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.
From the reviews:
"This work contains carefully selected problems in Algebra, Real Analysis, Geometry and Trigonometry, Number Theory and Combinatorics and Probability. ... The book is mainly intended to offer the principal skills and techniques for solving problems in elementary Mathematics. ... The reviewer recommends this book to all students curious about the force of mathematics, especially those who are bored at school and ready for a challenge. Teachers would find this book to be a welcome resource, as will contest organizers." (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1122 (24), 2007)
"I enjoyed this book ... . Not just because of the collection of problems, but also because of their sheer scope and depth. This is a great collection which is extremely well-organized! ... This extraordinary book can be read for fun. However, it can also serve as a textbook for preparation for the Putnam ... for an advanced problem-solving course, or even as an overview of undergraduate mathematics. ... it could certainly serve as a great review for senior-level students." (Donald L. Vestal, MathDL, December, 2007)
“A 935-problem and almost 800-page super-problem book with solutions, whose reading would certainly challenge, attract, and keep really busy any undergraduate student interested in acquiring various problem-solving techniques. ... the array of remarkable problem books has gained a new addition that could be really useful to undergraduate students. ... a book about excellence in mathematics, coming from a long cultural tradition whose history and experience can only help us deepen our understanding of how mathematics could be taught in a more attractive and inquisitive way.” (Bogdan D. Suceavă and Jack B. Gaumer, The Mathematical Intelligencer, Vol. 33 (2), 2011)
