Author : Joseph Landin
Publisher : Courier Corporation
Page : 275 pages
File Size : 40,89 MB
Release : 2012-08-29
Category : Mathematics
ISBN : 0486150410
This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
Author : Martyn R. Dixon
Publisher : John Wiley & Sons
Page : 544 pages
File Size : 25,13 MB
Release : 2011-07-15
Category : Mathematics
ISBN : 9780470640531
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
Author : George R. Kempf
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 29,72 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3322802787
In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.
Author : Dirk Hachenberger
Publisher : Springer Nature
Page : 785 pages
File Size : 15,33 MB
Release : 2020-09-29
Category : Mathematics
ISBN : 3030608069
This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.
Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 47,41 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.
Author : Ichiro Satake
Publisher : Princeton University Press
Page : 340 pages
File Size : 14,65 MB
Release : 2014-07-14
Category : Mathematics
ISBN : 1400856809
This book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Ian Stewart
Publisher : CRC Press
Page : 334 pages
File Size : 21,40 MB
Release : 2001-12-12
Category : Mathematics
ISBN : 143986408X
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 29,18 MB
Release : 2010-01-14
Category : Mathematics
ISBN : 0486474178
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Author : Harry Pollard
Publisher : American Mathematical Soc.
Page : 175 pages
File Size : 35,94 MB
Release : 1975-12-31
Category : Mathematics
ISBN : 1614440093
This 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 : S P Lam
Publisher : World Scientific
Page : 346 pages
File Size : 10,38 MB
Release : 1990-12-31
Category :
ISBN : 9814611425
In this proceedings, recent development on various aspects of algebra and number theory were discussed. A wide range of topics such as group theory, ring theory, semi-group theory, topics on algebraic structures, class numbers, quadratic forms, reciprocity formulae were covered.
