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.

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.

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.

The William Lowell Putnam Mathematical Competition 2001-2016
The William Lowell Putnam Mathematical Competition 2001-2016

Author: Kiran Sridhara Kedlaya

Publisher: MAA Press

Published: 2020

Total Pages: 363

ISBN-13: 9781470462604

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The William Lowell Putnam Mathematics Competition is the most prestigious undergraduate mathematics problem-solving contest in North America, with thousands of students taking part every year. This volume presents the contest problems for the years 2001-2016. The heart of the book is the solutions; these include multiple approaches, drawn from many sources, plus insights into navigating from the problem statement to a solution. There is also a section of hints, to encourage readers to engage deeply with the problems before consulting the solutions.The authors have a distinguished history of en.

The Cauchy-Schwarz Master Class
The Cauchy-Schwarz Master Class

Author: J. Michael Steele

Publisher: Cambridge University Press

Published: 2004-04-26

Total Pages: 320

ISBN-13: 9780521546775

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This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

D.H. Lawrence and Germany
D.H. Lawrence and Germany

Author: Carl Krockel

Publisher: Rodopi

Published: 2007

Total Pages: 345

ISBN-13: 9042021268

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D. H. Lawrence has suffered criticism for the emotional excess of his language, and for a suspected leaning towards right-wing politics. This book contextualises his style and political values in German culture, especially its Romantic tradition which has been subjected to the same criticism as himself. In his writing Lawrence struggles between opposing German cultural elements from thee eighteenth century onwards, to dramatise the conflicts in Modern European culture and history in the first half of the Twentieth century. The book demonstrates how his failures are integral to his achievements, and how the self-contradictory nature of his art is actually its saving grace. This volume surveys the whole span of Lawrence's career; it is intended for both students and teachers of the author, and for those interested in the cross cultural relations of European Modernism. Previous studies have tended to outline references in Lawrence's work to Germany without focusing on the historical, cultural and ideological issues at stake. These issues are the subject of this book.

Topics in Algebra and Analysis
Topics in Algebra and Analysis

Author: Radmila Bulajich Manfrino

Publisher: Birkhäuser

Published: 2015-02-09

Total Pages: 319

ISBN-13: 331911946X

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The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include polynomials, functional equations, sequences and an elementary treatment of complex numbers. The final chapters provide a comprehensive list of problems posed at national and international contests in recent years, and solutions to all exercises and problems presented in the book. It helps students in preparing for national and international mathematical contests form high school level to more advanced competitions and will also be useful for their first year of mathematical studies at the university. It will be of interest to teachers in college and university level, and trainers of the mathematical Olympiads.

The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary
The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary

Author: Kiran S. Kedlaya

Publisher: American Mathematical Soc.

Published: 2020-01-16

Total Pages: 353

ISBN-13: 1470451247

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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.

103 Trigonometry Problems
103 Trigonometry Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2006-03-04

Total Pages: 222

ISBN-13: 0817644326

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* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training