so much push back from my daughter the previous year that we went through some horrible battles just trying to pick up from where she left off. Finally I said fine, we'll concentrate on practical, real life application kinds of things. Measuring. Using cash in a business - making change, tallying receipts, and so on. We used a chalkboard and I had her work out problems on it. She can now do addition; subtraction; multiplication; division (including long division of large numbers); adding, subtracting, multiplying and dividing using fractions and decimals, measuring weight, volume, and distance, do squares and square roots. I occasionally check our work on a calculator but mostly we check it against itself, and she never uses one. Frankly I have been learning or relearning a lot of this a few steps ahead of her, and I improvise a LOT, trying to explain things however I can do it. Sometimes I let her be the teacher and I play the dumb student who just can't seem to get it.

Interestingly, there is a book called Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States in which the author, who is Chinese, finds through data analysis that most US math teachers actually don't understand elementary math principles very well and consequently don't know how to teach the concepts. One of the observations was US teachers teach rote formulas without actually being able to explain mathematically what is being done or why you'd want to do it in the first place, which would go a long way towards explaining why US schoolchildren don't do well compared to students from other countries.

Where did you get this? The things I've read suggest that chinese classrooms focus more on understanding than US classrooms. e.g. this.

Keep in mind that the creators of CrackACT have no credentials and the material may not be similar at all. Also, test prep books often have really good explanations, which could help you understand the problems better.

I recommend this book for math: https://www.amazon.com/gp/offer-listing/1936214601/ref=olp_f_used?ie=UTF8&f_new=true&f_used=true&f_usedAcceptable=true&f_usedGood=true&f_usedLikeNew=true&f_usedVeryGood=true

Is your class for the SAT subject tests? You can use the CollegeBoard book (http://www.amazon.com/dp/0874477727), but there are only two practice tests in it and not very many extra questions. If you have a lot of your own notes and/or practice problems, this could be a great book because it's actually written by the CollegeBoard and uses previous tests.

If it's for the general SAT math sections, I'd definitely recommend the CollegeBoard book (http://www.amazon.com/Official-SAT-Study-Guide-2nd/dp/0874478529/ref=sr_1_1?s=books&ie=UTF8&qid=1376237363&sr=1-1&keywords=official+sat+study+guide). I'm an SAT tutor and love using this - I can teach my own strategies and assign practice problems from previous SAT tests. There's 10 full-length previously administered practice tests, so there's plenty of material. I have a syllabus with 8 general lessons and homework, and there are still enough sections to have up to a month's worth of practice before the test.

I've been tutoring for six years now (and I used to teach classes for a large test prep company) so if you need any help I'd be glad to give you some pointers. Good luck on your class!

I'm happy to answer any questions! I'm in Social Industrial/Organizational Psych, which is an unusual combination but it's very interesting and fun stuff to learn. Social Psychology is all about examining persuasion/social influence, small group dynamics, social cognition (how people conceptualize their relationships and interactions with others), etc. I/O is business psychology. It's largely about how to design work environments such that workers are happy and productive. I/O is more my special interest. People with degrees in I/O often go on to work in HR or consulting firms. I'm currently planning to go into academia (to be a researcher/professor, meaning I'll need my Ph. D, not just a master's), but it's both extremely competitive and doesn't pay as well as consulting. For my thesis, I'm developing a scale to measure workplace interruptions. I'm interested in how people aren't able to get into a good flow at work, and how the modern workplace has tons of interruptions with higher presence of technology (email alerts) and with the fashion of open space floor plans in offices that encourage people to interrupt one another (as opposed to having offices with actual doors that can close).

Notes for how to apply to grad school:

1. Figure out what your flavor of Psychology is
   
   
2. Pick howevermany programs you want to apply to
   
   
3. Take the GRE
   
   
4. Ask for letters of recommendation
   
   Deadlines for Fall 2014 are often in December 2013, so you might want to consider getting your applications together nowish. You need to figure out what field you want to go into. Clinical Psychology is extremely competitive, just to let you know. Go to career counseling at your college to figure out your particular flavor. Do "me-search" - what is it about your own life that you're endlessly fascinated by? Go study that in grad school. For me, it's introversion and interruptions. I wanted to know why I flip the fuck out when I'm interrupted. Many research psychologists are studying things about their own lives - things they're personally either really good or really bad at, for instance.
   
