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| putnam math competition 2016 results: 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 competition 2016 results: 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 competition 2016 results: 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 competition 2016 results: 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 competition 2016 results: 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 competition 2016 results: 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 competition 2016 results: The Probabilistic Method Noga Alon, Joel H. Spencer, 2015-11-02 Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley. |
| putnam math competition 2016 results: 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 competition 2016 results: 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 competition 2016 results: A Survey of the Hodge Conjecture James Dominic Lewis, 1991 |
| putnam math competition 2016 results: Parenting Matters National Academies of Sciences, Engineering, and Medicine, Division of Behavioral and Social Sciences and Education, Board on Children, Youth, and Families, Committee on Supporting the Parents of Young Children, 2016-11-21 Decades of research have demonstrated that the parent-child dyad and the environment of the familyâ€which includes all primary caregiversâ€are at the foundation of children's well- being and healthy development. From birth, children are learning and rely on parents and the other caregivers in their lives to protect and care for them. The impact of parents may never be greater than during the earliest years of life, when a child's brain is rapidly developing and when nearly all of her or his experiences are created and shaped by parents and the family environment. Parents help children build and refine their knowledge and skills, charting a trajectory for their health and well-being during childhood and beyond. The experience of parenting also impacts parents themselves. For instance, parenting can enrich and give focus to parents' lives; generate stress or calm; and create any number of emotions, including feelings of happiness, sadness, fulfillment, and anger. Parenting of young children today takes place in the context of significant ongoing developments. These include: a rapidly growing body of science on early childhood, increases in funding for programs and services for families, changing demographics of the U.S. population, and greater diversity of family structure. Additionally, parenting is increasingly being shaped by technology and increased access to information about parenting. Parenting Matters identifies parenting knowledge, attitudes, and practices associated with positive developmental outcomes in children ages 0-8; universal/preventive and targeted strategies used in a variety of settings that have been effective with parents of young children and that support the identified knowledge, attitudes, and practices; and barriers to and facilitators for parents' use of practices that lead to healthy child outcomes as well as their participation in effective programs and services. This report makes recommendations directed at an array of stakeholders, for promoting the wide-scale adoption of effective programs and services for parents and on areas that warrant further research to inform policy and practice. It is meant to serve as a roadmap for the future of parenting policy, research, and practice in the United States. |
| putnam math competition 2016 results: Complex Numbers from A to ...Z Titu Andreescu, Dorin Andrica, 2008-11-01 * Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory |
| putnam math competition 2016 results: Indra's Pearls David Mumford, Caroline Series, David Wright, 2002-04-25 Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research. |
| putnam math competition 2016 results: Bitcoin and Cryptocurrency Technologies Arvind Narayanan, Joseph Bonneau, Edward Felten, Andrew Miller, Steven Goldfeder, 2016-07-19 An authoritative introduction to the exciting new technologies of digital money Bitcoin and Cryptocurrency Technologies provides a comprehensive introduction to the revolutionary yet often misunderstood new technologies of digital currency. Whether you are a student, software developer, tech entrepreneur, or researcher in computer science, this authoritative and self-contained book tells you everything you need to know about the new global money for the Internet age. How do Bitcoin and its block chain actually work? How secure are your bitcoins? How anonymous are their users? Can cryptocurrencies be regulated? These are some of the many questions this book answers. It begins by tracing the history and development of Bitcoin and cryptocurrencies, and then gives the conceptual and practical foundations you need to engineer secure software that interacts with the Bitcoin network as well as to integrate ideas from Bitcoin into your own projects. Topics include decentralization, mining, the politics of Bitcoin, altcoins and the cryptocurrency ecosystem, the future of Bitcoin, and more. An essential introduction to the new technologies of digital currency Covers the history and mechanics of Bitcoin and the block chain, security, decentralization, anonymity, politics and regulation, altcoins, and much more Features an accompanying website that includes instructional videos for each chapter, homework problems, programming assignments, and lecture slides Also suitable for use with the authors' Coursera online course Electronic solutions manual (available only to professors) |
