This undergraduate textbook with an emphasis on problem solving serves as both a study guide for the William Lowell Putnam Mathematics Competition and as an excellent transition book from high school problem solving to college level mathematical research. With numerous examples and problems with solutions that reflect the spirit of the Putnam exam, the work is structured topically to assist undergraduates in gaining proficiency across a broad spectrum of subjects (algebra, real analysis, geometry and trigonometry, number theory, combinatorics and probabilities) that comprise a core mathematics curriculum. From the authors of Mathematical Olympiad Challenges (Birkhäuser Boston, 2000), Putnam and Beyond fills a gap in the market for problem-based texts that specifically target the Putnam exams and undergraduate mathematics majors.

Putnam and Beyond 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 in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. 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.

Methods of Proof.- Algebra.- Real Analysis.- Geometry and Trigonometry.- Number Theory.- Combinatorics and Probability.