Basic Structures Of Modern Algebra

Author : Y. Bahturin
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 49,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401708395

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Basic Structures of Modern Algebra by Y. Bahturin Pdf

This book has developed from a series of lectures which were given by the author in mechanics-mathematics department of the Moscow State University. In 1981 the course "Additional chapters in algebra" replaced the course "Gen eral algebra" which was founded by A. G. Kurosh (1908-1971), professor and head of the department of higher algebra for a period of several decades. The material of this course formed the basis of A. G. Kurosh's well-known book "Lectures on general algebra" (Moscow,1962; 2-nd edition: Moscow, Nauka, 1973) and the book "General algebra. Lectures of 1969-1970. " (Moscow, Nauka, 1974). Another book based on the course, "Elements of general al gebra" (M. : Nauka, 1983) was published by L. A. Skorniakov, professor, now deceased, in the same department. It should be noted that A. G. Kurosh was not only the lecturer for the course "General algebra" but he was also the recognized leader of the scientific school of the same name. It is difficult to determine the limits of this school; however, the "Lectures . . . " of 1962 men tioned above contain some material which exceed these limits. Eventually this effect intensified: the lectures of the course were given by many well-known scientists, and some of them see themselves as "general algebraists". Each lecturer brought significant originality not only in presentation of the material but in the substance of the course. Therefore not all material which is now accepted as necessary for algebraic students fits within the scope of general algebra.

Author : Leo Corry
Publisher : Birkhäuser
Page : 463 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879170

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Modern Algebra and the Rise of Mathematical Structures by Leo Corry Pdf

This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

Author : Y. Bahturin
Publisher : Springer
Page : 440 pages
File Size : 51,6 Mb
Release : 1993-08-31
Category : Mathematics
ISBN : UOM:39076001486302

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Basic Structures of Modern Algebra by Y. Bahturin Pdf

This book has developed from a series of lectures which were given by the author in mechanics-mathematics department of the Moscow State University. In 1981 the course "Additional chapters in algebra" replaced the course "Gen eral algebra" which was founded by A. G. Kurosh (1908-1971), professor and head of the department of higher algebra for a period of several decades. The material of this course formed the basis of A. G. Kurosh's well-known book "Lectures on general algebra" (Moscow,1962; 2-nd edition: Moscow, Nauka, 1973) and the book "General algebra. Lectures of 1969-1970. " (Moscow, Nauka, 1974). Another book based on the course, "Elements of general al gebra" (M. : Nauka, 1983) was published by L. A. Skorniakov, professor, now deceased, in the same department. It should be noted that A. G. Kurosh was not only the lecturer for the course "General algebra" but he was also the recognized leader of the scientific school of the same name. It is difficult to determine the limits of this school; however, the "Lectures . . . " of 1962 men tioned above contain some material which exceed these limits. Eventually this effect intensified: the lectures of the course were given by many well-known scientists, and some of them see themselves as "general algebraists". Each lecturer brought significant originality not only in presentation of the material but in the substance of the course. Therefore not all material which is now accepted as necessary for algebraic students fits within the scope of general algebra.

Author : Anonim
Publisher : Krishna Prakashan Media
Page : 654 pages
File Size : 51,7 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 8182830567

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Modern Algebra (Abstract Algebra) by Anonim Pdf

Author : George R. Kempf
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802781

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Algebraic Structures by George R. Kempf Pdf

In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.

Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 243 pages
File Size : 41,7 Mb
Release : 2014-11-05
Category : Mathematics
ISBN : 9781118497760

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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 : Seth Warner
Publisher : Courier Corporation
Page : 852 pages
File Size : 46,9 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 : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 42,5 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 : David R. Finston,Patrick J. Morandi
Publisher : Springer
Page : 194 pages
File Size : 53,5 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 : Mary P. Dolciani
Publisher : Unknown
Page : 164 pages
File Size : 44,8 Mb
Release : 1962
Category : Algebra
ISBN : STANFORD:36105049307106

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Modern Algebra by Mary P. Dolciani Pdf

Author : Joseph Landin
Publisher : Courier Corporation
Page : 275 pages
File Size : 45,7 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9780486150413

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An Introduction to Algebraic Structures by Joseph Landin Pdf

This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.

Author : Mary P. Dolciani,William Wooton,Andrew M. Gleason,Albert E. Meder,Houghton Mifflin Company
Publisher : Unknown
Page : 305 pages
File Size : 40,5 Mb
Release : 1973
Category : Algebra
ISBN : 039514468X

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Modern Algebra by Mary P. Dolciani,William Wooton,Andrew M. Gleason,Albert E. Meder,Houghton Mifflin Company Pdf

Author : Joseph H. Silverman
Publisher : American Mathematical Society
Page : 567 pages
File Size : 44,6 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9781470468606

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Abstract Algebra by Joseph H. Silverman Pdf

This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.

Author : John R. Durbin
Publisher : John Wiley & Sons
Page : 354 pages
File Size : 54,8 Mb
Release : 2008-12-31
Category : Mathematics
ISBN : 9780470384435

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Modern Algebra by John R. Durbin Pdf

Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.

Author : Mahima Ranjan Adhikari,Avishek Adhikari
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 45,5 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.