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| putnam math questions: 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 math questions: 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 math questions: 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 math questions: 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 math questions: 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 math questions: 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 math questions: 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 math questions: 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 math questions: 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 math questions: A Primer for Mathematics Competitions Alexander Zawaira, Gavin Hitchcock, 2008-10-31 The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call beautiful problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive appetiser problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a toolchest of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring mathlete may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum. |
| putnam math questions: Mathematics for Human Flourishing Francis Su, 2020-01-07 The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.--Kevin Hartnett, Quanta Magazine This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all. |
| putnam math questions: Berkeley Problems in Mathematics Paulo Ney de Souza, Jorge-Nuno Silva, 2004-01-20 This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. |
| putnam math questions: 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 math questions: Kurt Gödel and the Foundations of Mathematics Matthias Baaz, Christos H. Papadimitriou, Hilary W. Putnam, Dana S. Scott, Charles L. Harper, Jr, 2011-06-06 This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers. |
| putnam math questions: Japanese Candlestick Charting Techniques Steve Nison, 2001-11-01 A form of technical analysis, Japanese candlestick charts are a versatile tool that can be fused with any other technical tool, and will help improve any technician's market analysis. They can be used for speculation and hedging, for futures, equities or anywhere technical analysis is applied. Seasoned technicians will discover how joining Japanese candlesticks with other technical tools can create a powerful synergy of techniques; amateurs will find out how effective candlestick charts are as a stand-alone charting method. In easy-to-understand language, this title delivers to the reader the author's years of study, research and practical experience in this increasingly popular and dynamic approach to market analysis. The comprehensive coverage includes everything from the basics, with hundreds of examples showing how candlestick charting techniques can be used in almost any market. |
| putnam math questions: 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 math questions: The Collapse of the Fact/Value Dichotomy and Other Essays Hilary Putnam, 2004-03-30 If philosophy has any business in the world, it is the clarification of our thinking and the clearing away of ideas that cloud the mind. In this book, one of the world's preeminent philosophers takes issue with an idea that has found an all-too-prominent place in popular culture and philosophical thought: the idea that while factual claims can be rationally established or refuted, claims about value are wholly subjective, not capable of being rationally argued for or against. Although it is on occasion important and useful to distinguish between factual claims and value judgments, the distinction becomes, Hilary Putnam argues, positively harmful when identified with a dichotomy between the objective and the purely subjective. Putnam explores the arguments that led so much of the analytic philosophy of language, metaphysics, and epistemology to become openly hostile to the idea that talk of value and human flourishing can be right or wrong, rational or irrational; and by which, following philosophy, social sciences such as economics have fallen victim to the bankrupt metaphysics of Logical Positivism. Tracing the problem back to Hume's conception of a matter of fact as well as to Kant's distinction between analytic and synthetic judgments, Putnam identifies a path forward in the work of Amartya Sen. Lively, concise, and wise, his book prepares the way for a renewed mutual fruition of philosophy and the social sciences. |
| putnam math questions: 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 math questions: A Part of the Sky Robert Newton Peck, 2011-08-31 In celebration of the twenty-fifth anniversary of the publication of Robert Newton Peck's bestselling classic, A Day No Pigs Would Die, here is the eagerly anticipated sequel. This must for schools, libraries, and summer reading lists is now available for the first time in paperback. Times are difficult during the Great Depression, and thirteen-year-old Rob Peck must struggle to keep his family together after the death of his father. Disaster after disaster strikes and the family is forced to sell their farm. Relying solely on their strong Shaker faith and close family ties, the Pecks finally prevail and young Rob learns that true wealth extends beyond money and that real values are priceless. |
| putnam math questions: 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 math questions: Sums and Products Titu Andreescu, Marian Tetiva, 2018-04 |
| putnam math questions: The Midnight Library: A GMA Book Club Pick Matt Haig, 2023-05-09 The #1 New York Times bestselling WORLDWIDE phenomenon Winner of the Goodreads Choice Award for Fiction | A Good Morning America Book Club Pick | Independent (London) Ten Best Books of the Year A feel-good book guaranteed to lift your spirits.—The Washington Post The dazzling reader-favorite about the choices that go into a life well lived, from the acclaimed author of How To Stop Time and The Comfort Book. Don’t miss Matt Haig’s latest instant New York Times besteller, The Life Impossible, available now Somewhere out beyond the edge of the universe there is a library that contains an infinite number of books, each one the story of another reality. One tells the story of your life as it is, along with another book for the other life you could have lived if you had made a different choice at any point in your life. While we all wonder how our lives might have been, what if you had the chance to go to the library and see for yourself? Would any of these other lives truly be better? In The Midnight Library, Matt Haig's enchanting blockbuster novel, Nora Seed finds herself faced with this decision. Faced with the possibility of changing her life for a new one, following a different career, undoing old breakups, realizing her dreams of becoming a glaciologist; she must search within herself as she travels through the Midnight Library to decide what is truly fulfilling in life, and what makes it worth living in the first place. |
