The Unreasonable Effectiveness Of Number Theory

Author : Stefan Andrus Burr,George E. Andrews
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 43,9 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855018

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The Unreasonable Effectiveness of Number Theory by Stefan Andrus Burr,George E. Andrews Pdf

"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.

Author : Stefan A. Burr
Publisher : American Mathematical Society(RI)
Page : 139 pages
File Size : 47,7 Mb
Release : 1992
Category : Number theory
ISBN : 0821892614

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The Unreasonable Effectiveness of Number Theory by Stefan A. Burr Pdf

This work is based on the AMS Short Course The Unreasonable Effectiveness of Number Theory held in Orono, Maine, USA, in August 1991. The 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 should be of use 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.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 47,8 Mb
Release : 1992
Category : Number theory
ISBN : 0821867512

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The Unreasonable Effectiveness of Number Theory by Anonim Pdf

Author : Manfred Schroeder
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 40,6 Mb
Release : 2008-11-06
Category : Science
ISBN : 9783540852971

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Number Theory in Science and Communication by Manfred Schroeder Pdf

"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner

Author : M.R. Schroeder
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 47,9 Mb
Release : 2006-01-06
Category : Mathematics
ISBN : 9783540265986

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Number Theory in Science and Communication by M.R. Schroeder Pdf

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.

Author : Manfred Robert Schroeder
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 47,9 Mb
Release : 1997
Category : Computers
ISBN : 3540620060

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Number Theory in Science and Communication by Manfred Robert Schroeder Pdf

Number Theory in Science and Communication is an introduction for non-mathematicians. The book stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primituve elements. Their applications to problems in the real world is one of the main themes of the book. This third 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.

Author : Tristin Cleveland
Publisher : Scientific e-Resources
Page : 328 pages
File Size : 41,6 Mb
Release : 2018-04-11
Category : Electronic
ISBN : 9781839473265

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Number Theory by Tristin Cleveland Pdf

In spite of the fact that arithmetic majors are generally familiar with number hypothesis when they have finished a course in conceptual polynomial math, different students, particularly those in training and the human sciences, regularly require a more essential prologue to the theme. In this book the writer takes care of the issue of keeping up the enthusiasm of understudies at the two levels by offering a combinatorial way to deal with basic number hypothesis. In concentrate number hypothesis from such a point of view, arithmetic majors are saved reiteration and furnished with new bits of knowledge, while different understudies advantage from the subsequent effortlessness of the verifications for some hypotheses. Of specific significance in this content is the creator's accentuation on the estimation of numerical cases in number hypothesis and the part of PCs in getting such illustrations. The point of this book is to acquaint the reader with essential subjects in number hypothesis: hypothesis of distinctness, arithmetrical capacities, prime numbers, geometry of numbers, added substance number hypothesis, probabilistic number hypothesis, hypothesis of Diophantine approximations and logarithmic number hypothesis.

Author : Harald Niederreiter,Arne Winterhof
Publisher : Springer
Page : 442 pages
File Size : 42,9 Mb
Release : 2015-09-01
Category : Mathematics
ISBN : 9783319223216

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Applied Number Theory by Harald Niederreiter,Arne Winterhof Pdf

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

Author : Anthony Vazzana,David Garth
Publisher : CRC Press
Page : 426 pages
File Size : 42,6 Mb
Release : 2015-11-18
Category : Mathematics
ISBN : 9781498717502

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Introduction to Number Theory by Anthony Vazzana,David Garth Pdf

Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert's tenth problem.

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 54,9 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662040539

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Number Theory for Computing by Song Y. Yan Pdf

Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.

Author : Carl Pomerance,Shafi Goldwasser
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 44,8 Mb
Release : 1990
Category : Computers
ISBN : 0821801554

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Cryptology and Computational Number Theory by Carl Pomerance,Shafi Goldwasser Pdf

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.

Author : Stephan Ramon Garcia,Steven J. Miller
Publisher : American Mathematical Soc.
Page : 581 pages
File Size : 50,5 Mb
Release : 2019-06-13
Category : Mathematics
ISBN : 9781470436520

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100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection by Stephan Ramon Garcia,Steven J. Miller Pdf

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.

Author : M.A. Bennett,Bruce Berndt,N. Boston,A.J. Hildebrand,H.G. Diamond,W. Philipp
Publisher : CRC Press
Page : 458 pages
File Size : 55,8 Mb
Release : 2023-03-17
Category : Mathematics
ISBN : 9780429611414

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Number Theory for the Millennium III by M.A. Bennett,Bruce Berndt,N. Boston,A.J. Hildebrand,H.G. Diamond,W. Philipp Pdf

Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field. The conference was the largest general number theory conference in recent history, featuring a total of 159 talks, with the plenary lectures given by George Andrews, Jean Bourgain, Kevin Ford, Ron Graham, Andrew Granville, Roger Heath-Brown, Christopher Hooley, Winnie Li, Kumar Murty, Mel Nathanson, Ken Ono, Carl Pomerance, Bjorn Poonen, Wolfgang Schmidt, Chris Skinner, K. Soundararajan, Robert Tijdeman, Robert Vaughan, and Hugh Williams. The Proceedings Volumes of the conference review some of the major number theory achievements of this century and to chart some of the directions in which the subject will be heading during the new century. These volumes will serve as a useful reference to researchers in the area and an introduction to topics of current interest in number theory for a general audience in mathematics.

Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 52,7 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223

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CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein Pdf

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Author : R.P. Bambah,V.C. Dumir,R.J. Hans-Gill
Publisher : Birkhäuser
Page : 525 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034870238

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Number Theory by R.P. Bambah,V.C. Dumir,R.J. Hans-Gill Pdf

The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.