Download or read book The Unreasonable Effectiveness of Number Theory written by Stefan Andrus Burr and published by American Mathematical Soc.. This book was released on 1992 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Number theory is one of the oldest and noblest branches of mathematics; indeed, it was already ancient in the time of Euclid...for almost all of its history it has seemed to be among the purest branches of mathematics. It is only within the last few decades that a large number of applications have been encountered, at least by the mathematical community. The applications to cryptology are now famous; but it is not as well known that number theory has found an enormous number and variety of real-world applications in many different fields." - From the Preface This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of application of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications.
Download or read book Mathematics without Apologies written by Michael Harris and published by Princeton University Press. This book was released on 2017-05-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
Download or read book Number Theory and Dynamical Systems written by M. M. Dodson and published by Cambridge University Press. This book was released on 1989-11-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.
Download or read book Soccermatics written by David Sumpter and published by Bloomsbury Publishing. This book was released on 2016-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Football looked at in a very different way' Pat Nevin, former Chelsea and Everton star and football media analyst Football – the most mathematical of sports. From shot statistics and league tables to the geometry of passing and managerial strategy, the modern game is filled with numbers, patterns and shapes. How do we make sense of them? The answer lies in the mathematical models applied in biology, physics and economics. Soccermatics brings football and mathematics together in a mind-bending synthesis, using numbers to help reveal the inner workings of the beautiful game. This new and expanded edition analyses the current big-name players and teams using mathematics, and meets the professionals working inside football who use numbers and statistics to boost performance. Welcome to the world of mathematical modelling, expressed brilliantly by David Sumpter through the prism of football. No matter who you follow – from your local non-league side to the big boys of the Premiership, La Liga, the Bundesliga, Serie A or the MLS – you'll be amazed at what mathematics has to teach us about the world's favourite sport.
Download or read book Nature s Numbers written by Ian Stewart and published by Basic Books. This book was released on 2008-08-04 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It appears to us that the universe is structured in a deeply mathematical way. Falling bodies fall with predictable accelerations. Eclipses can be accurately forecast centuries in advance. Nuclear power plants generate electricity according to well-known formulas. But those examples are the tip of the iceberg. In Nature's Numbers, Ian Stewart presents many more, each charming in its own way.. Stewart admirably captures compelling and accessible mathematical ideas along with the pleasure of thinking of them. He writes with clarity and precision. Those who enjoy this sort of thing will love this book."—Los Angeles Times
Download or read book How Mathematicians Think written by William Byers and published by Princeton University Press. This book was released on 2010-05-02 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Download or read book Role of Mathematics in the Rise of Science written by Salomon Bochner Trust and published by Princeton University Press. This book was released on 2014-07-14 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of these essays is the nature and role of mathematics, its growth and spread, and its involvement with ever-wider areas of knowledge. The author attempts to determine the decisive and creative aspects of the abstractness" of mathematics which have made it the dominant intellectual force that it is. He frequently confronts the mathematics and physics of today with the mathematics and physics of the Greeks, which, however renowned, was not yet capable of this abstractness. Originally published in 1966. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Mathematical Methods in Science written by George Pólya and published by Cambridge University Press. This book was released on 1977 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book captures some of Pólya's excitement and vision. Its distinctive feature is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics.
Download or read book Is God a Mathematician written by Mario Livio and published by Simon and Schuster. This book was released on 2011-02-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
Download or read book The Minimum Description Length Principle written by Peter D. Grünwald and published by MIT Press. This book was released on 2007 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the MDL Principle provides a reference accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection.
Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
Download or read book Cryptology and Computational Number Theory written by Carl Pomerance and published by American Mathematical Soc.. This book was released on 1990 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.
Download or read book Number Theory in Science and Communication written by M.R. Schroeder and published by Springer Science & Business Media. This book was released on 2006-01-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory in Science and Communication introductes non-mathematicians to the fascinating and diverse applications of number theory. This best-selling book stresses intuitive understanding rather than abstract theory. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Download or read book 100 Years of Math Milestones The Pi Mu Epsilon Centennial Collection written by Stephan Ramon Garcia and published by American Mathematical Soc.. This book was released on 2019-06-13 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics. In places, some knowledge of analysis or algebra, number theory or probability will be helpful. Put together, these problems will be appealing and accessible to energetic and enthusiastic math majors and aficionados of all stripes. Stephan Ramon Garcia is WM Keck Distinguished Service Professor and professor of mathematics at Pomona College. He is the author of four books and over eighty research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and other fields. He has coauthored dozens of articles with students, including one that appeared in The Best Writing on Mathematics: 2015. He is on the editorial boards of Notices of the AMS, Proceedings of the AMS, American Mathematical Monthly, Involve, and Annals of Functional Analysis. He received four NSF research grants as principal investigator and five teaching awards from three different institutions. He is a fellow of the American Mathematical Society and was the inaugural recipient of the Society's Dolciani Prize for Excellence in Research. Steven J. Miller is professor of mathematics at Williams College and a visiting assistant professor at Carnegie Mellon University. He has published five books and over one hundred research papers, most with students, in accounting, computer science, economics, geophysics, marketing, mathematics, operations research, physics, sabermetrics, and statistics. He has served on numerous editorial boards, including the Journal of Number Theory, Notices of the AMS, and the Pi Mu Epsilon Journal. He is active in enrichment and supplemental curricular initiatives for elementary and secondary mathematics, from the Teachers as Scholars Program and VCTAL (Value of Computational Thinking Across Grade Levels), to numerous math camps (the Eureka Program, HCSSiM, the Mathematics League International Summer Program, PROMYS, and the Ross Program). He is a fellow of the American Mathematical Society, an at-large senator for Phi Beta Kappa, and a member of the Mount Greylock Regional School Committee, where he sees firsthand the challenges of applying mathematics.
Download or read book Selected Papers II with Commentaries written by Chen Ning Yang and published by World Scientific. This book was released on 2013 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of Professor Chen Ning Yang's personally selected papers (1971-2012) supplemented by his commentaries. Its contents reflect the professor's changing interests after he reached age sixty.
