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

版	1st ed. 2007.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	XVI, 798 p : online resource
著者標目	*Gelca, Razvan author Andreescu, Titu author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Mathematical analysis LCSH:Mathematics LCSH:Geometry LCSH:Number theory LCSH:Discrete mathematics FREE:Algebra FREE:Analysis FREE:Mathematics FREE:Geometry FREE:Number Theory FREE:Discrete Mathematics
一般注記	Methods of Proof -- Algebra -- Real Analysis -- Geometry and Trigonometry -- Number Theory -- Combinatorics and Probability 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 HTTP:URL=https://doi.org/10.1007/978-0-387-68445-1

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