A Guide to Groups, Rings, and Fields

A Guide to Groups, Rings, and Fields

Author: Fernando Q. Gouvêa

Publisher: MAA

Published: 2012

Total Pages: 329

ISBN-13: 0883853558

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Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.


A Guide to Groups, Rings, and Fields

A Guide to Groups, Rings, and Fields

Author: Fernando Q. Gouvêa

Publisher: American Mathematical Soc.

Published: 2012-12-31

Total Pages: 309

ISBN-13: 1614442118

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Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.


Applied Discrete Structures

Applied Discrete Structures

Author: Ken Levasseur

Publisher: Lulu.com

Published: 2012-02-25

Total Pages: 574

ISBN-13: 1105559297

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''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--


Rings, Fields, and Vector Spaces

Rings, Fields, and Vector Spaces

Author: Bharath Sethuraman

Publisher: Springer Science & Business Media

Published: 1996-11-26

Total Pages: 210

ISBN-13: 0387948481

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Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.


Fields and Rings

Fields and Rings

Author: Irving Kaplansky

Publisher: University of Chicago Press

Published: 1972

Total Pages: 217

ISBN-13: 0226424510

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This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews


A First Course in Abstract Algebra

A First Course in Abstract Algebra

Author: Marlow Anderson

Publisher: CRC Press

Published: 2005-01-27

Total Pages: 684

ISBN-13: 1420057111

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Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there


A Book of Abstract Algebra

A Book of Abstract Algebra

Author: Charles C Pinter

Publisher: Courier Corporation

Published: 2010-01-14

Total Pages: 402

ISBN-13: 0486474178

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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.


Abstract Algebra and Solution by Radicals

Abstract Algebra and Solution by Radicals

Author: John Edward Maxfield

Publisher: Courier Corporation

Published: 2010-03-01

Total Pages: 228

ISBN-13: 0486477231

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The American Mathematical Monthly recommended this advanced undergraduate-level text for teacher education. It starts with groups, rings, fields, and polynomials and advances to Galois theory, radicals and roots of unity, and solution by radicals. Numerous examples, illustrations, commentaries, and exercises enhance the text, along with 13 appendices. 1971 edition.


Abstract Algebra

Abstract Algebra

Author: W. E. Deskins

Publisher: Courier Corporation

Published: 2012-05-24

Total Pages: 660

ISBN-13: 0486158462

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Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.