Author : James Fraser McKee
Publisher : Cambridge University Press
Page : 350 pages
File Size : 43,13 MB
Release : 2008-05-08
Category : Mathematics
ISBN : 0521714672
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Author : Jaime Gutierrez
Publisher : Springer
Page : 222 pages
File Size : 50,65 MB
Release : 2015-01-20
Category : Computers
ISBN : 3319150812
Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.
Author : Qazi Ibadur Rahman
Publisher : Oxford University Press
Page : 760 pages
File Size : 22,92 MB
Release : 2002
Category : Language Arts & Disciplines
ISBN : 9780198534938
Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications
Author : Gove W. Effinger
Publisher :
Page : 184 pages
File Size : 13,18 MB
Release : 1991
Category : Mathematics
ISBN :
This book helps gather the sum of additive number theory.
Author : Michael Rosen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 25,4 MB
Release : 2013-04-18
Category : Mathematics
ISBN : 1475760469
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.
Author : Theodore J. Rivlin
Publisher : Wiley-Interscience
Page : 200 pages
File Size : 32,89 MB
Release : 1974
Category : Mathematics
ISBN :
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 43,32 MB
Release : 2013-04-17
Category : 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 : Peter Borwein
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 30,81 MB
Release : 1995-09-27
Category : Mathematics
ISBN : 9780387945095
After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Müntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality round off the text. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis.
Author : Gradimir V. Milovanović
Publisher : Springer
Page : 873 pages
File Size : 27,79 MB
Release : 2014-07-08
Category : Mathematics
ISBN : 149390258X
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.
Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 31,41 MB
Release : 2001-02-22
Category : Mathematics
ISBN : 9780521004237
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
