Introduction To Abstract Algebra An Sets Groups Rings And Fields

Author : Steven Howard Weintraub
Publisher : World Scientific
Page : 438 pages
File Size : 44,6 Mb
Release : 2022-05-25
Category : Mathematics
ISBN : 9789811246685

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Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields by Steven Howard Weintraub Pdf

This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.

Author : R. B. J. T. Allenby
Publisher : Hodder Education
Page : 422 pages
File Size : 45,6 Mb
Release : 1983
Category : Mathematics
ISBN : UCSC:32106016516962

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Rings, Fields and Groups by R. B. J. T. Allenby Pdf

This book provides a stimulating and unusiual introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses in universities and polytechnics. The mixture of informal and formal presentation generates the enthusiasm of the reader without neglecting the axiomatic approach necessary for the serious study.

Author : Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
Publisher : JHU Press
Page : 583 pages
File Size : 52,6 Mb
Release : 2014-07-01
Category : Mathematics
ISBN : 9781421411774

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Introduction to Abstract Algebra by Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger Pdf

A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic

Author : Clive Reis
Publisher : World Scientific Publishing Company
Page : 508 pages
File Size : 42,8 Mb
Release : 2011-05-05
Category : Mathematics
ISBN : 9789813100718

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Abstract Algebra by Clive Reis Pdf

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. 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 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 in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems. Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with 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, even if there are alternative methods of proof.

Author : Jonathan D. H. Smith
Publisher : CRC Press
Page : 344 pages
File Size : 46,5 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 1420063723

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Introduction to Abstract Algebra by Jonathan D. H. Smith Pdf

Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra 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. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.

Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 46,9 Mb
Release : 2014-11-24
Category : Mathematics
ISBN : 9781118459829

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An Introduction to Essential Algebraic Structures by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf

A reader-friendly introduction to modern algebra with important examples from various areas of mathematics Featuring a clear and concise approach, An Introduction to Essential Algebraic Structures presents an integrated approach to basic concepts of modern algebra and highlights topics that play a central role in various branches of mathematics. The authors discuss key topics of abstract and modern algebra including sets, number systems, groups, rings, and fields. The book begins with an exposition of the elements of set theory and moves on to cover the main ideas and branches of abstract algebra. In addition, the book includes: Numerous examples throughout to deepen readers’ knowledge of the presented material An exercise set after each chapter section in an effort to build a deeper understanding of the subject and improve knowledge retention Hints and answers to select exercises at the end of the book A supplementary website with an Instructors Solutions manual An Introduction to Essential Algebraic Structures is an excellent textbook for introductory courses in abstract algebra as well as an ideal reference for anyone who would like to be more familiar with the basic topics of abstract algebra.

Author : Fernando Q. Gouvêa
Publisher : MAA
Page : 329 pages
File Size : 42,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780883853559

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A Guide to Groups, Rings, and Fields by Fernando Q. Gouvêa Pdf

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

Author : Clive Reis
Publisher : Unknown
Page : 574 pages
File Size : 48,8 Mb
Release : 2016
Category : Electronic books
ISBN : 9814730556

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Abstract Algebra by Clive Reis Pdf

Author : W. Keith Nicholson
Publisher : John Wiley & Sons
Page : 560 pages
File Size : 41,8 Mb
Release : 2012-03-20
Category : Mathematics
ISBN : 9781118135358

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Introduction to Abstract Algebra by W. Keith Nicholson Pdf

Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 456 pages
File Size : 43,6 Mb
Release : 2022-02-07
Category : Mathematics
ISBN : 9783110691160

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Abstract Algebra by Derek J.S. Robinson Pdf

This is the third edition of the book. In addition to introducing the main concepts of modern algebra, new topic are added: categories and functors; an introduction to representations of finite groups; projective and injective modules; an introduction to noetherian rings and modules and to Hilbert’s Nullstellensatz. There is ample material for a two semester course in abstract algebra.

Author : Gregory T. Lee
Publisher : Springer
Page : 301 pages
File Size : 40,5 Mb
Release : 2018-04-13
Category : Mathematics
ISBN : 9783319776491

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Abstract Algebra by Gregory T. Lee Pdf

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.

Author : Marlow Anderson,Todd Feil
Publisher : CRC Press
Page : 684 pages
File Size : 55,9 Mb
Release : 2005-01-27
Category : Mathematics
ISBN : 9781420057119

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A First Course in Abstract Algebra by Marlow Anderson,Todd Feil Pdf

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

Author : B.A. Sethuraman
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 41,5 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475727005

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Rings, Fields, and Vector Spaces by B.A. Sethuraman Pdf

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.

Author : Thomas Q. Sibley
Publisher : American Mathematical Soc.
Page : 478 pages
File Size : 47,6 Mb
Release : 2021-06-08
Category : Education
ISBN : 9781470460303

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Thinking Algebraically: An Introduction to Abstract Algebra by Thomas Q. Sibley Pdf

Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.

Author : Steve Warner
Publisher : Unknown
Page : 346 pages
File Size : 43,9 Mb
Release : 2019-07-28
Category : Mathematics
ISBN : 0999811789

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Abstract Algebra for Beginners by Steve Warner Pdf

"This book [provides] a basic but rigorous introduction to abstract algebra." --