Introduction To Abstract Algebra
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Rings Fields And Groups
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Author : R. B. J. T. Allenby
language : en
Publisher: Butterworth-Heinemann
Release Date : 1991
Rings Fields And Groups written by R. B. J. T. Allenby and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses
Introduction To Abstract Algebra
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Author : Jonathan D. H. Smith
language : en
Publisher:
Release Date : 2024-10-14
Introduction To Abstract Algebra written by Jonathan D. H. Smith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.
Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics. This edition 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 throughou
A Book Of Abstract Algebra
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2010-01-14
A Book Of Abstract Algebra written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
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.
An Introduction To Abstract Algebra
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Author : Derek J.S. Robinson
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
An Introduction To Abstract Algebra written by Derek J.S. Robinson and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with categories.
No detailed description available for "An Introduction to Abstract Algebra".
Introduction To Abstract Algebra
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Author : Benjamin Fine
language : en
Publisher: JHU Press
Release Date : 2014-07-01
Introduction To Abstract Algebra written by Benjamin Fine and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Mathematics categories.
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
Abstract Algebra
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Author : Gregory T. Lee
language : en
Publisher: Springer
Release Date : 2018-04-13
Abstract Algebra written by Gregory T. Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-13 with Mathematics categories.
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.
Introduction To Abstract Algebra
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Author : Jonathan D. H. Smith
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Introduction To Abstract Algebra written by Jonathan D. H. Smith and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
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.
Introduction To Modern Algebra And Its Applications
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Author : Nadiya Gubareni
language : en
Publisher: CRC Press
Release Date : 2021-06-23
Introduction To Modern Algebra And Its Applications written by Nadiya Gubareni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Mathematics categories.
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.
An Introduction To Abstract Algebra With Notes To The Future Teacher
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Author : Olympia E Nicodemi
language : en
Publisher: Pearson Education (Us)
Release Date : 2015-10-08
An Introduction To Abstract Algebra With Notes To The Future Teacher written by Olympia E Nicodemi and has been published by Pearson Education (Us) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with categories.
For courses in Abstract Algebra.Designed for future mathematics teachers as well as mathematics students who are not planning careers in secondary education, this text offers a traditional course in abstract algebra along with optional notes that connect its mathematical content toschool mathematics.Elementarynumber theory and rings ofpolynomials are treated before group theory. Prerequisites include some experience with proof. (A brief appendix reviews certain basics of logic, proof, set theory, and functions.) Students should also have access to a Computer Algebra System (CAS), or a calculator with CAS capabilities. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book."
Introduction To Abstract Algebra
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Author : W. Keith Nicholson
language : en
Publisher: John Wiley & Sons
Release Date : 2012-03-20
Introduction To Abstract Algebra written by W. Keith Nicholson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-20 with Mathematics categories.
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.