Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

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This is a very interesting book. If you have mastered the bare essentials of set theory (through the upside down A for ¡°for all¡± and the backwards E for ¡°there exists¡±), AND either 1) the bare essentials of combinatorics (through Pascals triangle), or 2) the bare essentials of number theory (through the definition of the Moebius function and the statement of the Chinese Remainder theorem), or 3) the bare essentials of geometry (through the law of cosines), AND if you are very talented in mathematics, then this book is a ¡°MUST READ¡±. It matters not whether you are a high school student or a professional mathematician. You will find new and fruitful insights and quite a few interesting problems in this book. For the beginner, there are several tantalizing (but somewhat oversimplified) references to advanced topics such as Paul Cohens proof of the independence of the continuum hypotheses and Wiles proof of Fermats last theorem. For the professional there are footnotes with references to

Dr. Jack Aiken, Jan 5, 2003

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