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| putnam problems and solutions: The William Lowell Putnam Mathematical Competition Gerald L. Alexanderson, Leonard F. Klosinski, Loren C. Larson, 2003 The Putnam Competition has since 1928 been providing a challenge to gifted college mathematics students. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions. In 1980, the MAA published the first William Lowell Putnam Mathematical Competition book, covering the contest from 1938 to 1964. In 2002 the third of the Putnam problem books appeared, covering the years 1985 through 2000. All three of these books belong on the bookshelf of students, teachers, and all interested in problem solving. |
| putnam problems and solutions: The William Lowell Putnam Mathematical Competition 1985-2000 Kiran Sridhara Kedlaya, Bjorn Poonen, Ravi Vakil, 2002 A collection of problems from the William Lowell Putnam Competition which places them in the context of important mathematical themes. |
| putnam problems and solutions: Putnam and Beyond Răzvan Gelca, Titu Andreescu, 2017-09-19 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. |
| putnam problems and solutions: The William Lowell Putnam Mathematical Competition 2001-2016 Kiran Sridhara Kedlaya, Daniel M. Kane, Jonathan Michael Kane, Evan M. O'Dorney, 2020 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. |
| putnam problems and solutions: The William Lowell Putnam Mathematical Competition Problems and Solutions Andrew M. Gleason, R. E. Greenwood, Leroy Milton Kelly, 1980 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. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. Valuable references and historical comments on many of the problems are presented. The book concludes with four articles on the Putnam competition written by G. Birkhoff, L. E. Bush, L. J. Mordell, and L. M. Kelly which are reprinted from the American Mathematical Monthly. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas.--Back cover. |
| putnam problems and solutions: Our Kids Robert D. Putnam, 2016-03-29 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-- |
| putnam problems and solutions: The William Lowell Putnam Mathematical Competition A. M. Gleason, R. E. Greenwood, L. M. Kelly, 2019-07-24 Back by popular demand, we are 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. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. Valuable references and historical comments on many of the problems are presented. The book concludes with four articles on the Putnam competition written by G. Birkhoff, L. E. Bush, L. J. Mordell, and L. M. Kelly which are reprinted from the American Mathematical Monthly. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas. |
| putnam problems and solutions: Problems and Solutions in Mathematics Ji-Xiu Chen, 2011 This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference. |
| putnam problems and solutions: The William Lowell Putnam Mathematical Competition Problems and Solutions Andrew M. Gleason, 1980 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 problems and solutions: Concepts and Problems for Mathematical Competitors Alexander Sarana, Anatoliy Pogorui, Ramón M. Rodríguez-Dagnino, 2020-08-12 This original work discusses mathematical methods needed by undergraduates in the United States and Canada preparing for competitions at the level of the International Mathematical Olympiad (IMO) and the Putnam Competition. The six-part treatment covers counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Includes problems with solutions plus 1,000 problems for students to finish themselves. |
| putnam problems and solutions: Problem-Solving Strategies Arthur Engel, 2008-01-19 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. |
| putnam problems and solutions: The Art and Craft of Problem Solving Paul Zeitz, 2016-11-14 Appealing to everyone from college-level majors to independent learners, The Art and Craft of Problem Solving, 3rd Edition introduces a problem-solving approach to mathematics, as opposed to the traditional exercises approach. The goal of The Art and Craft of Problem Solving is to develop strong problem solving skills, which it achieves by encouraging students to do math rather than just study it. Paul Zeitz draws upon his experience as a coach for the international mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems. |
| putnam problems and solutions: Problem-Solving Through Problems Loren C. Larson, 1992-09-03 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. |
| putnam problems and solutions: Bowling Alone Robert D. Putnam, 2000 Packed with provocative information about the social and political habits of twentieth-century Americans. |
| putnam problems and solutions: Hungarian Problem Book IV Robert Barrington Leigh, Chiang-Fung Andrew Liu, 2011 Forty-eight challenging problems from the oldest high school mathematics competition in the world. This book is a continuation of Hungarian Problem Book III and takes the contest from 1944 through to 1963. This book is intended for beginners, although the experienced student will find much here. |
