Basic Abstract Algebra

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486318117
Format: PDF
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Relations between groups and sets, results and methods of abstract algebra in terms of number theory and geometry, and noncommutative and homological algebra. Solutions. 2006 edition.

Basic Abstract Algebra

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486453561
Format: PDF, ePub, Docs
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Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.

A Course in Algebraic Number Theory

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486477541
Format: PDF, ePub, Mobi
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This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.

Elements of Abstract Algebra

Author: Allan Clark
Publisher: Courier Corporation
ISBN: 9780486647258
Format: PDF, Mobi
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Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

Abstract Algebra

Author: W. E. Deskins
Publisher: Courier Corporation
ISBN: 0486158462
Format: PDF, Kindle
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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.

Real Variables with Basic Metric Space Topology

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486151492
Format: PDF, Docs
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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.

A First Graduate Course in Abstract Algebra

Author: W.J. Wickless
Publisher: CRC Press
ISBN: 135198974X
Format: PDF, ePub, Mobi
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Since abstract algebra is so important to the study of advanced mathematics, it is critical that students have a firm grasp of its principles and underlying theories before moving on to further study. To accomplish this, they require a concise, accessible, user-friendly textbook that is both challenging and stimulating. A First Graduate Course in Abstract Algebra is just such a textbook. Divided into two sections, this book covers both the standard topics (groups, modules, rings, and vector spaces) associated with abstract algebra and more advanced topics such as Galois fields, noncommutative rings, group extensions, and Abelian groups. The author includes review material where needed instead of in a single chapter, giving convenient access with minimal page turning. He also provides ample examples, exercises, and problem sets to reinforce the material. This book illustrates the theory of finitely generated modules over principal ideal domains, discusses tensor products, and demonstrates the development of determinants. It also covers Sylow theory and Jordan canonical form. A First Graduate Course in Abstract Algebra is ideal for a two-semester course, providing enough examples, problems, and exercises for a deep understanding. Each of the final three chapters is logically independent and can be covered in any order, perfect for a customized syllabus.

Abstract Algebra and Solution by Radicals

Author: John Edward Maxfield
Publisher: Courier Corporation
ISBN: 0486477231
Format: PDF, Docs
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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.

Basic Algebra

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817645292
Format: PDF, ePub, Mobi
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Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

Linear Algebra and Matrix Theory

Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486265218
Format: PDF, Docs
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One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition.