Reddit mentions: The best study & teaching mathematics books

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!

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!

> 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.

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!

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!

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?

I'd say focus almost exclusively on the MC for the writing section, since the essay isn't nearly as important as people think. I was actually thinking of starting an SAT essay subreddit to practice critiquing essays because that is something I could use practice with to get better at.

Reading is the hardest section to raise your score in, and you're already in the 92nd percentile. Therefore, the return on investment for any studying that you would do for the reading section is quite low. But if you're trying to get in a top 20 college, it might be worth a little studying with these:

• The Direct Hits series is quite good for vocab
  
• The author of the Ultimate Guide just released a book for the critical reading section literally today. It's probably excellent, but I can't wholeheartedly recommend it yet
  
  For math, it's a similar problem; you're in the 96th percentile, so you don't have much room to improve. That said here are some resources:
  
  
• I'm a huge fan of PWN the SAT, and here's his book
  
• Much of the information in the book is available for free on his website
  
• I've heard good things about this book, and the kindle version is on sale for $3 today
  
• Dr. Chung's book is great if you need to drill exercises
  
  75% of your studying time should be devoted to the writing section.

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).

You need some grounding in foundational topics like Propositional Logic, Proofs, Sets and Functions for higher math. If you've seen some of that in your Discrete Math class, you can jump straight into Abstract Algebra, Rigorous Linear Algebra (if you know some LA) and even Real Analysis. If thats not the case, the most expository and clearly written book on the above topics I have ever seen is Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.

Some user friendly books on Real Analysis:

1. Understanding Analysis by Steve Abbot
   
   
2. Yet Another Introduction to Analysis by Victor Bryant
   
   
3. Elementary Analysis: The Theory of Calculus by Kenneth Ross
   
   
4. Real Mathematical Analysis by Charles Pugh
   
   
5. A Primer of Real Functions by Ralph Boas
   
   
6. A Radical Approach to Real Analysis by David Bressoud
   
   
7. The Way of Analysis by Robert Strichartz
   
   
8. Foundations of Analysis by Edmund Landau
   
   
9. A Problem Book in Real Analysis by Asuman Aksoy and Mohamed Khamzi
   
   
10. Calculus by Spivak
    
    
11. Real Analysis: A Constructive Approach by Mark Bridger
    
    
12. Differential and Integral Calculus by Richard Courant, Edward McShane, Sam Sloan and Marvin Greenberg
    
    
13. You can find tons more if you search the internet. There are more superstars of advanced Calculus like Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra by Tom Apostol, Advanced Calculus by Shlomo Sternberg and Lynn Loomis... there are also more down to earth titles like Limits, Limits Everywhere:The Tools of Mathematical Analysis by david Appelbaum, Analysis: A Gateway to Understanding Mathematics by Sean Dineen...I just dont have time to list them all.
    
    Some user friendly books on Linear/Abstract Algebra:
    
    
14. A Book of Abstract Algebra by Charles Pinter
    
    
15. Matrix Analysis and Applied Linear Algebra Book and Solutions Manual by Carl Meyer
    
    
16. Groups and Their Graphs by Israel Grossman and Wilhelm Magnus
    
    
17. Linear Algebra Done Wrong by Sergei Treil-FREE
    
    
18. Elements of Algebra: Geometry, Numbers, Equations by John Stilwell
    
    Topology(even high school students can manage the first two titles):
    
    
19. Intuitive Topology by V.V. Prasolov
    
    
20. First Concepts of Topology by William G. Chinn, N. E. Steenrod and George H. Buehler
    
    
21. Topology Without Tears by Sydney Morris- FREE
    
    
22. Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev and and V. M. Kharlamov
    
    Some transitional books:
    
    
23. Tools of the Trade by Paul Sally
    
    
24. A Concise Introduction to Pure Mathematics by Martin Liebeck
    
    
25. How to Think Like a Mathematician: A Companion to Undergraduate Mathematics by Kevin Houston
    
    
26. Introductory Mathematics: Algebra and Analysis by Geoffrey Smith
    
    
27. Elements of Logic via Numbers and Sets by D.L Johnson
    
    Plus many more- just scour your local library and the internet.
    
    Good Luck, Dude/Dudette.

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

It's a common occurrence in mathematics to come across some Greek you don't know, which then means that you'll have to do "the usual yoga" -- make up exercises and examples until you've worked yourself into whatever you're looking at, as opposed to expecting to understand everything by reading about it.

From what you say I infer that you can do and have done that, as such I doubt you can really put yourself into the mother's shoes -- because this fundamental stumbling block of not learning a thing because you believe you can't ever learn it vanishes once you've had the experience that with some yoga, everything can suddenly very well work out.

How can you invest time and effort into understanding something if you haven't learned that you can understand things that way?

That's btw also why not few people who aced maths in school drop out of maths at university: The smarter you are and the easier and "obvious" things for you are in school, the less likely are you to actually develop that skill. If then on top of that you're arrogant enough to miss the pointers your professors throw at you, you've set yourself up for failure.

Raw intelligence without grit and the wisdom of how to apply it to things amounts to little. And makes you quite likely to end up linked on this sub. Have grit and sufficient wisdom, however, and it doesn't matter much how much raw intelligence backs it up, you'll excel in one way or the other.

