elementary number theory with programming

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Elementary Number Theory With Programming

Author : Marty Lewinter
ISBN : 9781119062769
Genre : Mathematics
File Size : 42. 70 MB
Format : PDF
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Filling a much-needed gap in the current literature, this book expertly bridges the subjects of number theory and programming and features a multitude of examples and programming exercises in each chapter. It provides an introduction to elementary number theory with fundamental coverage of computer programming and is appropriate for students of mathematics and computer science alike who need to become acquainted with the most famous theorems, problems, and concepts of number theory. In addition, the authors provide a comprehensive presentation of the methodology and applications for readers with various levels of experience, and while theorems are provided, the authors avoid the standard theorem/proof format to aid in reader comprehension. The book features sample programs and research challenges at the end of each chapter for readers to work through, as well as an appendix that provides select answers to the chapter exercises. The authors also maintain a supplementary material website that provides additional working examples of the computer programs. Topical coverage includes: special numbers; Fibonacci sequence, primes, and the Pell equation; Pascal's triangle; divisors and prime decomposition; modular arithmetic; number theoretic functions; Euler's Phi function; sums and partitions; and cryptography. Prerequisites include basic algebra and some knowledge of any computer language.

Elementary Number Theory Cryptography And Codes

Author : M. Welleda Baldoni
ISBN : 3540692002
Genre : Mathematics
File Size : 72. 36 MB
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In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.

Number Theory For Computing

Author : Song Y. Yan
ISBN : 9783662047736
Genre : Computers
File Size : 74. 30 MB
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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.

Elementary Number Theory With Applications

Author : Thomas Koshy
ISBN : 0080547095
Genre : Mathematics
File Size : 78. 49 MB
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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

Elementary Number Theory Primes Congruences And Secrets

Author : William Stein
ISBN : 9780387855257
Genre : Mathematics
File Size : 82. 38 MB
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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

Author : James K. Strayer
ISBN : 9781478610403
Genre : Mathematics
File Size : 53. 85 MB
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In this student-friendly text, Strayer presents all of the topics necessary for a first course in number theory. Additionally, chapters on primitive roots, Diophantine equations, and continued fractions allow instructors the flexibility to tailor the material to meet their own classroom needs. Each chapter concludes with seven Student Projects, one of which always involves programming a calculator or computer. All of the projects not only engage students in solving number-theoretical problems but also help familiarize them with the relevant mathematical literature.

A Course In Number Theory And Cryptography

Author : Neal Koblitz
ISBN : 9781441985927
Genre : Mathematics
File Size : 28. 74 MB
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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 Computational Introduction To Number Theory And Algebra

Author : Victor Shoup
ISBN : 9780521516440
Genre : Computers
File Size : 75. 60 MB
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An introductory graduate-level text emphasizing algorithms and applications. This second edition includes over 200 new exercises and examples.

A Guide To Elementary Number Theory

Author : Underwood Dudley
ISBN : 0883853477
Genre : Mathematics
File Size : 23. 47 MB
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"A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through traditional texts, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for qualifying exams. Though Plato did not quite say, "He is unworthy of the name of man who does not know which integers are the sums of two squares," he came close. This guide can make everyone more worthy."--P. [4] of cover.

Elementary Number Theory And Its Applications

Author : Kenneth H. Rosen
ISBN : STANFORD:36105028630296
Genre : Nombres, Théorie des
File Size : 59. 54 MB
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The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

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