 Second edition includes new sections on quadratic polynomials, functions in real analysis, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory
 Second edition includes added problems and theoretical expansion of several sections
 Undergraduate textbook with an emphasis on problemsolving; driven by over 1300 problems
 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
 Fills a gap in the market for problembased texts that specifically target the Putnam exams and undergraduate mathematics majors
Buy this book
 About this Textbook

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
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 problemsolving 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 problemsolving 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.  About the authors

Răzvan Gelca, Texas Tech University, works in ChernSimons 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 coauthor 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, University of TexasDallas, is highly involved with mathematics contests and olym
piads. He was the Director of AMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and olympiadstyle mathematics including the first edition of “Putnam and Beyond” (with Razvan Gelca), “Mathematical Olympiad Treasures” and “Mathematical Olympiad Challenges” (with Razvan Gelca). Additional Springer publications include “Mathematical Bridges”, “Complex Numbers from A to …Z”, “Number Theory” and a new monograph on Pell’s Equations to be published in 2015.
 Table of contents (6 chapters)


Methods of Proof
Pages 123

Algebra
Pages 25105

Real Analysis
Pages 107209

Geometry and Trigonometry
Pages 211255

Number Theory
Pages 257290

Table of contents (6 chapters)
 Download Preface 1 PDF (49.7 KB)
 Download Sample pages 2 PDF (653.7 KB)
 Download Table of contents PDF (196 KB)
Buy this book
Services for this Book
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 Putnam and Beyond
 Authors

 Răzvan Gelca
 Titu Andreescu
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing AG
 eBook ISBN
 9783319589886
 DOI
 10.1007/9783319589886
 Softcover ISBN
 9783319589862
 Edition Number
 2
 Number of Pages
 XVIII, 850
 Number of Illustrations
 297 b/w illustrations
 Topics