A Course In Computational Number Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A Course In Computational Number Theory PDF full book. Access full book title A Course In Computational Number Theory.
Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 556 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662029456 |
Download A Course in Computational Algebraic Number Theory Book in PDF, ePub and Kindle
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Author | : David Bressoud |
Publisher | : Wiley |
Total Pages | : 0 |
Release | : 2008-06-10 |
Genre | : Mathematics |
ISBN | : 9780470412152 |
Download A Course in Computational Number Theory Book in PDF, ePub and Kindle
A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell’s equation, and the Gaussian primes.
Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 591 |
Release | : 2012-10-29 |
Genre | : Mathematics |
ISBN | : 1441984895 |
Download Advanced Topics in Computational Number Theory Book in PDF, ePub and Kindle
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Author | : Abhijit Das |
Publisher | : CRC Press |
Total Pages | : 614 |
Release | : 2016-04-19 |
Genre | : Computers |
ISBN | : 1482205823 |
Download Computational Number Theory Book in PDF, ePub and Kindle
Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract
Author | : David Bressoud |
Publisher | : Springer |
Total Pages | : 394 |
Release | : 2000-05-11 |
Genre | : Mathematics |
ISBN | : |
Download A Course in Computational Number Theor Book in PDF, ePub and Kindle
"The accompanying CD-Rom contains Mathematica files with all the commands and programs."--P. [4] of cover.
Author | : Peter Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 220 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0387216529 |
Download Computational Excursions in Analysis and Number Theory Book in PDF, ePub and Kindle
This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
Author | : Neal Koblitz |
Publisher | : Springer Science & Business Media |
Total Pages | : 245 |
Release | : 2012-09-05 |
Genre | : Mathematics |
ISBN | : 1441985921 |
Download A Course in Number Theory and Cryptography Book in PDF, ePub and Kindle
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.
Author | : William Stein |
Publisher | : Springer Science & Business Media |
Total Pages | : 173 |
Release | : 2008-10-28 |
Genre | : Mathematics |
ISBN | : 0387855254 |
Download Elementary Number Theory: Primes, Congruences, and Secrets Book in PDF, ePub and Kindle
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.
Author | : Marius Overholt |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 2014-12-30 |
Genre | : Mathematics |
ISBN | : 1470417065 |
Download A Course in Analytic Number Theory Book in PDF, ePub and Kindle
This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Author | : Harald Niederreiter |
Publisher | : Springer |
Total Pages | : 452 |
Release | : 2015-09-01 |
Genre | : Mathematics |
ISBN | : 3319223216 |
Download Applied Number Theory Book in PDF, ePub and Kindle
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.