Advertisement
| putnam exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: Model Rules of Professional Conduct American Bar Association. House of Delegates, Center for Professional Responsibility (American Bar Association), 2007 The Model Rules of Professional Conduct provides an up-to-date resource for information on legal ethics. Federal, state and local courts in all jurisdictions look to the Rules for guidance in solving lawyer malpractice cases, disciplinary actions, disqualification issues, sanctions questions and much more. In this volume, black-letter Rules of Professional Conduct are followed by numbered Comments that explain each Rule's purpose and provide suggestions for its practical application. The Rules will help you identify proper conduct in a variety of given situations, review those instances where discretionary action is possible, and define the nature of the relationship between you and your clients, colleagues and the courts. |
| putnam exam practice problems: 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 exam practice problems: CliffsNotes ASVAB AFQT Cram Plan 2nd Edition Pat Proctor, Carolyn C. Wheater, Jane R. Burstein, 2019 Proctor, Wheater and Burstein have a plan to help you ace the Armed Services Vocational Battery (ASVAB) Armed Forces Qualifying Test (AFQT) exam -- whether you have two months, one month or one week left to prepare. They provide week-by-week and day-by-day schedules of the best ways to focus your study according to your unique timeline. And the plan includes a diagnostic test, review of subject areas, and a practice exam, so you can make the most of the time you have left. -- adapted from back cover |
| putnam exam practice problems: 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 exam practice problems: Excursions in Classical Analysis Hongwei Chen, 2010-12-31 Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The [Author]; presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order. |
| putnam exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: 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 exam practice problems: The Survival of a Mathematician Steven George Krantz, 2009 One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration. In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide.--BOOK JACKET. |
| putnam exam practice problems: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| putnam exam practice problems: 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 exam practice problems: A Mathematical Mosaic Ravi Vakil, 1996 Powerful problem solving ideas that focus on the major branches of mathematics and their interconnections. |
| putnam exam practice problems: How I Became a Quant Richard R. Lindsey, Barry Schachter, 2011-01-11 Praise for How I Became a Quant Led by two top-notch quants, Richard R. Lindsey and Barry Schachter, How I Became a Quant details the quirky world of quantitative analysis through stories told by some of today's most successful quants. For anyone who might have thought otherwise, there are engaging personalities behind all that number crunching! --Ira Kawaller, Kawaller & Co. and the Kawaller Fund A fun and fascinating read. This book tells the story of how academics, physicists, mathematicians, and other scientists became professional investors managing billions. --David A. Krell, President and CEO, International Securities Exchange How I Became a Quant should be must reading for all students with a quantitative aptitude. It provides fascinating examples of the dynamic career opportunities potentially open to anyone with the skills and passion for quantitative analysis. --Roy D. Henriksson, Chief Investment Officer, Advanced Portfolio Management Quants--those who design and implement mathematical models for the pricing of derivatives, assessment of risk, or prediction of market movements--are the backbone of today's investment industry. As the greater volatility of current financial markets has driven investors to seek shelter from increasing uncertainty, the quant revolution has given people the opportunity to avoid unwanted financial risk by literally trading it away, or more specifically, paying someone else to take on the unwanted risk. How I Became a Quant reveals the faces behind the quant revolution, offering you?the?chance to learn firsthand what it's like to be a?quant today. In this fascinating collection of Wall Street war stories, more than two dozen quants detail their roots, roles, and contributions, explaining what they do and how they do it, as well as outlining the sometimes unexpected paths they have followed from the halls of academia to the front lines of an investment revolution. |
| putnam exam practice problems: Discrete Mathematics László Lovász, József Pelikán, K. Vesztergombi, 2003-01-27 Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book. |
| putnam exam practice problems: Problems in Mathematical Analysis Wieslawa J. Kaczor, Maria T. Nowak, 2000 |
| putnam exam practice problems: Introduction to Algebra Richard Rusczyk, 2009 |