| putnam math competition 2016 results: A TeXas Style Introduction to Proof Ron Taylor, Patrick X. Rault , 2019-07-26 A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the “bridge course”) that also introduces TeX as a tool students can use to communicate their work. As befitting “textless” text, the book is, as one reviewer characterized it, “minimal.” Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult. |
| putnam math competition 2016 results: Global Business Regulation John Braithwaite, Peter Drahos, 2000-02-13 How has the regulation of business shifted from national to global institutions? What are the mechanisms of globalization? Who are the key actors? What of democratic sovereignty? In which cases has globalization been successfully resisted? These questions are confronted across an amazing sweep of the critical areas of business regulation--from contract, intellectual property and corporations law, to trade, telecommunications, labor standards, drugs, food, transport and environment. This book examines the role played by global institutions such as the World Trade Organization, World Health Organization, the OECD, IMF, Moodys and the World Bank, as well as various NGOs and significant individuals. Incorporating both history and analysis, Global Business Regulation will become the standard reference for readers in business, law, politics, and international relations. |
| putnam math competition 2016 results: Harmonic Function Theory Sheldon Axler, Paul Bourdon, Ramey Wade, 2013-11-11 This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer. |
| putnam math competition 2016 results: Parable of the 5 Wise and 5 Foolish Virgins by Lord Jesus Christ with Church Fathers in First Christianity and Protestant Reformers Martin Luther & John Wesley Jonathan Ramachandran, 2021-10-04 The Parable of the 5 Wise and 5 Foolish Virgins has been interpreted in many ways in Christianity. Here we look at First Christianity and the oldest way of interpreting it via the Church Fathers which was maintained in Principle even in the First protestant Martin Luther's Writings likewise till even John Wesley the Co-Founder of Methodism also held to it likewise as referring to Love God and Love your neighbour as yourself with Good Works in Action. |
| putnam math competition 2016 results: Euclidean Geometry in Mathematical Olympiads Evan Chen, 2021-08-23 This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class. |
| putnam math competition 2016 results: Teaching Civic Engagement Alison Rios Millett McCartney, Elizabeth A. Bennion, Dick W. Simpson, 2013 Teaching Civic Engagement provides an exploration of key theoretical discussions, innovative ideas, and best practices in educating citizens in the 21st century. The book addresses theoretical debates over the place of civic engagement education in Political Science. It offers pedagogical examples in several sub-fields, including evidence of their effectiveness and models of appropriate assessment. Written by political scientists from a range of institutions and subfields, Teaching Civic Engagement makes the case that civic and political engagement should be a central part of our mission as a discipline. |
| putnam math competition 2016 results: Values and Valuing in Mathematics Education Philip Clarkson, Wee Tiong Seah, JeongSuk Pang, 2019-04-24 This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education systems. It also clearly shows that teaching mathematics involves not only reasoning and feelings, but also students’ interactions with their cultural setting and each other. The book brings together the work of world leaders and new thinkers in mathematics educational research to improve the learning and teaching of mathematics. Addressing themes such as discovering hidden cultural values, a multicultural society and methodological issues in the investigation of values in mathematics, it stimulates readers to consider these topics in cross-cultural ways, and offers suggestions for research and classroom practice. It is a valuable resource for scholars of mathematics education, from early childhood through to higher education and an inspiring read for all mathematics teachers. |
| putnam math competition 2016 results: The Magic of Math Arthur Benjamin, 2015-09-08 The world's greatest mental mathematical magician takes us on a spellbinding journey through the wonders of numbers (and more) Arthur Benjamin . . . joyfully shows you how to make nature's numbers dance. -- Bill Nye (the science guy) The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the mathemagician, Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike. A positively joyful exploration of mathematics. -- Publishers Weekly, starred review Each [trick] is more dazzling than the last. -- Physics World |
