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9.2 MB
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9209419A69638BF29674FE3DFE15FC777D4B659C
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July 10, 2025, 2:06 p.m.
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| ['Gelca R., Andreescu T. Putnam and Beyond 2ed 2017.pdf'] | 0 bytes |
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SOURCE: Gelca R., Andreescu T. Putnam and Beyond 2ed 2017
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MEDIAINFO
Textbook in PDF format 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. The first edition of the book has generated great interest and a large amount of input from the readers, who have expressed their views and have suggested corrections and improvements. We are deeply grateful to all, as their contributions have significantly impacted the book. At the same time, the authors have remained involved in mathematics competitions, being exposed to the constant flow of problems and to the evolution of ideas. The first author has continued training the United States International Mathematical Olympiad team. The second author has started and perfected the Awesome Math Summer program, and as editor-in-chief of Mathematical Reflections, has established it as one of the important journals promoting problem solving at high-school and college levels. Both authors have continued writing problems for mathematics contests at high school and collegiate levels. Some new perspectives in problem solving that appeared since the publication of the first edition have thus found their way into the book. Also, by using Putnam and Beyond in teaching and coaching, the authors have realized that some material had to be improved and expanded to make it more accessible and complete. The new edition adds 180 new problems and examples, eight new sections, some new solutions to previously existing problems, and corrects all the errors and typos that have been found in the first edition. It gives more substance to some topics that had a rather shallow treatment before. The experience of ten years of use gave rise to a more polished product. Front Matter Methods of Proof Algebra Real Analysis Geometry and Trigonometry Number Theory Combinatorics and Probability Back Matter
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