| putnam exam practice problems: 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 exam practice problems: 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 exam practice problems: The Perimeter Jeff Putnam, 2021-06 THE FIRES HAVE BEEN LIT. The Perimeter is a follow-up to Empire Divided that challenged the global-centric idealism that plagues our modern world. If a noble culture based on virtue and greatness is to once again emerge, the battle lines must be drawn. The way of the tribe is the way of man as he was meant to be. In order to bring about order to the dark forces that seek the destruction of masculinity and personal sovereignty, Men must take their light and journey beyond the border fires. They must meet the enemy on their own turf and invade the hearts and minds of those that can still be saved. |
| putnam exam practice problems: Blackstone's Statutes on Intellectual Property Andrew Christie, Stephen Gare, 2008 This volume gives coverage of international intellectual property law, containing all the up-to-date legislation relevant to undergraduate law degrees. |
| putnam exam practice problems: U.S.A. Mathematical Olympiads, 1972-1986 , 1988 |
| putnam exam practice problems: THE CRUCIBLE ARTHUR MILLER, 1971 |
| putnam exam practice problems: 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 exam practice problems: Prealgebra Richard Rusczyk, David Patrick, Ravi Bopu Boppana, 2011-08 Prealgebra prepares students for the rigors of algebra, and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8.Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual contains full solutions to all of the problems, not just answers. |
| putnam exam practice problems: 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 exam practice problems: Hard Math for Middle School Glenn Ellison, 2010-09-11 MIT Professor Glenn Ellison has spent more than a decade coaching math teams and developing math enrichment materials for his daughters and their classmates. His middle school Hard Math textbook and workbook contain the materials he used while coaching many successful Mathcounts teams. They are a labor of love sold at bargain prices with the hope that they will help students around the world develop a deep understanding of middle school math and enjoy every minute of it. The topics align with modern middle school curricula: fractions, decimals, percents, prime factorization, plane and spatial geometry, probability, statistics, combinatorics, algebra, modular arithmetic, etc. But Hard Math challenges students to develop a deeper understanding: it asks much harder questions than standard texts and teaches the material and problem solving strategies students need to attack them. For example, rather than asking students to write 2/5 as a decimal, it might ask students to use the fact that 99999 = 9 × 41 × 271 to find the tenth digit in the decimal expansion for 1/271. (It might ask this, but never actually does.) The personal and somewhat irreverent prose in the IMLEM Plus edition of Hard Math for Middle School speaks directly to students participating in both the Intermediate Math League of Eastern Massachusetts and Mathcounts(r). The organization of the book is also designed to serve IMLEM students. But middle school math is middle school math and the book should be great for students preparing for other math contests or just looking for general enrichment or hard problems to do. Hard Math for Middle School: Workbook, sold separately, contains over 100 worksheets. The worksheets have problems at different difficulty levels that students can use to solidify their understanding of the material in each section of the textbook. It would be crazy to buy this text and not also get a copy of the workbook unless your child is using this book in school or in an enrichment program that is already providing plenty of practice problems. Solutions to many of the problems in the workbook are currently available for free on Prof. Ellison's website. Mathcounts(r) is a registered trademark of the Mathcounts Foundation, which was not involved in the production of, and does not endorse, this book. |
| putnam exam practice problems: 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 exam practice problems: A Hilbert Space Problem Book P.R. Halmos, 2012-12-06 From the Preface: This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book. |
| putnam exam practice problems: Introduction to Counting and Probability Solutions Manual David Patrick, 2007-08 |
| putnam exam practice problems: Networks, Crowds, and Markets David Easley, Jon Kleinberg, 2010-07-19 Are all film stars linked to Kevin Bacon? Why do the stock markets rise and fall sharply on the strength of a vague rumour? How does gossip spread so quickly? Are we all related through six degrees of separation? There is a growing awareness of the complex networks that pervade modern society. We see them in the rapid growth of the internet, the ease of global communication, the swift spread of news and information, and in the way epidemics and financial crises develop with startling speed and intensity. This introductory book on the new science of networks takes an interdisciplinary approach, using economics, sociology, computing, information science and applied mathematics to address fundamental questions about the links that connect us, and the ways that our decisions can have consequences for others. |
| putnam exam practice problems: Mathematical Miniatures Svetoslav Savchev, Titu Andreescu, 2003-02-27 Problems illustrating important mathematical techniques with solutions and accompanying essays. |
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.
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.