| putnam math competition 2016 results: 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 competition 2016 results: Grit Angela Duckworth, 2016-05-03 In this instant New York Times bestseller, Angela Duckworth shows anyone striving to succeed that the secret to outstanding achievement is not talent, but a special blend of passion and persistence she calls “grit.” “Inspiration for non-geniuses everywhere” (People). The daughter of a scientist who frequently noted her lack of “genius,” Angela Duckworth is now a celebrated researcher and professor. It was her early eye-opening stints in teaching, business consulting, and neuroscience that led to her hypothesis about what really drives success: not genius, but a unique combination of passion and long-term perseverance. In Grit, she takes us into the field to visit cadets struggling through their first days at West Point, teachers working in some of the toughest schools, and young finalists in the National Spelling Bee. She also mines fascinating insights from history and shows what can be gleaned from modern experiments in peak performance. Finally, she shares what she’s learned from interviewing dozens of high achievers—from JP Morgan CEO Jamie Dimon to New Yorker cartoon editor Bob Mankoff to Seattle Seahawks Coach Pete Carroll. “Duckworth’s ideas about the cultivation of tenacity have clearly changed some lives for the better” (The New York Times Book Review). Among Grit’s most valuable insights: any effort you make ultimately counts twice toward your goal; grit can be learned, regardless of IQ or circumstances; when it comes to child-rearing, neither a warm embrace nor high standards will work by themselves; how to trigger lifelong interest; the magic of the Hard Thing Rule; and so much more. Winningly personal, insightful, and even life-changing, Grit is a book about what goes through your head when you fall down, and how that—not talent or luck—makes all the difference. This is “a fascinating tour of the psychological research on success” (The Wall Street Journal). |
| putnam math competition 2016 results: Mathematical Olympiad in China (2009-2010) Bin Xiong, 2013 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 of comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2009 to 2010. Mathematical Olympiad problems with solutions for the years 2002OCo2008 appear in an earlier volume, Mathematical Olympiad in China. |
| putnam math competition 2016 results: Perfectoid Spaces: Lectures from the 2017 Arizona Winter School Bryden Cais, Bhargav Bhatt, Ana Caraiani, Kiran S. Kedlaya, Peter Scholze, Jared Weinstein, 2019-10-01 Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic p, and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018. This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues–Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in p-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group. This book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications. |
| putnam math competition 2016 results: (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 competition 2016 results: The Psychology of Problem Solving Janet E. Davidson, Robert J. Sternberg, 2003-06-09 Problems are a central part of human life. The Psychology of Problem Solving organizes in one volume much of what psychologists know about problem solving and the factors that contribute to its success or failure. There are chapters by leading experts in this field, including Miriam Bassok, Randall Engle, Anders Ericsson, Arthur Graesser, Keith Stanovich, Norbert Schwarz, and Barry Zimmerman, among others. The Psychology of Problem Solving is divided into four parts. Following an introduction that reviews the nature of problems and the history and methods of the field, Part II focuses on individual differences in, and the influence of, the abilities and skills that humans bring to problem situations. Part III examines motivational and emotional states and cognitive strategies that influence problem solving performance, while Part IV summarizes and integrates the various views of problem solving proposed in the preceding chapters. |
| putnam math competition 2016 results: Proofs in Competition Math: Volume 1 Alexander Toller, Freya Edholm, Dennis Chen, 2019-07-04 All too often, through common school mathematics, students find themselves excelling in school math classes by memorizing formulas, but not their applications or the motivation behind them. As a consequence, understanding derived in this manner is tragically based on little or no proof.This is why studying proofs is paramount! Proofs help us understand the nature of mathematics and show us the key to appreciating its elegance.But even getting past the concern of why should this be true? students often face the question of when will I ever need this in life? Proofs in Competition Math aims to remedy these issues at a wide range of levels, from the fundamentals of competition math all the way to the Olympiad level and beyond.Don't worry if you don't know all of the math in this book; there will be prerequisites for each skill level, giving you a better idea of your current strengths and weaknesses and allowing you to set realistic goals as a math student. So, mathematical minds, we set you off! |
