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Putnam and Beyond

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Release : 2017-09-19
Genre : Mathematics
Kind : eBook
Book Rating : 881/5 ( reviews)

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Book Synopsis Putnam and Beyond by : Răzvan Gelca

Download or read book Putnam and Beyond written by Răzvan Gelca. This book was released on 2017-09-19. Available in PDF, EPUB and Kindle. Book excerpt: 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 quad ratic 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 gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

The William Lowell Putnam Mathematical Competition 1985-2000

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Author :
Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 073/5 ( reviews)

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Book Synopsis The William Lowell Putnam Mathematical Competition 1985-2000 by : Kiran Sridhara Kedlaya

Download or read book The William Lowell Putnam Mathematical Competition 1985-2000 written by Kiran Sridhara Kedlaya. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.

Sums and Products

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Release : 2018-04
Genre : Algebra
Kind : eBook
Book Rating : 817/5 ( reviews)

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Book Synopsis Sums and Products by : Titu Andreescu

Download or read book Sums and Products written by Titu Andreescu. This book was released on 2018-04. Available in PDF, EPUB and Kindle. Book excerpt:

Bowling Alone: Revised and Updated

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Release : 2020-10-13
Genre : History
Kind : eBook
Book Rating : 849/5 ( reviews)

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Book Synopsis Bowling Alone: Revised and Updated by : Robert D. Putnam

Download or read book Bowling Alone: Revised and Updated written by Robert D. Putnam. This book was released on 2020-10-13. Available in PDF, EPUB and Kindle. Book excerpt: Updated to include a new chapter about the influence of social media and the Internet—the 20th anniversary edition of Bowling Alone remains a seminal work of social analysis, and its examination of what happened to our sense of community remains more relevant than ever in today’s fractured America. Twenty years, ago, Robert D. Putnam made a seemingly simple observation: once we bowled in leagues, usually after work; but no longer. This seemingly small phenomenon symbolized a significant social change that became the basis of the acclaimed bestseller, Bowling Alone, which The Washington Post called “a very important book” and Putnam, “the de Tocqueville of our generation.” Bowling Alone surveyed in detail Americans’ changing behavior over the decades, showing how we had become increasingly disconnected from family, friends, neighbors, and social structures, whether it’s with the PTA, church, clubs, political parties, or bowling leagues. In the revised edition of his classic work, Putnam shows how our shrinking access to the “social capital” that is the reward of communal activity and community sharing still poses a serious threat to our civic and personal health, and how these consequences have a new resonance for our divided country today. He includes critical new material on the pervasive influence of social media and the internet, which has introduced previously unthinkable opportunities for social connection—as well as unprecedented levels of alienation and isolation. At the time of its publication, Putnam’s then-groundbreaking work showed how social bonds are the most powerful predictor of life satisfaction, and how the loss of social capital is felt in critical ways, acting as a strong predictor of crime rates and other measures of neighborhood quality of life, and affecting our health in other ways. While the ways in which we connect, or become disconnected, have changed over the decades, his central argument remains as powerful and urgent as ever: mending our frayed social capital is key to preserving the very fabric of our society.

Problem-Solving Through Problems

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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 981/5 ( reviews)

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Book Synopsis Problem-Solving Through Problems by : Loren C. Larson

Download or read book Problem-Solving Through Problems written by Loren C. Larson. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

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