| putnam problems and solutions: A Path to Combinatorics for Undergraduates Titu Andreescu, Zuming Feng, 2013-12-01 The main goal of the two authors is to help undergraduate students understand the concepts and ideas of combinatorics, an important realm of mathematics, and to enable them to ultimately achieve excellence in this field. This goal is accomplished by familiariz ing students with typical examples illustrating central mathematical facts, and by challenging students with a number of carefully selected problems. It is essential that the student works through the exercises in order to build a bridge between ordinary high school permutation and combination exercises and more sophisticated, intricate, and abstract concepts and problems in undergraduate combinatorics. The extensive discussions of the solutions are a key part of the learning process. The concepts are not stacked at the beginning of each section in a blue box, as in many undergraduate textbooks. Instead, the key mathematical ideas are carefully worked into organized, challenging, and instructive examples. The authors are proud of their strength, their collection of beautiful problems, which they have accumulated through years of work preparing students for the International Math ematics Olympiads and other competitions. A good foundation in combinatorics is provided in the first six chapters of this book. While most of the problems in the first six chapters are real counting problems, it is in chapters seven and eight where readers are introduced to essay-type proofs. This is the place to develop significant problem-solving experience, and to learn when and how to use available skills to complete the proofs. |
| putnam problems and solutions: The William Lowell Putnam Mathematical Competition A. M. Gleason, 1938 |
| putnam problems and solutions: Gödel, Putnam, and Functionalism Jeff Buechner, 2007-09-21 The first systematic examination of Hilary Putnam's arguments against computational functionalism challenges each of Putnam's main arguments. With mind-brain identity theories no longer dominant in philosophy of mind in the late 1950s, scientific materialists turned to functionalism, the view that the identity of any mental state depends on its function in the cognitive system of which it is a part. The philosopher Hilary Putnam was one of the primary architects of functionalism and was the first to propose computational functionalism, which views the human mind as a computer or an information processor. But, in the early 1970s, Putnam began to have doubts about functionalism, and in his masterwork Representation and Reality (MIT Press, 1988), he advanced four powerful arguments against his own doctrine of computational functionalism. In Gödel, Putnam, and Functionalism, Jeff Buechner systematically examines Putnam's arguments against functionalism and contends that they are unsuccessful. Putnam's first argument uses Gödel's incompleteness theorem to refute the view that there is a computational description of human reasoning and rationality; his second, the “triviality argument,” demonstrates that any computational description can be attributed to any physical system; his third, the multirealization argument, shows that there are infinitely many computational realizations of an arbitrary intentional state; his fourth argument buttresses this assertion by showing that there cannot be local computational reductions because there is no computable partitioning of the infinity of computational realizations of an arbitrary intentional state into a single package or small set of packages (equivalence classes). Buechner analyzes these arguments and the important inferential connections among them—for example, the use of both the Gödel and triviality arguments in the argument against local computational reductions—and argues that none of Putnam's four arguments succeeds in refuting functionalism. Gödel, Putnam, and Functionalism will inspire renewed discussion of Putnam's influential book and will confirm Representation and Reality as a major work by a major philosopher. |
| putnam problems and solutions: The Cauchy-Schwarz Master Class J. Michael Steele, 2004-04-26 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. |
| putnam problems and solutions: Problems in Real Analysis Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu, 2009-06-12 Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis. |
| putnam problems and solutions: The Green Book of Mathematical Problems Kenneth Hardy, Kenneth S. Williams, 2013-11-26 Rich selection of 100 practice problems — with hints and solutions — for students preparing for the William Lowell Putnam and other undergraduate-level mathematical competitions. Features real numbers, differential equations, integrals, polynomials, sets, other topics. Hours of stimulating challenge for math buffs at varying degrees of proficiency. References. |
| putnam problems and solutions: Problems , 1994 This is an outstanding collection of challenging problems of Olympiad-style mathematics for High School students. Taken from the annual Austrian-Polish Mathematics Competition (APMC), these problems are appropriate for students & teachers who are interested in supplementing their normal mathematical curriculums with advanced problem-solving exercises. Each problem has a solution that is presented with elegant style & clarity, reflecting the long-standing tradition associated with Polish mathematicians. THIS BOOK SHOULD BE ON EVERY HIGH SCHOOL LIBRARY SHELF IN ORDER TO GIVE HIGHLY MOTIVATED MATH STUDENTS EVERY OPPORTUNITY TO STRENGTHEN THEIR SKILLS & TO FACE NEW CHALLENGES. Problems will also help students prepare for local, national or international mathematics competitions. Students & teachers will enjoy the refreshing nature of Dr. Kuczma's intelligence & style of writing. Dr. Marcin Kuczma, from the University of Warsaw, Poland, is devoted to teaching & to mathematics competitions. He has been active in the Polish Mathematical Olympiad for about twenty years. He is responsible for the proposal of several International Mathematical Olympiad (IMO) problems, as well as numerous Austrian-Polish Mathematics Competition problems. He is also the recipient of many honors, including the prestigious David Hilbert Medal, awarded in 1992 by the World Federation of National Mathematics Competitions. Ordering information: Academic Distribution Center, 1218 Walker Rd., Freeland, MD 21053, phone#/FAX#: (410) 343-0409. |
