Putnam and Beyond

Beschreibung

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 quadratic 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 problem-solving 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 problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and graduate students,

Reviews of the first edition:

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

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 problem-solving; 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 problem-based texts that specifically target the Putnam exams and undergraduate mathematics majors

Autor*in

Răzvan Gelca

Themen in »Putnam and Beyond«

Putnam mathematics competition mathematical induction pigeonhole principle Cauchy-Schwarz Inequality one-variable polynomials Chebyshev polynomials linear algebra Perron-Frobenius theorem Cayley-Hamilton theorem definite integrals Taylor series Fourier series combinatorics

Stimmen zu »Putnam and Beyond«

Details

Link teilen