Basic Modern Algebra With Applications

Author : Mahima Ranjan Adhikari,Avishek Adhikari
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 55,9 Mb
Release : 2013-12-08
Category : Mathematics
ISBN : 9788132215998

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Basic Modern Algebra with Applications by Mahima Ranjan Adhikari,Avishek Adhikari Pdf

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Author : William J Gilbert
Publisher : John Wiley & Sons
Page : 366 pages
File Size : 55,5 Mb
Release : 2008-09
Category : Electronic
ISBN : 8126518308

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MODERN ALGEBRA WITH APPLICATIONS by William J Gilbert Pdf

Market_Desc: Upper undergraduate and graduate level modern algebra courses Special Features: · Includes applications so students can see right away how to use the theory· This classic text has sold almost 12,000 units· Contains numerous examples· Includes chapters on Boolean Algebras, groups, quotient groups, symmetry groups in three dimensions, Polya-Burnside method of enumeration, monoids and machines, rings and fields, polynomial and Euclidean rings, quotient rings, field extensions, Latin squares, geometrical constructions, and error-correcting codes· Andwers to odd-numbered exercises so students can check their work About The Book: The book covers all the group, ring, and field theory that is usually contained in a standard modern algebra course; the exact sections containing this material are indicated in the Table of Contents. It stops short of the Sylow theorems and Galois theory. These topics could only be touched on in a first course, and the author feels that more time should be spent on them if they are to be appreciated.

Author : Thomas Judson
Publisher : Orthogonal Publishing L3c
Page : 0 pages
File Size : 49,8 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 : Nadiya Gubareni
Publisher : CRC Press
Page : 363 pages
File Size : 51,7 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 : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 47,8 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 : Audrey Terras
Publisher : Cambridge University Press
Page : 331 pages
File Size : 50,5 Mb
Release : 2018-12-20
Category : Mathematics
ISBN : 9781107164079

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Abstract Algebra with Applications by Audrey Terras Pdf

This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.

Author : William J. Gilbert,W. Keith Nicholson
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 50,5 Mb
Release : 2004-01-30
Category : Mathematics
ISBN : 9780471469896

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Modern Algebra with Applications by William J. Gilbert,W. Keith Nicholson Pdf

Praise for the first edition "This book is clearly written and presents a large number ofexamples illustrating the theory . . . there is no other book ofcomparable content available. Because of its detailed coverage ofapplications generally neglected in the literature, it is adesirable if not essential addition to undergraduate mathematicsand computer science libraries." –CHOICE As a cornerstone of mathematical science, the importance ofmodern algebra and discrete structures to many areas of science andtechnology is apparent and growing–with extensive use incomputing science, physics, chemistry, and data communications aswell as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instructionof modern algebra, Modern Algebra with Applications, Second Editionprovides interesting and important applications of thissubject–effectively holding your interest and creating a moreseamless method of instruction. Incorporating the applications of modern algebra throughout itsauthoritative treatment of the subject, this book covers the fullcomplement of group, ring, and field theory typically contained ina standard modern algebra course. Numerous examples are included ineach chapter, and answers to odd-numbered exercises are appended inthe back of the text. Chapter topics include: Boolean Algebras Polynomial and Euclidean Rings Groups Quotient Rings Quotient Groups Field Extensions Symmetry Groups in Three Dimensions Latin Squares Pólya—Burnside Method of Enumeration Geometrical Constructions Monoids and Machines Error-Correcting Codes Rings and Fields In addition to improvements in exposition, this fully updatedSecond Edition also contains new material on order of an elementand cyclic groups, more details about the lattice of divisors of aninteger, and new historical notes. Filled with in-depth insights and over 600 exercises of varyingdifficulty, Modern Algebra with Applications, Second Edition canhelp anyone appreciate and understand this subject.

Author : David R. Finston,Patrick J. Morandi
Publisher : Springer
Page : 194 pages
File Size : 51,9 Mb
Release : 2014-08-29
Category : Mathematics
ISBN : 9783319044989

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Abstract Algebra by David R. Finston,Patrick J. Morandi Pdf

This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.

Author : Robert B. Ash
Publisher : Courier Corporation
Page : 432 pages
File Size : 50,9 Mb
Release : 2013-06-17
Category : Mathematics
ISBN : 9780486318110

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Basic Abstract Algebra by Robert B. Ash Pdf

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.

Author : William J. Gilbert
Publisher : Wiley-Interscience
Page : 376 pages
File Size : 40,7 Mb
Release : 1976-11-30
Category : Mathematics
ISBN : UVA:X001446507

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Modern Algebra with Applications by William J. Gilbert Pdf

This book blends the theoretical with the practical in the instruction of modern algebra. Modern algebra is usually taught from the point of view of its intrinsic interest, without using applications. Many readers lose interest when they do not see the relevance of the subject and often become skeptical of the explanation that the material will be used later. The author believes by providing interesting and nontrivial applications, the student will better appreciate and understand the subject.

Author : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 51,5 Mb
Release : 2003
Category : Algebra
ISBN : 9780821833186

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A Course in Algebra by Ėrnest Borisovich Vinberg Pdf

Great book! The author's teaching experinece shows in every chapter. --Efim Zelmanov, University of California, San Diego Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It is plain that years of teaching abstract algebra have enabled him to say the right thing at the right time. --Irving Kaplansky, MSRI This is a comprehensive text on modern algebra written for advanced undergraduate and basic graduate algebra classes. The book is based on courses taught by the author at the Mechanics and Mathematics Department of Moscow State University and at the Mathematical College of the Independent University of Moscow. The unique feature of the book is that it contains almost no technically difficult proofs. Following his point of view on mathematics, the author tried, whenever possible, to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. Another important feature is that the book presents most of the topics on several levels, allowing the student to move smoothly from initial acquaintance to thorough study and deeper understanding of the subject. Presented are basic topics in algebra such as algebraic structures, linear algebra, polynomials, groups, as well as more advanced topics like affine and projective spaces, tensor algebra, Galois theory, Lie groups, associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. Written with extreme care and supplied with more than 200 exercises and 70 figures, the book is also an excellent text for independent study.

Author : I. N. Herstein
Publisher : Macmillan College
Page : 322 pages
File Size : 42,6 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015049346839

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Abstract Algebra by I. N. Herstein Pdf

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 347 pages
File Size : 43,5 Mb
Release : 2015-05-19
Category : Mathematics
ISBN : 9783110340877

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Abstract Algebra by Derek J.S. Robinson Pdf

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.

Author : Allan Clark
Publisher : Courier Corporation
Page : 224 pages
File Size : 50,9 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 : Anonim
Publisher : Krishna Prakashan Media
Page : 654 pages
File Size : 41,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8182830567

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Modern Algebra (Abstract Algebra) by Anonim Pdf