The Art of Problem Solving, Vol. 2: And Beyond

This book teaches math with problems and challenges you to solve them. It's full of topics, from trigonometry to matrices to partition numbers. This book is mainly designed for helping you with competition math, and it is great at that, but it is an excellent math book for any purpose. It's extremely well written, and the authors have definitely spent a lot of time making it the best they could. Just be warned the solution manual comes separately. It is well worth the money, especially if you can get a deal. It has great solutions that I didn't think of and I've thought "Why didn't I think of that" several times looking through it.

Man, this book is brilliant for AMC12, AIME, and the AHSME. This book can be used with concurrently with precalculus. Covered proofs, logarithms, trig, geometry, conics, polar coordinates, polynomials, functions, limits (great for a precalculus class), complex numbers, vectors (like things covered in calc 3), matrices, determinants, inequalities, combinations, sequences, series, counting (advanced), probability, locus, number theory, and even Diophantine equations and graph theory! Very satisfied with this book.

I was introduced to this book back when I was in high school, but now that I'm in college I still try to do some problems from there to keep my brain "in shape". I really recommend this to anyone, not just someone interested in math but in any technical field as it will greatly improve your problem solving abilities. I still have a long way to go!

This book meets all my expectations. It offers a great collection of challenging problems and shows how to apply elementary techniques in a creative manner. THX

Great book with clear explanations and reasonably manageable problems (not too hard, not too easy). Good for filling in gaps and working on the basics. Essential in my high school math career

Really works

Good book for kids. Well written. Classic book for learning essential math skills. I use it to teach my own kid.

As you can see, I bought two sets of these books. For the physics son and excellent daughter- quoting the latter: "if you didn't fully get math the first time these will do it for you. Also, you do not need to have done particularly well in math."