Putnam and Beyond

by Razvan Gelca, Titu Andreescu

This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics.  Putnam and Beyond  is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

Genres: Mathematics, Science, Textbooks

868 pages, Paperback

First published August 23, 2007

Reviews

[Klock Robbie · Rating 5 out of 5]

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[Pat Maloyan · Rating 5 out of 5]

Obviously a go to for Putnam prep, but beware that it gets very difficult quickly. The first chapter all the problems are gold, but as you go it becomes very abstract. The problems start to be best for A4/B4 and up. For I certainly first recommend "The art and craft of problem solving" by Paul Zietz for performing decently (top 500) on Putnam.

[Jędrzej Biedrzycki · Rating 5 out of 5]

Highly engaging, orderly and challenging book covering olympiad-level mathematics.

[NumberLord · Rating 4 out of 5]

An excellent collection of math problems, ranging from moderately easy to Putnam-level difficulty.