Customer Reviews

Matters Mathematical (AMS Chelsea Publishing)

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This is really a great introduction to many key fields in mathematics, e.g., number theory, permutations, group theory, finite geometry, game theory and infinite sets. The authors start from very basic concepts and do not assume very much mathematical background. This book also serves as an excellent first course on mathematical proofs. I particularly like the way the authors show how to explore and get insight into various proofs.

Just one caution: although the book starts from basic concepts and does not assume much prior knowledge, it does assume the ability to reason abstractly. In particular, many of the exercises (at the end of each section) are quite difficult. For example, the reader is asked to prove the general Chinese Remainder Theorem. The book does provide a proof for the case of two integers, but the general case requires a non-obvious trick. Some of the exercises would be hard to very difficult for junior or senior undergraduate math majors.