Автор: N. Jacobson Название: Lectures in Abstract Algebra ISBN: 0387901248 ISBN-13(EAN): 9780387901244 Издательство: Springer Рейтинг: Цена: 11173.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: N. Jacobson Название: Lectures in Abstract Algebra ISBN: 1468470558 ISBN-13(EAN): 9781468470550 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup- posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu- dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.
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: Smith Название: Introduction to Abstract Algebra, Second Edition ISBN: 1498731619 ISBN-13(EAN): 9781498731614 Издательство: Taylor&Francis Рейтинг: Цена: 16078.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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, Lagrange's 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.
Автор: Ed Dubinsky; Uri Leron Название: Learning Abstract Algebra with ISETL ISBN: 1461276101 ISBN-13(EAN): 9781461276104 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Rudolf Lidl; G?nter Pilz Название: Applied Abstract Algebra ISBN: 1441931171 ISBN-13(EAN): 9781441931177 Издательство: Springer Рейтинг: Цена: 8798.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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