---

Thinking about it, I guess /s would've been a better choice than :) in my previous post. I do get it, I just have enough practice to usually overlook that path.

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.

That's a fair point tbh. A lecturer at my uni specialises in undergrad maths education so she really knows how students learn best. She actually gave us a document of a chapter on time management from her book on how to study for a maths degree, but I have to be honest, I haven't read it yet. If anyone's interested it's this one. We also have a Maths Learning Support Centre where we can drop in and ask lecturers for help on something, not like office hours.

Is it required? Not in all roles, but definitely can be depending on what you're doing. I used vector maths pretty much daily, not the most complicated area of maths but still.

Is it worth limiting yourself because you neglected to learn relatively simple maths? Definitely not.

Maths is not scary, it's just a very hard topic to teach to everyone (everyone learns differently and at different paces) and when you fall behind it feels impossible since you've missed a step in your learning. As an adult, you can teach yourself fairly easily.

If you want a decent start to it all I can recommend this book - https://www.amazon.co.uk/gp/product/0521017076/, it's not written like most maths books which target mathematicians, rather tries to target engineering students and those who aren't necessarily so mathematically inclined. Helped me loads during university doing a Games Programming course which had a fair bit of maths involved.

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.

Have you taken the full physics series? If not my recommendation is to do that. In my opinion, if you have a good grasp of applied math and physics lots else (engineering, bio-mathematics, operations research) will follow pretty easily. I don't think that there's any need to go too focused at the undergrad level. Take the applied math, and take some of those biology courses too since that's an interest. Don't be afraid to stay another year and keep taking classes if you can afford it financially.

I also recommend you check out the book 101 Careers in Mathematics for some ideas about what else may be out there.

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?

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!

I have rarely had an easy time with math. I think somehow Calc III went rather smoothy. Despite this I eventually received an MS in Environmental Engineering. I am certain my inclinations and talents are verbal. Note that I actually try to expose myself to more math, though with work, side jobs and hobbies I have little time for that.

True, what I wrote is all about myself. As to your question: you cannot control natural talents, and can only control your exposure to novel ways of learning. I'd say that in your case, if you want to become better in Mathematics, then just keep plugging away. I recommend Mathematics for the Million. That presents a historical perspective on the subject, which might be more to your liking.

Good luck tmrw! You've got this!

Just to clarify bc you listed 3 CB scores I thought you had the CB Math 2 book with 4 exams. It's PT 1 and 2 in the 4 exam Math 2 book that are the most recently released exams. If you have the older 2 exam CB Math 1 and 2 book, PT 1 is still pretty accurate but PT 2 is not (it's from 1995 despite being republished in a book with a more recent copyright). Hope that's clear.

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!

Math content knowledge on a subject is pre-requisite to pedagogical knowledge. If a teacher can't divide fractions, xe won't be able to effectively teach xir students how to divide fractions either. This point was highlighted in Liping Ma's book that has been making the rounds in math ed community.

You are right that just knowing how to divide fractions doesn't mean that you can effectively teach it; that's where the jingle "ours isn't to ask why/ just invert and multiply" came from: well-meaning teachers who are trying the best they know how to get their students to pass the tests.

When Borders was closing, I was studying for 5161. I picked up several books absurdly cheap. Most of them were crap, but the Cliff Notes one was so good that I actually kept it as a math resource. The topics were clear and well organized, and the practice tests were the most helpful of all the simulations that I took.

If you want to only teach middle school, do the middle school math Praxis. It might hinder your flexibility later if you want to move up later, but at least you'll get started. Additionally, as a math teacher, you shouldn't have as much difficulty finding a job.

However, I strongly encourage you master topics above the level that you teach. It'll give what you teach context, and you'll know what you're preparing your kids for. I didn't take that much calculus and no stats in college. You bet I had to study my ass off and practice to teach myself in preparation for 5161.

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.

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.

I'd suggest this mathematics resource book by Van de Walle and colleagues if you really want to understand mathematical concepts. It is really well-written, easy to read, based on mathematics education research, and even fun!

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 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.

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!

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

I wonder how much of it has to do with how the arithmetic is taught though. I read Knowing and Teaching Elementary Mathematics even though I teach high school because I found it fascinating. Basically it contrasts US elementary teachers with Chinese elementary teachers and the difference in approach to teaching the basic techniques is pretty amazing...

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.

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

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.

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.

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.

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.

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

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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/

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

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

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

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

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.

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.

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.

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.

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."

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.

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
  
  
  

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 recommend this

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.

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

​

Math: Dr. Chung's SAT Math

English: Erica Meltzer's Grammar Book

Reading: Powerscore Reading Bible

​

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

https://www.amazon.com/CliffsNotes-Praxis-Mathematics-Content-Knowledge/dp/0544628268/ref=sr_1_2?ie=UTF8&qid=1536453143&sr=8-2&keywords=praxis+5161 try this. Go through Khan Academy on areas you're weak in for a quick refresher. There are plenty of youtube videos on specific problems in regards to praxis 5161. YOU CAN DO THIS! good luck!

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.

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.

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

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

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.

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

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

Read this book.

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

• 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.

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