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Its not a textbook, but I used it to supplement my textbooks: khan academy. Great videos on a wide array of math and science topics, from very simple to stuff I learned in 3rd and 4th year.

For actual book, I learned using Calculus Early Transcendentals by James Stewart. It was a good book. Used it for close to two years, and still have it for reference.

Best of luck in your studies

I thought it was pretty good. There's a two page summary that I found that you can look through as well.

How To Solve It pdf

How To Solve It Summary

Superb! Thanks for the link; this guy is an earthly saint. For convenience, I decided to compile it into one PDF and bookmark the chapters--otherwise unaltered. Uploaded it 2 places in case anyone else would like to grab an all-in-one copy.

http://hotfile.com/dl/113704983/26eed37/Multivariable_and_Vector_Analysis_by_WWL_Chen.pdf.html http://rapidshare.com/files/456393972/Multivariable_and_Vector_Analysis__by_WWL_Chen.pdf

>The print version of the book is available through Amazon here.

I'm currently using this book in my Mathematical proofs class. It's very clear, concise, and has sample exercises in the back.

In addition, the book doesn't cost too much and the author has a very distinct sense of humor :)

Linear systems, especially ones with 2 variables, are covered in most ODE text books. Check if your library has Boyce & Di Prima but any number of ODE texts cover this topic well.

Cool idea but let me first let you know what's already out there.

b-ok.org or libgen.is both let you download illegally which is super great.

Second, on any given topic, there are lots of discussions about which are the best book. Google for example "best book for abstract algebra" and you'll get lots of recommendations with lots of reasons for them.

That's about how most people decide on a book. Maybe your site can improve upon the process.

Based on 'doodles [of] socrates' and 'taught mathematical thinking' it could be ['Thinking Mathematically' by Mason, Burton and Stacey|https://www.amazon.com/Thinking-Mathematically-2nd-J-Mason/dp/0273728911]. There's a book preview on amazon - check out page 'IX' from the preface if the doodle looks familiar to you.

Just to vouch: I recently bought a used physical copy of Operations Research (10th ed.) for just under USD$50 on Abe. It was 200 on Amazon.

AbeBooks+++

Looks like you may be a math major. You might consider Walter Rudin's Principles of Mathematical Analysis, which takes you through Dedekind cuts.

Look into catastrophe theory.

https://web.ma.utexas.edu/users/davis/375/popecol/lec13/catast.html

Catastrophe Theory and Its Applications https://www.amazon.ae/dp/048669271X/ref=cm_sw_r_cp_api_fabc_A8D4FbQ5RWY5M

For an introduction: a "discrete math" textbook might be helpful. When I took discrete math in undergrad, I used the text by Epp (a few editions ago). It was a nice introduction, and also covers some baseline information that's useful if you're starting entirely from the ground up (e.g. truth tables, methods of mathematical proof, basic set theory, etc). If you're more familiar with statistics-ish math, some introductory probability texts will also cover some combinatorics (I don't have a good recommendation off-the-cuff tho).

For a more in-depth, applied approach, Concrete Mathematics by Graham, Knuth, and Patashnik is a really great text. It has a fairly steep learning curve and is targeted at an upper-undergraduate level, particularly for computer science students (though I know CS grad students who would probably find it a challenge too), but you'll know a lot more than the basic "how to count balls in buckets" stuff from an introductory discrete math or probability text after going through it.

Based on how you're asking this question, I'd guess the above options should satisfy what you're looking for. But, if you're aiming for even more advanced books in combinatorics: If you want to approach it from an algebraic perspective, works by Stanley are really solid. From an analytic perspective, the gold standard is Analytic Combinatorics by Flajolet and Sedgewick.

Lang also wrote a separate book on Geometry for high school which is pretty good.

I use Dixit and Skeath's book *Games of Strategy* in my game theory course: https://www.amazon.com/Games-Strategy-Fourth-Avinash-Dixit/dp/0393124444

Is your objective to build a comprehensive understanding of the underlying topics of Calculus or is your objective to master quick problem solving, tricks, etc? If it is the latter I would suggest you pick this up as an auxiliary resource; Stuart is good but mastery of the mechanics of solving the problems will come only through ardent practice. You will need to see, and solve, a wider set of examples than is typically found in Stewart.

If your objective is the former I would grab this instead. Probably look for it on a used book seller's site like abebooks.com, though.

The Dover information theory book is also the same price.

Now I'm hunting for other Dover books I may want. Thanks!

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

For the Mathematics for the Millions there are two books. Is it this one or this one?. 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?

This might be a little below what you're looking for, but Mathematics: A Very Short Introduction is a nice general survey of the field and might point you in the direction of things to explore further.

Edit: a typo

My university used Briggs and Cochran's Early Transcendentals. Otherwise, try Khan Academy or Paul's Online Notes (it looks like his site just went through a revamp so I'm not sure how user-friendly it is now)

You could just get a ~$25 used copy of an advanced engineering mathematics text like this: http://www.amazon.com/dp/0471488852

I would suggest a version where you can "find" a solutions manual online that you can refer to when you get stuck, as there may not be a professor available that you can ask for help.

Going into that area, you should definitely read Strogatz's Nonlinear Dynamics and Chaos. Excellent writing. I linked to the third edition, which came out pretty recently, but you can probably find a second edition cheaply. This includes info on systems of differential equations and on discrete dynamical systems as well.

If your intro class did not get into systems (linear, nonlinear, and the connections between them via linearization at equilibria), you should probably read something like Logan's A First Course in Differential Equations, before you jump into Strogatz. Logan's text is not the most popular intro text out there, but it does a great job on systems (and I think the writing style is quite good, treating the audience a bit more as if they have brains). Blanchard, Devaney, and Hall is also good in this area (but tremendously more expensive).

As a physics student I struggled with pretty much every proof I had to perform until, in my final year, my university began offering a new course titled Intro to Proofs. Taking this class rekindled my love of mathematics and I've since reworked most of my undergraduate maths classes completing all the proofs in the texts.

The book that we used for that class was Mathematical Proofs: A Transition to Advanced Mathematics.

http://www.amazon.ca/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094

I really loved that class and the text was quite good. I enjoyed it more than Velleman's How to Prove It.

I took a class that was specifically dedicated to writing proofs, so I haven't personally read this myself, but I've heard a lot of people say good things about it.

At what level? Sutherland's Introduction is good. I also recommend Korner's lecture notes.