The Art of Problem Solving, Vol. 1: The Basics Paperback – August 1, 2006

This book (and most likely the entire series) is fantastic. Concepts are explained fully and in the logical ordering necessary to build upon one another. Furthermore, mathematical properties (e.g. the fact that raising a non-zero number to the zeroth power is one, the divisibility shortcuts for some numbers, etc.) Are never hand-waived; the logic and proof of each concept is demonstrated.The lessons are rather dense, and the problems require more thought than the average math textbook's practice sets, but I feel that this actually makes the problems more engaging and less tedious. Do not be fooled by the "lower" page count. This book is absolutely worth it.A friend of mine, who recommended the series, was worried that her homeschooled child would be unable to pass standardized tests with just this course of study. I argued that her brilliant child didn't need to be stifled by a "standard" curriculum, and that she should instead supplement The Art of Problem Solving with instruction specifically aimed at test-taking strategies for standardized math tests. The knowledge expressed in The Art of Problem Solving is TRUE mathematics, and is more valuable than the goal of high marks on the SAT.

Sandor Lehoczky and Richard Rusczyk have done us all a tremendous favor. They have laid out the concepts in an incredibly clear learning path, and the volume covers the gamut of elementary and intermediate mathematics topics. In addition to the breadth of material is the tantalizing depth of material that the authors have taken time to draw from various mathematics mathematics competitions. In fact, I'd be confident to say that no high school curriculum or standardized test would pose a challenge to any student who has mastered the first volume of this series.When my friends ask for recommendations on educational books for their children, I am always sure to include this series. Even though I majored in economics and mathematics, I still have an incredibly fun time working on a few of the more challenging problems; I could only wish that I had been introduced to this book when I had first started learning math. This book is truly an invaluable resource.Richard and Sandor - thank you.DanielYale Class of 2014

I bought this book for my middle school kid whose level of math is a little beyond the normal class in school can offer. This is a very solid book for studying advanced math concepts in middle/high school math. The layout of each chapter is very clear, and it is not that difficult to learn the challenge concepts since each topic starts with pretty basic material and advances to the more difficult level. Unlike lots of math book, the instruction is to the point and the logic is clear. Even if you are not planning to attend math competitions, this is a good book for anyone interested in math. Being a professor in the engineering field and having a pretty good math background, I enjoy reading this book because being able to conquer some of the problems in the book gives me satisfaction. If you are planning on getting good score in math competitions, be serious about the exercises and the problems in the book. Those problems are on the right track.

This book explains in great detail what I have learned, it is very helpful for my children to learn.

My kids really enjoy the way it explains

At times it feels to me that this is a cheat book for the AMC, since it covers so many theorems that are used directly on the contests. More importantly though, this is a great book for any high school student to take their understanding of math to the next level. It covers a very wide range of topics and does not hesitate to talk about proofs and mathematical rigor, which are some things that may never appear in the standard curriculum.

I originally bought this book just to help me learn a few math techniques for school and math competitions, but soon realized that it was much more. Honestly, I would have to say that this book is really beneficial to almost anyone who wants to improve in mathematics. Not only are the theorems the book teaches valuable, but the problem solving skills that you learn through reading and working on problems is amazing!

I believe I've reviewed this book and vol. 1 in another area but amazon doesn't agree. this book is fantastic-particularly if you need a review of "basic" concepts. We found it when looking for a review book for the college testing but I notice it continues to have its place among college textbooks.