   One of the biggest things you need to decide is whether you want to do research or do applied work. If you like statistics or even just don't mind them, go into research. If you don't, stick with a school with an applied focus. Big state schools are generally research universities, and small private colleges generally have an applied focus (and are much more expensive to attend). Keep a spreadsheet of all the schools that you want to apply to.
   
   I applied to 10 schools and got into 3. I had like a 1320 on my GRE and a 3.7 GPA, but practically no undergraduate research experience. 10 applications ended up costing me about $500 in application fees, so think about that now and set aside some cash. It took me about 40 hours of work to get all those applications done, and I'm a fast worker. The school I chose is a big state school, the only state school I applied to. I wish I had applied to more, though, because state schools are the ones that really fund their students. I have guaranteed free tuition for as long as it takes me to get my degree with a cap of like 9 years, but I want to be out in 6. I'll get both my master's and my phd during these 6 years. I get a monthly stipend that's about $1,100, which isn't a lot, but combined with the free schooling - I'm not complaining.
   
   You're going to want to study for the GRE. Study for at least a month. Take a practice GRE test to find out where your difficulties lie. If you're like me and need to brush up on non-statistics math, look into using this book - it's perfect. Check out those reviews, they explain why I loved it so much.
   
   When you ask for your letters of recommendation, you need to be organized. You need to give people at least 6 weeks (maybe even a few months would be good) before the deadline. This is the main reason why you should get started nowish - remember, December is the deadline for a lot of programs. I gave my professors a packet that included: 1) A letter about myself, my accomplishments, my GPA, what I want to do, for them to reference while they wrote my letters. 2) Each school's form for letters of rec, already filled out. 3) Addressed envelopes with stamps. 4) A letter with instructions and copious thanks that included a list of the 10 schools with a check mark next to each one.
   
   The application process serves as a weeding out process for universities. Many more people start applications than finish them, because it's fucking complicated. But if you approach it with the right attitude and determination, you can do it! You will find the program that's right for you. Not all programs are like mine - you can find tons of different master's programs that are just a couple years and you're out. Best of luck!
   
   Oh, and also check out [impostor syndrome] (http://en.wikipedia.org/wiki/Impostor_syndrome) - it's a big block for many people in graduate school, so be aware of it!
   
   If you've read this far, I commend you - one final thing. Grad school has been hands down the best educational experience of my life, and all the work I put into soul searching and finding my niche has totally paid off. All my peers are fucking brilliant. Do it - it's hard but I'd totally recommend it!

I ordered this book based on the excellent reviews and the tons of recommendations I've gotten https://www.amazon.com/gp/product/1936214601/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1

Alright I'm definitely gonna pick that up! Do you by chance know which of these two books is best for the math section? -

28 new sat lessons
http://www.amazon.com/gp/aw/d/1519617372/ref=pd_aw_sbs_14_2?ie=UTF8&dpID=51OZj4HZNIL&dpSrc=sims&preST=_AC_UL130_SR130%2C130_&refRID=1J3CK98RW3DFBHBHP4YQ

PWN the SAT math guide
http://www.amazon.com/gp/aw/d/1523963573/ref=ox_sc_act_image_2?ie=UTF8&psc=1&smid=ATVPDKIKX0DER

If not its cool but thanks!

Lara Alcock How to think about Analysis, How to study as a Mathematics Major

Define "being a mathematician" because the job market is fantastic at the moment for people with MAs, Ph.Ds, and even BA/BSs in math. Data science, quantitative analysis, actuarial science, or algorithmic trading, to name a few, are all jobs that if you have the chops and maybe a bit of coding experience are available. I'd consider anybody working in those positions a mathematician, as their daily work is going to involve a good bit of mathematical machinery. Maybe take a look at this book if you need inspiration.

The job market in academia on the other hand is extremely competitive, and if you haven't started on grad school yet, I don't have any hard evidence to back this up but I think you may be running out of time to achieve that, especially if you want to start a family, etc. So if you define being a mathematician as being a researcher in academia, you're right to be scared, and taking the risk is going to be a tough call. But if you feel like the inability to be a research mathematician means you have to work "crap jobs," rise above that - there are plenty of fine jobs out there that use math that are a hell of a lot easier to attain than academia. Even if you make it through grad school and find yourself not able to enter academia, a Ph.D is well respected in industry and unless you studied a very esoteric topic, you'll be easily employable.

