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Mathematics - Algebra | Putnam and Beyond

Putnam and Beyond

Gelca, Razvan, Andreescu, Titu

2007, XVI, 798 p.

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  • Undergraduate textbook with an emphasis on problem solving
  • Helps undergraduates gain 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 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.

Key features of Putnam and Beyond

* 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 every section according to the specific topic.

* The exposition is driven by more than 1100 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors.

* Complete solutions to all problems are given at the end of the book. The source, author, and historical background are cited whenever possible.

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 self-study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

Content Level » Lower undergraduate

Keywords » Algebra - Applied Mathematics - Invariant - Problem-solving - Variable - calculus - equation - geometry - mathematical induction - mathematics - number theory - pigeonhole principle - proof

Related subjects » Algebra - Analysis - Geometry & Topology - Mathematics - Number Theory and Discrete Mathematics

Table of contents 

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

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