Putnam And Beyond Hardcover 2

Razvan Gelca

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 proof: 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

3319589865

9783319589862

English

Springer International Publishing AG

18th Oct 2017

850

Răzvan Gelca, Texas Tech University, works in Chern-Simons theory, a field of mathematics that blends low dimensional topology, mathematical physics, geometry, and the theory of group representations. He is also involved in mathematics competitions such as the mathematical Olympiads and the W.L. Putnam Mathematical Competition. He is co-author of 2 published books (with Titu Andreescu), namely “Mathematical Olympiad Challenges” and the first edition of “Putnam and Beyond.” In 2015 Gelca and Andreescu will also publish a monograph on Pell’s Equations.

Titu Andreescu

2