Not gonna tell you how to live life, or what your current situation is though. It's your call in the end.

ACT Prep Black Book, Ultimate Guide to the Math ACT and Top 50 ACT Math Skills for a Top Score are used by lots of students and tutors. I won't recommend you reading the whole book though. Smart prep is all about finding your weak knowledge points first through practice and work on those specific skills through targeted and focused practice or reading related materials to fill the content gaps.

figure out what you're weaknesses are by taking practice tests and target those. here are my book recommendations:

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Math: Dr. Chung's SAT Math

English: Erica Meltzer's Grammar Book

Reading: Powerscore Reading Bible

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Also, I feel like if you're prepping for the PSAT you might as well just take the SAT

I used to tutor ACT back in the day and found this book really helpful for students struggling to remember math concepts from a few years prior. CliffsNotes Math Review for Standardized Tests, 2nd Edition (CliffsTestPrep) https://www.amazon.com/dp/0470500778/ref=cm_sw_r_cp_api_sscZxbMXVF5MM

Ich fand das Buch hier ganz hilfreich: Einstellungstest Bundeswehr: Fit für den Eignungstest im Auswahlverfahren | Sprache, Mathe, Wissen, Logik, technisches Verständnis, Konzentration und mehr | Über 800 Aufgaben mit allen Lösungswegen https://www.amazon.de/dp/3956240650/ref=cm_sw_r_cp_apa_i_8-8sDbGPYJKJ0

Die Tests im Internet waren für gewöhnlich immer nur ausgewählte Fragen und, wie mir scheint, damit nicht umfassend genug.

https://www.amazon.com/Math-Myth-Other-STEM-Delusions/dp/1620970686

1)https://www.amazon.com/ACT-Prep-Black-Book-Strategies-ebook/dp/B00K6L2L9Q/ref=pd_sim_351_1?ie=UTF8&dpID=51fhqm2hBrL&dpSrc=sims&preST=_UX300_PJku-sticker-v3%2CTopRight%2C0%2C-44_OU01_AC_UL320_SR248%2C320_&psc=1&refRID=VFKQ5W3ADG88DD77P1HJ
2)https://www.amazon.com/gp/product/B01FWOROA2/ref=s9_simh_gw_g351_i4_r?ie=UTF8&fpl=fresh&pf_rd_m=ATVPDKIKX0DER&pf_rd_s=desktop-5&pf_rd_r=B3XBC5AH9V5FV6PN42XN&pf_rd_t=36701&pf_rd_p=cca70e28-a3b0-4f0d-b847-0ae9cb54558a&pf_rd_i=desktop
3)https://www.amazon.com/gp/product/B007ZFIJPQ/ref=s9_simh_gw_g351_i12_r?ie=UTF8&fpl=fresh&pf_rd_m=ATVPDKIKX0DER&pf_rd_s=desktop-5&pf_rd_r=B3XBC5AH9V5FV6PN42XN&pf_rd_t=36701&pf_rd_p=cca70e28-a3b0-4f0d-b847-0ae9cb54558a&pf_rd_i=desktop
4)https://www.amazon.com/College-Pandas-ACT-English-Advanced/dp/0989496406/ref=sr_1_7?ie=UTF8&qid=1467451882&sr=8-7&keywords=ACT+english
5)https://www.amazon.com/Ultimate-Guide-Math-Richard-Corn/dp/1936214601/ref=sr_1_8?ie=UTF8&qid=1467451882&sr=8-8&keywords=ACT+english

and if you need help with reading comp try this one : https://www.amazon.com/Complete-Guide-ACT-Reading/dp/1496126750/ref=sr_1_1?ie=UTF8&qid=1467452199&sr=8-1&keywords=ACT+reading. I haven't read this book, but I heard people say good things about it.

Hard to say without knowing your exact course (is it taught or research based?). Speak to your supervisor and/or current students to get an idea of what you'll be doing. If you can, read some relevant and current academic papers to get a grasp of where you have gaps in your knowledge.

