Smith Introduction to Abstract Algebra, Second Edition 9781498731614

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Автор: Smith
Название: Introduction to Abstract Algebra, Second Edition
ISBN: 9781498731614
Издательство: Taylor&Francis
Классификация:

Алгебра

Комбинаторика и теория графов

ISBN-10: 1498731619
Обложка/Формат: Hardback
Страницы: 352
Вес: 0.64 кг.
Дата издания: 20.10.2015
Серия: Textbooks in mathematics
Язык: English
Издание: 2 ed
Иллюстрации: 1 tables, black and white; 52 illustrations, black and white
Размер: 239 x 158 x 23
Читательская аудитория: Undergraduate
Ключевые слова: Combinatorics & graph theory, MATHEMATICS / Algebra / General,MATHEMATICS / Combinatorics
Ссылка на Издательство: Link
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Поставляется из: Европейский союз
Описание:

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.
This new edition of a widely adopted textbook covers applications from biology, science, and engineering. It offers numerous updates based on feedback from first edition adopters, as well as improved and simplified proofs of a number of important theorems. Many new exercises have been added, while new study projects examine skewfields, quaternions, and octonions.
The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. These three chapters provide a quick introduction to algebra, sufficient to exhibit irrational numbers or to gain a taste of cryptography.
Chapters four through seven cover abstract groups and monoids, orthogonal groups, stochastic matrices, Lagranges theorem, groups of units of monoids, homomorphisms, rings, and integral domains. The first seven chapters provide basic coverage of abstract algebra, suitable for a one-semester or two-quarter course.
Each chapter includes exercises of varying levels of difficulty, chapter notes that point out variations in notation and approach, and study projects that cover an array of applications and developments of the theory.
The final chapters deal with slightly more advanced topics, suitable for a second-semester or third-quarter course. These chapters delve deeper into the theory of rings, fields, and groups. They discuss modules, including vector spaces and abelian groups, group theory, and quasigroups.
This textbook is suitable for use in an undergraduate course on abstract algebra for mathematics, computer science, and education majors, along with students from other STEM fields.

Introduction to Abstract Algebra, Second Edition, Smith