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Author: James Fraser McKee
Publisher: Cambridge University Press
Published: 2008-05-08
Total Pages: 350
ISBN-13: 0521714672
DOWNLOAD EBOOKContributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Author: Jaime Gutierrez
Publisher: Springer
Published: 2015-01-20
Total Pages: 222
ISBN-13: 3319150812
DOWNLOAD EBOOKAlgebra 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: Gove W. Effinger
Publisher:
Published: 1991
Total Pages: 184
ISBN-13:
DOWNLOAD EBOOKThis book helps gather the sum of additive number theory.
Author: Harry Pollard
Publisher: American Mathematical Soc.
Published: 1975-12-31
Total Pages: 175
ISBN-13: 1614440093
DOWNLOAD EBOOKThis monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Author: Michael Rosen
Publisher: Springer Science & Business Media
Published: 2013-04-18
Total Pages: 355
ISBN-13: 1475760469
DOWNLOAD EBOOKEarly 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: Qazi Ibadur Rahman
Publisher: Oxford University Press
Published: 2002
Total Pages: 760
ISBN-13: 9780198534938
DOWNLOAD EBOOKPresents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications
Author: Theodore J. Rivlin
Publisher: Wiley-Interscience
Published: 1974
Total Pages: 200
ISBN-13:
DOWNLOAD EBOOKAuthor: Peter Borwein
Publisher: Springer Science & Business Media
Published: 1995-09-27
Total Pages: 508
ISBN-13: 9780387945095
DOWNLOAD EBOOKAfter 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: Henri Cohen
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 556
ISBN-13: 3662029456
DOWNLOAD EBOOKA 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: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
Published: 2001-02-22
Total Pages: 164
ISBN-13: 9780521004237
DOWNLOAD EBOOKBroad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
