Putnam and Beyond

Putnam and Beyond

Author: Răzvan Gelca

Publisher: Springer

Published: 2017-09-19

Total Pages: 857

ISBN-13: 3319589881

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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.


Book Synopsis Putnam and Beyond by : Răzvan Gelca

Download or read book Putnam and Beyond written by Răzvan Gelca and published by Springer. This book was released on 2017-09-19 with total page 857 pages. 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

The William Lowell Putnam Mathematical Competition 1985-2000

Author: Kiran Sridhara Kedlaya

Publisher: MAA

Published: 2002

Total Pages: 360

ISBN-13: 9780883858073

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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.


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 and published by MAA. This book was released on 2002 with total page 360 pages. 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

Sums and Products

Author: Titu Andreescu

Publisher:

Published: 2018-04

Total Pages: 340

ISBN-13: 9780999342817

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Book Synopsis Sums and Products by : Titu Andreescu

Download or read book Sums and Products written by Titu Andreescu and published by . This book was released on 2018-04 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:


Bowling Alone: Revised and Updated

Bowling Alone: Revised and Updated

Author: Robert D. Putnam

Publisher: Simon & Schuster

Published: 2020-10-13

Total Pages: 592

ISBN-13: 1982130849

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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.


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 and published by Simon & Schuster. This book was released on 2020-10-13 with total page 592 pages. 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

Problem-Solving Through Problems

Author: Loren C. Larson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 322

ISBN-13: 1461254981

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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.


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

Download or read book Problem-Solving Through Problems written by Loren C. Larson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. 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.


Our Kids

Our Kids

Author: Robert D. Putnam

Publisher: Simon and Schuster

Published: 2016-03-29

Total Pages: 400

ISBN-13: 1476769907

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"The bestselling author of Bowling Alone offers [an] ... examination of the American Dream in crisis--how and why opportunities for upward mobility are diminishing, jeopardizing the prospects of an ever larger segment of Americans"--


Book Synopsis Our Kids by : Robert D. Putnam

Download or read book Our Kids written by Robert D. Putnam and published by Simon and Schuster. This book was released on 2016-03-29 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The bestselling author of Bowling Alone offers [an] ... examination of the American Dream in crisis--how and why opportunities for upward mobility are diminishing, jeopardizing the prospects of an ever larger segment of Americans"--


The William Lowell Putnam Mathematical Competition Problems and Solutions

The William Lowell Putnam Mathematical Competition Problems and Solutions

Author: Andrew M. Gleason

Publisher: MAA

Published: 1980

Total Pages: 668

ISBN-13: 9780883854624

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Back by popular demand, the MAA is pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions.


Book Synopsis The William Lowell Putnam Mathematical Competition Problems and Solutions by : Andrew M. Gleason

Download or read book The William Lowell Putnam Mathematical Competition Problems and Solutions written by Andrew M. Gleason and published by MAA. This book was released on 1980 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Back by popular demand, the MAA is pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions.


Problem-Solving Strategies

Problem-Solving Strategies

Author: Arthur Engel

Publisher: Springer Science & Business Media

Published: 2008-01-19

Total Pages: 404

ISBN-13: 0387226419

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A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.


Book Synopsis Problem-Solving Strategies by : Arthur Engel

Download or read book Problem-Solving Strategies written by Arthur Engel and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.


Introduction to Functional Equations

Introduction to Functional Equations

Author: Costas Efthimiou

Publisher: American Mathematical Soc.

Published: 2011-10-13

Total Pages: 381

ISBN-13: 0821853147

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Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.


Book Synopsis Introduction to Functional Equations by : Costas Efthimiou

Download or read book Introduction to Functional Equations written by Costas Efthimiou and published by American Mathematical Soc.. This book was released on 2011-10-13 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.


George Palmer Putnam

George Palmer Putnam

Author: Ezra Greenspan

Publisher: Penn State Press

Published: 2000

Total Pages: 540

ISBN-13: 9780271020051

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"There are many books viewing the world through the eyes of politicians. This is an exciting book that views nineteenth-century America through the eyes of one of its most important publishers, George Palmer Putman. Putnam's publisher's eyes are amazing lenses because of his total involvement and patronage of the leading authors of his time. He toiled to give their voices greater exposure to the world". -- Patricia Schroeder, President & CEO, Association of American Publishers Inc.


Book Synopsis George Palmer Putnam by : Ezra Greenspan

Download or read book George Palmer Putnam written by Ezra Greenspan and published by Penn State Press. This book was released on 2000 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: "There are many books viewing the world through the eyes of politicians. This is an exciting book that views nineteenth-century America through the eyes of one of its most important publishers, George Palmer Putman. Putnam's publisher's eyes are amazing lenses because of his total involvement and patronage of the leading authors of his time. He toiled to give their voices greater exposure to the world". -- Patricia Schroeder, President & CEO, Association of American Publishers Inc.