| putnam problems and solutions: Functional Equations and How to Solve Them Christopher G. Small, 2007-04-03 Over the years, a number of books have been written on the theory of functional equations. However, very little has been published which helps readers to solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. The student who encounters a functional equation on a mathematics contest will need to investigate solutions to the equation by finding all solutions, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning a family of solutions to each functional equation in explicit form. At the end of each chapter, readers will find a list of problems associated with the material in that chapter. The problems vary greatly, with the easiest problems being accessible to any high school student who has read the chapter carefully. The most difficult problems will be a reasonable challenge to advanced students studying for the International Mathematical Olympiad at the high school level or the William Lowell Putnam Competition for university undergraduates. The book ends with an appendix containing topics that provide a springboard for further investigation of the concepts of limits, infinite series and continuity. |
| putnam problems and solutions: Calculus: A Rigorous First Course Daniel J. Velleman, 2017-01-05 Rigorous and rewarding text for undergraduate math majors covers usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Requires only background in algebra and trigonometry. Solutions available to instructors. 2016 edition. |
| putnam problems and solutions: U.S.A. Mathematical Olympiads, 1972-1986 , 1988 |
| putnam problems and solutions: Fifty Challenging Problems in Probability with Solutions Frederick Mosteller, 2012-04-26 Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions. |
| putnam problems and solutions: 103 Trigonometry Problems Titu Andreescu, Zuming Feng, 2004-12-15 * 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 |
| putnam problems and solutions: Mathematical Olympiad in China (2007-2008) Bin Xiong, Peng Yee Lee, 2009 The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of golds for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2006 to 2008. Mathematical Olympiad problems with solutions for the years 2002?2006 appear in an earlier volume, Mathematical Olympiad in China. |
| putnam problems and solutions: Challenging Mathematical Problems with Elementary Solutions ?. ? ?????, Isaak Moiseevich I?Aglom, Basil Gordon, 1987-01-01 Volume II of a two-part series, this book features 74 problems from various branches of mathematics. Topics include points and lines, topology, convex polygons, theory of primes, and other subjects. Complete solutions. |
| putnam problems and solutions: Index to Mathematical Problems, 1975-1979 Stanley Rabinowitz, Mark Bowron, 1999 |
| putnam problems and solutions: Problems in Mathematical Analysis: Real numbers, sequences, and series Wiesława J. Kaczor, Maria T. Nowak, 2000 Solutions for all the problems are provided.--BOOK JACKET. |
| putnam problems and solutions: Philosophy in an Age of Science Hilary Putnam, 2012-04-17 Hilary Putnam's unceasing self-criticism has led to the frequent changes of mind he is famous for, but his thinking is also marked by considerable continuity. A simultaneous interest in science and ethicsÑunusual in the current climate of contentionÑhas long characterized his thought. In Philosophy in an Age of Science, Putnam collects his papers for publicationÑhis first volume in almost two decades. Mario De Caro and David Macarthur's introduction identifies central themes to help the reader negotiate between Putnam past and Putnam present: his critique of logical positivism; his enduring aspiration to be realist about rational normativity; his anti-essentialism about a range of central philosophical notions; his reconciliation of the scientific worldview and the humanistic tradition; and his movement from reductive scientific naturalism to liberal naturalism. Putnam returns here to some of his first enthusiasms in philosophy, such as logic, mathematics, and quantum mechanics. The reader is given a glimpse, too, of ideas currently in development on the subject of perception. Putnam's work, contributing to a broad range of philosophical inquiry, has been said to represent a Òhistory of recent philosophy in outline.Ó Here it also delineates a possible future. |
| putnam problems and solutions: 101 Problems in Algebra Titu Andreescu, Zuming Feng, 2001 |
| putnam problems and solutions: The Wohascum County Problem Book George Thomas Gilbert, Mark Krusemeyer, Loren C. Larson, 1993 |
| putnam problems and solutions: Thnking Mathematically J Mason, L. Burton, K. Stacey, 2011-01-10 Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience. |
| putnam problems and solutions: Mathematical Olympiad Challenges Titu Andreescu, Rǎzvan Gelca, 2000-04-26 A collection of problems put together by coaches of the U.S. International Mathematical Olympiad Team. |
| putnam problems and solutions: Calculus David Patrick, 2013-04-15 A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations. |
| putnam problems and solutions: A Mathematical Mosaic Ravi Vakil, 1996 Powerful problem solving ideas that focus on the major branches of mathematics and their interconnections. |
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