This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.
This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.
Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.
In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.
This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.
Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.
In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Автор: Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf Название: Discrete Algebraic Methods: Arithmetic, Cryptography, Automata and Groups ISBN: 3110413329 ISBN-13(EAN): 9783110413328 Издательство: Walter de Gruyter Цена: 6499.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups
Автор: Reis Clive Название: Abstract Algebra: An Introduction To Groups, Rings And Fields ISBN: 9814335649 ISBN-13(EAN): 9789814335645 Издательство: World Scientific Publishing Рейтинг: Цена: 18374.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Suitable for second to fourth year undergraduates, this title contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space.
Автор: Rowen Louis Название: Algebra Groups Rings & Fields ISBN: 0367449234 ISBN-13(EAN): 9780367449230 Издательство: Taylor&Francis Рейтинг: Цена: 10104.00 р. Наличие на складе: Нет в наличии.
Описание: This book provides the traditional role of exercises in a course to provide more-or-less routine applications of the main results, for the student`s edification and also as possible material for examinations. It discusses Noetherian rings and prime ideals for algebraic geometry.
Описание: This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. Written for beginning graduate students and advanced undergraduates, the material will find use across disciplines including number theory, representation theory, algebraic geometry, and algebraic topology.
Автор: Hazrat Название: Graded Rings and Graded Grothendieck Groups ISBN: 1316619583 ISBN-13(EAN): 9781316619582 Издательство: Cambridge Academ Рейтинг: Цена: 9029.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra, and brings together results scattered across the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.
Описание: This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.
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