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Putnam and Beyond by Răzvan Gelca and Titu Andreescu (2017, Trade Paperback)

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By Gelca, Răzvan; Andreescu, Titu. Putnam and Beyond.

About this product

Product Identifiers

PublisherSpringer International Publishing A&G

ISBN-103319589865

ISBN-139783319589862

eBay Product ID (ePID)237619985

Product Key Features

Number of PagesXviii, 850 Pages

Publication NamePutnam and Beyond

LanguageEnglish

Publication Year2017

SubjectGeometry / General, General, Study & Teaching, Algebra / General, Mathematical Analysis

TypeTextbook

Subject AreaMathematics

AuthorRăZvan Gelca, Titu Andreescu

FormatTrade Paperback

Dimensions

Item Weight57.4 Oz

Item Length10 in

Item Width7 in

Additional Product Features

Edition Number2

Number of Volumes1 vol.

IllustratedYes

Table Of ContentPreface to the Second Edition.- Preface to the First Edition.- A Study Guide.- 1. Methods of Proof.- 2. Algebra.- 3. Real Analysis.- 4. Geometry and Trigonometry.- 5. Number Theory.- 6. Combinatorics and Probability.- Solutions.- Index of Notation.- Index.

SynopsisSecond 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, 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 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 gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

LC Classification NumberQA150-272