---

＜電子ブック＞
Putnam and Beyond / by Răzvan Gelca, Titu Andreescu

版	2nd ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	XVIII, 850 p. 297 illus : online resource
著者標目	*Gelca, Răzvan author Andreescu, Titu author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Mathematical analysis LCSH:Geometry LCSH:Number theory LCSH:Discrete mathematics FREE:Algebra FREE:Analysis FREE:Geometry FREE:Number Theory FREE:Discrete Mathematics
一般注記	Preface 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 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, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons. 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   …This extraordinary book can be read for fun. However, it can also serve as a textbook for preparation for the Putnam … for an advanced problem-solving course, or even as an overview of undergraduate mathematics. … it could certainly serve as a great review for senior-level students.    — Donald L. Vestal, MathDL, December, 2007 HTTP:URL=https://doi.org/10.1007/978-3-319-58988-6

 類似資料