Modern Algebra Abstract Algebra

Author : Joseph J. Rotman
Publisher : American Mathematical Society
Page : 570 pages
File Size : 48,7 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470472757

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Advanced Modern Algebra by Joseph J. Rotman Pdf

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 40,7 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175

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A Book of Abstract Algebra by Charles C Pinter Pdf

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.

Author : Jeremy Gray
Publisher : Springer
Page : 415 pages
File Size : 44,7 Mb
Release : 2018-08-07
Category : Mathematics
ISBN : 9783319947730

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A History of Abstract Algebra by Jeremy Gray Pdf

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

Author : Seth Warner
Publisher : Courier Corporation
Page : 852 pages
File Size : 42,6 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9780486137094

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Modern Algebra by Seth Warner Pdf

Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.

Author : Anonim
Publisher : Krishna Prakashan Media
Page : 654 pages
File Size : 55,6 Mb
Release : 2024-06-07
Category : Electronic
ISBN : 8182830567

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Modern Algebra (Abstract Algebra) by Anonim Pdf

Author : Israel Kleiner
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 51,5 Mb
Release : 2007-09-20
Category : Mathematics
ISBN : 9780817646851

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A History of Abstract Algebra by Israel Kleiner Pdf

This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
Page : 713 pages
File Size : 48,6 Mb
Release : 2021-11-09
Category : Education
ISBN : 9781470465711

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Algebra: Chapter 0 by Paolo Aluffi Pdf

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Author : Thomas Judson
Publisher : Orthogonal Publishing L3c
Page : 0 pages
File Size : 52,7 Mb
Release : 2023-08-11
Category : Electronic
ISBN : 1944325190

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Abstract Algebra by Thomas Judson Pdf

Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

Author : Dan Saracino
Publisher : Waveland Press
Page : 320 pages
File Size : 44,9 Mb
Release : 2008-09-02
Category : Mathematics
ISBN : 9781478610137

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Abstract Algebra by Dan Saracino Pdf

The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

Author : Nadiya Gubareni
Publisher : CRC Press
Page : 363 pages
File Size : 43,5 Mb
Release : 2021-06-23
Category : Mathematics
ISBN : 9781000209532

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Introduction to Modern Algebra and Its Applications by Nadiya Gubareni Pdf

The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.

Author : Allan Clark
Publisher : Courier Corporation
Page : 224 pages
File Size : 51,7 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486140353

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Elements of Abstract Algebra by Allan Clark Pdf

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.

Author : Garrett Birkhoff,Saunders Mac Lane
Publisher : Unknown
Page : 462 pages
File Size : 54,6 Mb
Release : 1965
Category : Algebra
ISBN : UOM:39015000494321

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A Survey of Modern Algebra by Garrett Birkhoff,Saunders Mac Lane Pdf

Author : Albert Cuoco,Joseph Rotman
Publisher : MAA
Page : 481 pages
File Size : 45,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9781939512017

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Learning Modern Algebra by Albert Cuoco,Joseph Rotman Pdf

A guide to modern algebra for mathematics teachers. It makes explicit connections between abstract algebra and high-school mathematics.

Author : W. W. Sawyer
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 51,5 Mb
Release : 2018-08-15
Category : Mathematics
ISBN : 9780486824611

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Concrete Approach to Abstract Algebra by W. W. Sawyer Pdf

Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.

Author : Frederick Goodman
Publisher : SemiSimple Press (Frederick Goodman)
Page : 586 pages
File Size : 51,5 Mb
Release : 2014-01-10
Category : Mathematics
ISBN : 9780979914218

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Algebra: Abstract and Concrete, edition 2.6 by Frederick Goodman Pdf

This text provides a thorough introduction to “modern” or “abstract” algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme. This subject matter is central and ubiquitous in modern mathematics and in applications ranging from quantum physics to digital communications. The most important goal of this book is to engage students in the ac- tive practice of mathematics.