I also recommend 2 general books:

• All the mathematics you missed (but need to know for graduate school) - concise and obviously geared towards the post grads. I'd suggest this first.
  
• Maths: A student's survival guide - Big and friendly. I used it during my undergrad as I had not taken mathematics at A level and keep it around.
  
  There are probably better books for you depending on what you'll be doing. For example, my particular research involves multivariate analysis, so I have a variety of dedicated statistics books, including course materials from another school that teaches relevant topics.
  
  I would suggest you find out more about the work to come (courses and schools can vary quite a lot), get one of those books and learn the maths you need as you go along.

For math, we love these books

My pleasure, I am sure that you will find much pleasure in learning math and that it will be a very rewarding experience for you.
I personally always have been interested in math but never had the discipline to truly master it when I was young.
I finally decided to go back to school 3 years ago at the age of 31 and had to start back at the beginning by reviewing my algebra and trigonometry.
I'm now completing my Calculus 3 this semester, I have grown tremendously since the beginning of this wonderful journey and wish I had taken that decision sooner.
My best advice is DON'T BE SHY TO ASK FOR HELP, BE PATIENT AND DON'T GIVE UP you'll be very happy you did.

I recommend you read the following book : Letters to a Young Mathematician by Ian Stewart
https://www.amazon.com/Letters-Young-Mathematician-Mentoring-Paperback/dp/0465082327/ref=sr_1_1?ie=UTF8&qid=1523505140&sr=8-1&keywords=letters+to+a+young+mathematician&dpID=41VlldpRAAL&preST=_SY291_BO1,204,203,200_QL40_&dpSrc=srch

It is not a math heavy book and will give you many insights into learning mathematics.

I wish you the best, have fun!

I'd recommend starting with this book:
http://www.amazon.com/Maths-Students-Survival-Self-Help-Engineering/dp/0521017076

It basically goes through all the math you'll need from basic algebra up to calculus.

https://www.amazon.com/Hard-Elementary-School-Glenn-Ellison/dp/1489507175

Lancelot Hogben Mathematics for the Million

History of Math, but very interesting

I especially second Apology and The Music of the Primes. Those were excellent reads.

I find that knowing the historical context in which different leaps were made in mathematics tends to impart momentum to my interest. The stories are wonderful. A lot of these stories are contained in God Created the Integers, Hawking does a good job to write interesting bios of the original authors of the aforementioned seminal works.

I might add a couple of books, one that I think especially applies to somebody in high school considering a venture into math at university:

Letters to a Young Mathematician and Why Beauty is Truth . Both are by Ian Stewart

Sometimes it's nice to have a ton of worked examples, so you can get to the point where you don't even have to think about what to do next-- it'll be muscle memory.

The best thing I've found for that is Schaum's Outlines. Here's the one for Elementary Math, which I think has fractions in it. It'll give you a quick, clear explanation of the rules of the process and then give you tons of problems and all the problems have answers in the back, with all the steps worked out. They're only like $15, too, and there are ones for pretty much every subject in math and a lot of science.

I like Khan Academy, but there are never enough problems. It just gets you to the point where you understand the concept, but have to work hard to remember the topic when you need to use it. That's not very helpful for tests or in practice.

Good luck!

For the Mathematics for the Millions there are two books. Is it this one or this [one?] (https://www.amazon.com/Mathematics-Million-Lancelot-Hogben/dp/1291585451). Also, I read the Amazon description for Mathematics for the Nonmathematician and the book itself seems a bit advanced for me. However, it does seem like a fascinating read. You've had this book so tell me, is great for even a beginner or is designed for someone with more advanced mathematics skills?

I took a long, long break between undergrad and grad school (think decades). I found this GRE math prep book very helpful. (The GRE math section tests high school math knowledge), I'd take the sample tests, see where I fell short, and focus on understanding why. I also found Practical Algebra to be a good review-and-practice guide, for the fundamentals. I boned up on discrete math by buying an old copy of Rosen and the matching solutions guide. And, I watched a bunch of videos of this guy explaining various facets of the math you need for computer science.

5 Practices for Orchestrating Productive Mathematics Discussions

Start. Right. Now.

