Problem Solving Russian Style

math circles book cover
You’ve read about the lack of proper problem solving in schools and you’ve even started thinking about a few recommended nonstandard elementary problems, now what? You could browse the Web looking for puzzles or math olympiad problems, but a much better approach would be to find a source of problems that is structured by topic, ability level, and that has been tested on tens of thousands of students of all backgrounds. Mathematical Circles: Russian Experience is exactly what you need. Most of the topics in this book, including parity, combinatorics, basic number theory, the pigeon hole principle, proof by induction, invariants, and inequalities often appear in math competitions, but the goal of this book is not narrowly focused on competition preparation. In some ways that would be just as bad as “teaching to the test.” The ultimate aim of Mathematical Circles (Russian Experience) is to start with quite simple problems that anyone can solve and then, in bite-size increments, increase the difficulty of the problems until a whole branch of mathematics has been introduced. The selection of the problems, the detailed guide for teachers, and the depth of coverage makes this book stand out among other great problem solving books. It is geared towards middle school and high school teachers who would like to enrich the standard school curriculum, but even regular students who don’t attend math clubs and competitions would benefit. In fact, we would recommend this book as the best form of standardized test preparation. Anyone who can solve at least a few of the problems in each of the sections of the book is, in our experience, ready to tackle the hardest SAT problem. As is typical for Russian math literature there are a few extra fun topics included, such as strategy games, that one rarely encounters in English-language books. If you’re looking for one book that contains a complete problem solving curriculum that has stood the test of time, this is a good place to start.

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