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Introduction To Modern Abstract Algebra


Introduction To Modern Abstract Algebra
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Introduction To Modern Abstract Algebra


Introduction To Modern Abstract Algebra
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Author : David M. Burton
language : en
Publisher:
Release Date : 1967

Introduction To Modern Abstract Algebra written by David M. Burton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Algebra, Abstract categories.




Introduction To Modern Algebra And Its Applications


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 Essential Algebraic Structures


An Introduction To Essential Algebraic Structures
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Author : Martyn R. Dixon
language : en
Publisher: John Wiley & Sons
Release Date : 2014-11-24

An Introduction To Essential Algebraic Structures written by Martyn R. Dixon 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 2014-11-24 with Mathematics categories.


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.



Introduction To Modern Algebra And Its Applications


Introduction To Modern Algebra And Its Applications
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Author : Nadezhda Mikhaĭlovna Gubareni
language : en
Publisher: CRC Press
Release Date : 2020

Introduction To Modern Algebra And Its Applications written by Nadezhda Mikhaĭlovna 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 2020 with Algebra, Abstract 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 Grèobner basis. The Cayley-Dickson construction for finite dimensional algebras is described. The structure and properties of quaternions and octonions are studied in details and their applications in the number theory and computer graphics are presented"--



Modern Algebra An Introduction 5th Ed


Modern Algebra An Introduction 5th Ed
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Author : John R. Durbin
language : en
Publisher: John Wiley & Sons
Release Date : 2008-12

Modern Algebra An Introduction 5th Ed written by John R. Durbin 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 2008-12 with Algebra, Abstract categories.


This book presents an introduction to modern (abstract) algebra covering the basic ideas of groups, rings, and fields. The first part of the book treats ideas that are important but neither abstract nor complicated, and provides practice in handling mathematical statements - their meaning, quantification, negation, and proof. This edition features a new section to give more substance to the introduction to Galois theory, updated lists of references and discussions of topics such as Fermat's Last Theorem and the finite simple groups.· Mappings and Operations· Introduction to Groups· Equivalence, Congruence, Divisibility· Groups· Group Homomorphisms· Introduction to Rings· The Familiar Number Systems· Polynomials· Quotient Rings· Field Extensions· Galois Theory· Geometric Constructions· Applications of Permutation Groups· Symmetry· Cryptography and Algebraic Coding· Lattices and Boolean Algebras



Abstract Algebra


Abstract Algebra
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Author : Derek J.S. Robinson
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-05-19

Abstract Algebra written by Derek J.S. Robinson and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-19 with Mathematics categories.


This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe, and should ease the transition to (post)graduate studies.



Introduction To Modern Algebra


Introduction To Modern Algebra
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Author : Neal Henry McCoy
language : en
Publisher: WCB/McGraw-Hill
Release Date : 1992

Introduction To Modern Algebra written by Neal Henry McCoy and has been published by WCB/McGraw-Hill this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.




Modern Algebra


Modern Algebra
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Author : John R. Durbin
language : en
Publisher:
Release Date : 1979-03

Modern Algebra written by John R. Durbin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-03 with categories.


This book presents an introduction to modern (abstract) algebra covering the basic ideas of groups, rings, and fields. The first part of the book treats ideas that are important but neither abstract nor complicated, and provides practice in handling mathematical statements - their meaning, quantification, negation, and proof. This edition features a new section to give more substance to the introduction to Galois theory, updated lists of references and discussions of topics such as Fermat's Last Theorem and the finite simple groups.



Introductory Modern Algebra


Introductory Modern Algebra
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Author : Saul Stahl
language : en
Publisher: Wiley
Release Date : 2013-08-19

Introductory Modern Algebra written by Saul Stahl and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-19 with Mathematics categories.


Praise for the First Edition "Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra." —CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pivotal algebraic ideas. The author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the Second Edition also includes: An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's ideals Historical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminology A new appendix on logic and proofs, sets, functions, and equivalence relations Over 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summaries Introductory Modern Algebra: A Historical Approach, Second Edition is an excellent textbook for upper-undergraduate courses in modern and abstract algebra.



Abstract Algebra


Abstract Algebra
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Author : Pierre Antoine Grillet
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-21

Abstract Algebra written by Pierre Antoine Grillet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-21 with Mathematics categories.


A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.