I used this book: https://www.amazon.com/Math-Lessons-Improve-Score-Month/dp/1519617372/ref=asap_bc?ie=UTF8


These Erika Metzler books: https://www.amazon.com/3rd-Ultimate-Guide-SAT-Grammar/dp/1511944137/ref=sr_1_2?s=books&ie=UTF8&qid=1500323642&sr=1-2&keywords=erika+meltzer+sat

https://www.amazon.com/Critical-Reader-2nd-Erica-Meltzer/dp/1515182061/ref=sr_1_1?s=books&ie=UTF8&qid=1500323642&sr=1-1&keywords=erika+meltzer+sat

Sadly, that is not the case.

Mathematics for the Millions was recommended to me. It walks through the history of math and builds upon principles similarly to how we learned them over time.

> Income for the average American is not keeping up even remotely with education, health care, and real estate costs.

You should have a source for all of this. real estate is the only one for which I see costs ballooning and that's typically regional. For instance, most people in texas should still be able to afford a decent starter house. You have a point with highly populated parts of cali for instance, but there still exist many low housing price locations.

>the notion that a congressman thinks there is nothing for him to work on is straight nonsense.

This is why i'm unsure that you're interpreting him correctly. Because even to just keep us still, that takes work.

>Social security is insolvent.

Kind of. Choice quote: "under the worst-case scenario, meaning that a poor economy in coming years deprives the system of money and no changes to the program’s financing are made, then Social Security recipients will find themselves getting smaller checks than they ought to."

SS will still be able to dole out checks. Just not as big as they promised. it's not entirely insolvent. And the solution is rather simple. Increase revenue or decrease benefits. It's not as if we're doomed to just watch as the fund goes to mush. There's a reason even republicans are hesitant to cut benefits. because the old vote is so influential. So things will happen to address SS insolvency if not earlier, then at the 11th hour, like it always does.

>American public schools are continuing to fall behind the rest of the world.

depends on who you measure and how you measure. for instance, white affluent kids in the US do as well as the top kids from the top countries in the TIMS study. Also, most education researchers don't point to our relative ranking (which is actually rather mid to high tier) and fret. It definitely points out that there are things to improve, but it's not even close to being an apples to apples comparison. for instance, japan scores higher than us in math for 8th graders. Consider the stakes of their standardized tests and the age at which those types of tests are administered in japan versus the US. US students don't have an equivalent and equally life altering pressure to excel at the time that japanese students do due to differing social conventions and institutional policies. Japan has one of the higher suicide rates in the world. There's a lot about this discussion that should not be reduced to a bumper sticker of comparative rankings. In fact, the principle investigators of the TIMS study point to teacher professional development as one of the biggest reasons for the gap. they wrote a book on it.

>Money is poring into politics at an unprecedented rate.

honestly, that gets a pretty big shrug from me personally. trump has proven how ineffective money is in this race. sanders as well. Sanders ended up outspending clinton in the trail end of his days pretty substantially. also, it's fairly well documented that in higher level races (e.g. federal), money plays an extremely limited role. also, that there are diminishing returns and counteracting forces upon large scale donations. You're right that more transparency would be ideal, but money isn't quite as absolutely corrupting as people believe it is.

also, please don't link the princeton oligarchy study. it does not establish causality in any way and there are obvious alternative hypotheses that are just as convincing (e.g. smarter people are more likely to converge on certain issues and are more likely to earn more) based on the evidence.

>Even UN officials are calling the war on drugs a global disaster, but we continue to bury our heads in the sand and send people of color to jail for decades for mere possession but let white rapists get our after 6 months (Brock turner).

Point noted and agreed about drug policy. I think the comparison is kind of hamfisted, but it's a provocative point. i don't disagree.

>Since 2010, congress has produced far less legislation than normal. The last couple congresses have been the most unproductive in history. Government has grinded to a halt.

good governance isn't necessarily fast governance. i agree that partisanship, gridlock, and obstructionism aren't ideal. I'm sure we both feel the same way about the debt ceiling crises. And that's why i think it's crucial to move against behavior that resemble the M.O. of the tea party. moderate republicans like paul ryan, although incredibly stoogey right now in their support of trump, can actually be quite smart, sincere and passionate in their beliefs for reasons unrelated to personal gain. What i mean to say is that this stuff is complicated. The tea party rejects that and opts for simple, "truths." And that's why we should likewise reject tea-party reminiscent methodology on our side of the aisle.