| putnam math questions: 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 math questions: Princeton Problems in Physics, with Solutions Nathan Newbury, 1991-02-21 Aimed at helping the physics student to develop a solid grasp of basic graduate-level material, this book presents worked solutions to a wide range of informative problems. These problems have been culled from the preliminary and general examinations created by the physics department at Princeton University for its graduate program. The authors, all students who have successfully completed the examinations, selected these problems on the basis of usefulness, interest, and originality, and have provided highly detailed solutions to each one. Their book will be a valuable resource not only to other students but to college physics teachers as well. The first four chapters pose problems in the areas of mechanics, electricity and magnetism, quantum mechanics, and thermodynamics and statistical mechanics, thereby serving as a review of material typically covered in undergraduate courses. Later chapters deal with material new to most first-year graduate students, challenging them on such topics as condensed matter, relativity and astrophysics, nuclear physics, elementary particles, and atomic and general physics. |
| putnam math questions: Sharpening Mathematical Analysis Skills Alina Sîntămărian, Ovidiu Furdui, 2021-10-25 This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks. |
| putnam math questions: Index to Mathematical Problems, 1975-1979 Stanley Rabinowitz, Mark Bowron, 1999 |
| putnam math questions: Additive Combinatorics Bela Bajnok, 2018-04-27 Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods. The book is divided into five parts which are compared to a meal. The first part is called Ingredients and includes relevant background information about number theory, combinatorics, and group theory. The second part, Appetizers, introduces readers to the book’s main subject through samples. The third part, Sides, covers auxiliary functions that appear throughout different chapters. The book’s main course, so to speak, is Entrees: it thoroughly investigates a large variety of questions in additive combinatorics by discussing what is already known about them and what remains unsolved. These include maximum and minimum sumset size, spanning sets, critical numbers, and so on. The final part is Pudding and features numerous proofs and results, many of which have never been published. Features: The first book of its kind to explore the subject Students of any level can use the book as the basis for research projects The text moves gradually through five distinct parts, which is suitable both for beginners without prerequisites and for more advanced students Includes extensive proofs of propositions and theorems Each of the introductory chapters contains numerous exercises to help readers |
| putnam math questions: 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 math questions: 101 Problems in Algebra Titu Andreescu, Zuming Feng, 2001 |
| putnam math questions: Quant Job Interview Questions and Answers Mark Joshi, Nick Denson, Nicholas Denson, Andrew Downes, 2013 The quant job market has never been tougher. Extensive preparation is essential. Expanding on the successful first edition, this second edition has been updated to reflect the latest questions asked. It now provides over 300 interview questions taken from actual interviews in the City and Wall Street. Each question comes with a full detailed solution, discussion of what the interviewer is seeking and possible follow-up questions. Topics covered include option pricing, probability, mathematics, numerical algorithms and C++, as well as a discussion of the interview process and the non-technical interview. All three authors have worked as quants and they have done many interviews from both sides of the desk. Mark Joshi has written many papers and books including the very successful introductory textbook, The Concepts and Practice of Mathematical Finance. |
| putnam math questions: 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 math questions: Geometric Transformations Răzvan Gelca, Ionuţ Onişor, Carlos Yuzo Shine, 2023-11-16 This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work. |
| putnam math questions: Competition Math for Middle School Jason Batteron, 2011-01-01 |
| putnam math questions: Problems in Mathematical Analysis Wieslawa J. Kaczor, Maria T. Nowak, 2000 |
| putnam math questions: The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil, 2020-01-16 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. |
| putnam math questions: The Art of Problem Solving, Volume 1 Sandor Lehoczky, Richard Rusczyk, 2006 ... offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition.--Back cover |
| putnam math questions: 250 Problems in Elementary Number Theory Wacław Sierpiński, 1970 |
| putnam math questions: (Almost) Impossible Integrals, Sums, and Series Cornel Ioan Vălean, 2019-05-24 This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series. |
| putnam math questions: 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 Investments - Individual Investors
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Use our Tax-Equivalent Yield Calculator to evaluate Putnam municipal bond funds with other income fund options. The tool offers a custom comparison based on income, filing status, and …
Traditional IRA - Putnam Investments
Take advantage: Putnam Traditional IRA Offers tax-deferred earnings and tax-deductible contributions. May be used for qualified higher education expenses without penalty. Helps …
529 Plan - Putnam Investments
Since offering an advisor-sold 529 plan over a decade ago, we have helped families across America build their futures. Discover the Putnam 529 for America.
Putnam Investments - Individual Investors
Access your accounts, make investment choices, and find educational resources.
Financial Advisor - Putnam Investments
For a prospectus, or a summary prospectus if available, containing this and other information for any Putnam fund or product, call the Putnam Client Engagement Center at 1-800-354-4000 or …
Retirement - Putnam Investments
Learn more about Putnam's retirement accounts for individuals, small businesses, and employer-sponsored retirement plans.
Help and guidance - Putnam Investments
Check this quick and easy reference page to help you find what you are looking for on Putnam's site.
Accounts - Putnam Investments
The third-party information accessible through this site was prepared by, and is the sole responsibility of, independent providers who are not affiliated with Putnam. Putnam has not …
Institutional Investors - Putnam Investments
May 31, 2025 · Putnam Investments is a global asset manager serving institutions worldwide, offering traditional and alternative strategies for any product structure.
Contact Us - Putnam Investments
Call Putnam on our toll-free number or contact us by mail with questions about your account or our investment choices.
Muni bond funds and pricing – Tax-Exempt Income Funds | Putnam
Use our Tax-Equivalent Yield Calculator to evaluate Putnam municipal bond funds with other income fund options. The tool offers a custom comparison based on income, filing status, and …
Traditional IRA - Putnam Investments
Take advantage: Putnam Traditional IRA Offers tax-deferred earnings and tax-deductible contributions. May be used for qualified higher education expenses without penalty. Helps …
529 Plan - Putnam Investments
Since offering an advisor-sold 529 plan over a decade ago, we have helped families across America build their futures. Discover the Putnam 529 for America.