| putnam math competition 2016 results: Mathematical Miniatures Svetoslav Savchev, Titu Andreescu, 2003-02-27 Problems illustrating important mathematical techniques with solutions and accompanying essays. |
| putnam math competition 2016 results: Elementary Methods in Number Theory Melvyn B. Nathanson, 2008-01-11 This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion. |
| putnam math competition 2016 results: p-adic Differential Equations Kiran S. Kedlaya, 2010-06-10 Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study. |
| putnam math competition 2016 results: Introduction to Algebra Richard Rusczyk, 2009 |
| putnam math competition 2016 results: Introduction to Analysis with Complex Numbers Irena Swanson, 2021 This is a self-contained book that covers the standard topics in introductory analysis and that in addition, constructs the natural, rational, real and complex numbers, also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head. The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials. |
| putnam math competition 2016 results: Dream Hoarders Richard V. Reeves, 2018 Dream Hoarders sparked a national conversation on the dangerous separation between the upper middle class and everyone else. Now in paperback and newly updated for the age of Trump, Brookings Institution senior fellow Richard Reeves is continuing to challenge the class system in America. In America, everyone knows that the top 1 percent are the villains. The rest of us, the 99 percent--we are the good guys. Not so, argues Reeves. The real class divide is not between the upper class and the upper middle class: it is between the upper middle class and everyone else. The separation of the upper middle class from everyone else is both economic and social, and the practice of opportunity hoarding--gaining exclusive access to scarce resources--is especially prevalent among parents who want to perpetuate privilege to the benefit of their children. While many families believe this is just good parenting, it is actually hurting others by reducing their chances of securing these opportunities. There is a glass floor created for each affluent child helped by his or her wealthy, stable family. That glass floor is a glass ceiling for another child. Throughout Dream Hoarders, Reeves explores the creation and perpetuation of opportunity hoarding, and what should be done to stop it, including controversial solutions such as ending legacy admissions to school. He offers specific steps toward reducing inequality and asks the upper middle class to pay for it. Convinced of their merit, members of the upper middle class believes they are entitled to those tax breaks and hoarded opportunities. After all, they aren't the 1 percent. The national obsession with the super rich allows the upper middle class to convince themselves that they are just like the rest of America. In Dream Hoarders, Reeves argues that in many ways, they are worse, and that changes in policy and social conscience are the only way to fix the broken system. |
| putnam math competition 2016 results: Successful School Leadership Christopher Day, Pam Sammons, 2017-12 |
| putnam math competition 2016 results: Cracking the Hich School Math Competitions Kevin Wang, Kelly Ren, John Lensmire, 2016-01-20 This book contains the curriculum materials of the Math Challenge courses at Areteem Institute. The math competitions for middle and high school students generally do not involve college mathematics such as calculus and linear algebra. There are four main topics covered in the competitions: Number Theory, Algebra, Geometry, and Combinatorics. The problems in the math competitions are usually challenging problems for which conventional methods are not sufficient, and students are required to use more creative ways to combine the methods they have learned to solve these problems. This book covers these topics, along with fundamental concepts required and problem solving strategies useful for solving problems in the math competitions such as AMC 10 & 12, ARML, and ZIML Division JV. For information about Areteem Institute, visit http: //www.areteem.org. |
| putnam math competition 2016 results: A Primer for the Mathematics of Financial Engineering Dan Stefanica, 2008 |
| putnam math competition 2016 results: The Art of Problem Solving Paul Zeitz, 2021-11-19 The wound is the place where the Light enters you |
| putnam math competition 2016 results: Mathematical Analysis I Vladimir A. Zorich, 2008-11-21 This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books. The first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor. |
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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.
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.
