Putnam and Beyond
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Putnam and Beyond

Putnam and Beyond


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About the Book

This undergraduate textbook with an emphasis on problem solving can serve as both a study guide for the William Lowell Putnam Mathematics Competition and as an excellent transition book for Olympiad veterans moving on to college level mathematical research. Containing numerous problems that reflect the spirit of the Putnam exam, the work is structured topically to assist undergraduates in gaining proficiency across a broad spectrum of subjects that comprise a core mathematics curriculum. Important features:* The presentation begins with an overview of common methods of proofs, including: argument by contradiction, orderings on a set, invariants, mathematical induction, and maximal elements* Individual chapters cover a succession of key topics in algebra, real analysis, geometry and trigonometry, number theory, combinatorics and probabilities* The problems are clustered into sections within chapters that offer a brief theoretical background of the topic and illustrate its application to one or more detailed examples* Most problems are original to the authors; for those that are adaptations, the source, author, and historical background are cited whenever possible* Complete solutions appear at the end of the book, along with a glossary of definitions and an index of notationFrom the authors of Mathematical Olympiad Challenges (Birkhauser Boston, 2000), Putnam and Beyond fills a gap in the market for problem-based texts that specifically target the Putnam exams and undergraduate mathematics majors. Razvan Gelca has served as coach of the University of Michigan and Texas Tech University Putnam teams and of the Indian and US International Mathematical Olympiad Teams. Titu Andreescu has served as the leader of the US International Mathematical Olympiad Team, Director of the American Mathematics Competitions, and as a member of the Questions Committee of the Putnam competition.

Table of Contents:
Methods of Proof.- Algebra.- Real Analysis.- Geometry and Trigonometry.- Number Theory.- Combinatorics and Probability.

Review :
From the reviews: "This work contains carefully selected problems in Algebra, Real Analysis, Geometry and Trigonometry, Number Theory and Combinatorics and Probability. … The book is mainly intended to offer the principal skills and techniques for solving problems in elementary Mathematics. … 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) "I enjoyed this book … . Not just because of the collection of problems, but also because of their sheer scope and depth. This is a great collection which is extremely well-organized! … 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) “A 935-problem and almost 800-page super-problem book with solutions, whose reading would certainly challenge, attract, and keep really busy any undergraduate student interested in acquiring various problem-solving techniques. … the array of remarkable problem books has gained a new addition that could be really useful to undergraduate students. … a book about excellence in mathematics, coming from a long cultural tradition whose history and experience can only help us deepen our understanding of how mathematics could be taught in a more attractive and inquisitive way.” (Bogdan D. Suceavă and Jack B. Gaumer, The Mathematical Intelligencer, Vol. 33 (2), 2011)


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Product Details
  • ISBN-13: 9780387257655
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 254 mm
  • No of Pages: 798
  • Weight: 3060 gr
  • ISBN-10: 0387257659
  • Publisher Date: 23 Aug 2007
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Width: 178 mm


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