Putnam and Beyond. 2nd ed. 2017

種類:

電子ブック

責任表示:

by Răzvan Gelca, Titu Andreescu

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Gelca, Răzvan.
• Andreescu, Titu.
• SpringerLink (Online service)

ISBN:

9783319589886 [3319589881]    

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

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