A Computational Introduction To Number Theory And Algebra
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Author | : Victor Shoup |
Publisher | : Cambridge University Press |
Total Pages | : 599 |
Release | : 2009 |
Genre | : Computers |
ISBN | : 0521516447 |
An introductory graduate-level text emphasizing algorithms and applications. This second edition includes over 200 new exercises and examples.
Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 556 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662029456 |
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 | : M.E. Pohst |
Publisher | : Springer Science & Business Media |
Total Pages | : 108 |
Release | : 1993-09 |
Genre | : Gardening |
ISBN | : 9783764329136 |
Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker-Vereinigung initiated an introductory graduate seminar on this topic in Dusseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. The workshops organized by the Gesselschaft fur mathematische Forschung in cooperation with the Deutsche Mathematiker-Vereinigung (German Mathematics Society) are intended to help, in particular, students and younger mathematicians, to obtain an introduction to fields of current research. Through the means of these well-organized seminars, scientists from other fields can also be introduced to new mathematical ideas. The publication of these workshops in the series DMV SEMINAR will make the material available to an even larger audience.
Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 591 |
Release | : 2012-10-29 |
Genre | : Mathematics |
ISBN | : 1441984895 |
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 |
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 | : Wieb Bosma |
Publisher | : Springer Science & Business Media |
Total Pages | : 326 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401711089 |
Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.
Author | : Anthony Vazzana |
Publisher | : CRC Press |
Total Pages | : 530 |
Release | : 2007-10-30 |
Genre | : Computers |
ISBN | : 1584889381 |
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
Author | : Harold M. Edwards |
Publisher | : American Mathematical Soc. |
Total Pages | : 228 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821844397 |
Among the topics featured in this textbook are: congruences; the fundamental theorem of arithmetic; exponentiation and orders; primality testing; the RSA cipher system; polynomials; modules of hypernumbers; signatures of equivalence classes; and the theory of binary quadratic forms. The book contains exercises with answers.
Author | : W.A. Coppel |
Publisher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2006-02-02 |
Genre | : Mathematics |
ISBN | : 9780387298511 |
This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.
Author | : George E. Andrews |
Publisher | : Courier Corporation |
Total Pages | : 292 |
Release | : 2012-04-30 |
Genre | : Mathematics |
ISBN | : 0486135101 |
Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.