Elementary Number Theory With Programming

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Elementary Number Theory with Programming

Marty Lewinter,Jeanine Meyer
Elementary Number Theory with Programming Book PDF

Author : Marty Lewinter,Jeanine Meyer
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 41,5 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9781119062769

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Elementary Number Theory with Programming by Marty Lewinter,Jeanine Meyer Pdf

A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.

Elementary Number Theory: Primes, Congruences, and Secrets

William Stein
Elementary Number Theory Primes Congruences and Secrets Book PDF

Author : William Stein
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 53,7 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 9780387855257

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Elementary Number Theory: Primes, Congruences, and Secrets by William Stein Pdf

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Elementary Number Theory with Applications

Thomas Koshy
Elementary Number Theory with Applications Book PDF

Author : Thomas Koshy
Publisher : Elsevier
Page : 801 pages
File Size : 47,8 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9780080547091

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Elementary Number Theory with Applications by Thomas Koshy Pdf

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

An Introductory Course in Elementary Number Theory

Wissam Raji
An Introductory Course in Elementary Number Theory Book PDF

Author : Wissam Raji
Publisher : The Saylor Foundation
Page : 171 pages
File Size : 52,8 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 8210379456XXX

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An Introductory Course in Elementary Number Theory by Wissam Raji Pdf

These notes serve as course notes for an undergraduate course in number theory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required. The exercises are carefully chosen to broaden the understanding of the concepts. Moreover, these notes shed light on analytic number theory, a subject that is rarely seen or approached by undergraduate students. One of the unique characteristics of these notes is the careful choice of topics and its importance in the theory of numbers. The freedom is given in the last two chapters because of the advanced nature of the topics that are presented.

Elementary Number Theory

James S. Kraft,Lawrence C. Washington
Elementary Number Theory Book PDF

Author : James S. Kraft,Lawrence C. Washington
Publisher : CRC Press
Page : 412 pages
File Size : 50,5 Mb
Release : 2014-11-24
Category : Mathematics
ISBN : 9781498702683

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Elementary Number Theory by James S. Kraft,Lawrence C. Washington Pdf

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat’s, Euler’s, and Wilson’s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments. The book offers many pedagogical features. The "check your understanding" problems scattered throughout the chapters assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.

Number Theory for Computing

Song Y. Yan
Number Theory for Computing Book PDF

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 40,7 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783662047736

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Number Theory for Computing by Song Y. Yan Pdf

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.

Discrete Mathematics and Its Applications

Kenneth H. Rosen
Discrete Mathematics and Its Applications Book PDF

Author : Kenneth H. Rosen
Publisher : Unknown
Page : 109 pages
File Size : 50,8 Mb
Release : 2007
Category : Computer science
ISBN : 0071244743

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Discrete Mathematics and Its Applications by Kenneth H. Rosen Pdf

The companion Web site -- To the student -- The foundations : logic, sets, and functions -- The fundamentals : algorithms, the integers, and matrices -- Mathematical reasoning -- Counting -- Advanced counting techniques -- Relations -- Graphs -- Trees -- Boolean algebra -- Modeling computation

Elementary Number Theory

James S. Kraft,Lawrence C. Washington
Elementary Number Theory Book PDF

Author : James S. Kraft,Lawrence C. Washington
Publisher : CRC Press
Page : 407 pages
File Size : 51,8 Mb
Release : 2014-11-24
Category : Mathematics
ISBN : 9781498702690

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Elementary Number Theory by James S. Kraft,Lawrence C. Washington Pdf

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the tex

Elementary Number Theory

Charles Vanden Eynden
Elementary Number Theory Book PDF

Author : Charles Vanden Eynden
Publisher : Waveland Press
Page : 278 pages
File Size : 54,6 Mb
Release : 2006-02-15
Category : Electronic
ISBN : 9781478639152

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Elementary Number Theory by Charles Vanden Eynden Pdf

This practical and versatile text evolved from the author’s years of teaching experience and the input of his students. Vanden Eynden strives to alleviate the anxiety that many students experience when approaching any proof-oriented area of mathematics, including number theory. His informal yet straightforward writing style explains the ideas behind the process of proof construction, showing that mathematicians develop theorems and proofs from trial and error and evolutionary improvement, not spontaneous insight. Furthermore, the book includes more computational problems than most other number theory texts to build students’ familiarity and confidence with the theory behind the material. The author has devised the content, organization, and writing style so that information is accessible, students can gain self-confidence with respect to mathematics, and the book can be used in a wide range of courses—from those that emphasize history and type A problems to those that are proof oriented.

Excursions in Number Theory

Charles Stanley Ogilvy,John Timothy Anderson
Excursions in Number Theory Book PDF

Author : Charles Stanley Ogilvy,John Timothy Anderson
Publisher : Courier Corporation
Page : 196 pages
File Size : 49,7 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 0486257789

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Excursions in Number Theory by Charles Stanley Ogilvy,John Timothy Anderson Pdf

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

An Illustrated Theory of Numbers

Martin H. Weissman
An Illustrated Theory of Numbers Book PDF

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
Page : 341 pages
File Size : 41,7 Mb
Release : 2020-09-15
Category : Education
ISBN : 9781470463717

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An Illustrated Theory of Numbers by Martin H. Weissman Pdf

News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

Number Theory

Mark A. Herkommer
Number Theory Book PDF

Author : Mark A. Herkommer
Publisher : McGraw-Hill Companies
Page : 425 pages
File Size : 43,6 Mb
Release : 1999
Category : Computers
ISBN : 0079130747

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Number Theory by Mark A. Herkommer Pdf

Number theory is used by mathematicians, computer scientists, and programmers to solve real-world programming problems. In turn, computers are used to solve problems in number theory. Until now, the literature has provided far more theory than practice, which means the field is poorly understood and underutilized. This book provides practical guidelines and source code for everyday applications.

A Course in Number Theory and Cryptography

Neal Koblitz
A Course in Number Theory and Cryptography Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 43,8 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9781441985927

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

A Classical Introduction to Modern Number Theory

K. Ireland,M. Rosen
A Classical Introduction to Modern Number Theory Book PDF

Author : K. Ireland,M. Rosen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475717792

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A Classical Introduction to Modern Number Theory by K. Ireland,M. Rosen Pdf

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

Elementary Number Theory and Its Applications

Kenneth H. Rosen
Elementary Number Theory and Its Applications Book PDF

Author : Kenneth H. Rosen
Publisher : Addison Wesley Publishing Company
Page : 752 pages
File Size : 42,9 Mb
Release : 2005
Category : Mathematics
ISBN : UCSC:32106017555654

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Elementary Number Theory and Its Applications by Kenneth H. Rosen Pdf

Elementary Number Theory and Its Applicationsis noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years.