Lectures In Abstract Algebra

Author : N. Jacobson
Publisher : Springer
Page : 304 pages
File Size : 46,5 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:49015002165802

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Lectures in Abstract Algebra by N. Jacobson Pdf

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.

Author : Nathan Jacobson
Publisher : Unknown
Page : 280 pages
File Size : 44,7 Mb
Release : 1953
Category : Electronic
ISBN : OCLC:7707891

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Lectures in Abstract Algebra: Linear algebra by Nathan Jacobson Pdf

Author : Nathan Jacobson
Publisher : Unknown
Page : 280 pages
File Size : 48,5 Mb
Release : 2000
Category : Algebra, Abstract
ISBN : 7506200619

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抽象代数讲义 by Nathan Jacobson Pdf

著者译名:雅各布松。

Author : Nathan Jacobson
Publisher : Courier Corporation
Page : 530 pages
File Size : 55,7 Mb
Release : 2012-12-11
Category : Mathematics
ISBN : 9780486135229

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Basic Algebra I by Nathan Jacobson Pdf

A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.

Author : Shreeram Shankar Abhyankar
Publisher : World Scientific
Page : 758 pages
File Size : 49,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812568267

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Lectures on Algebra by Shreeram Shankar Abhyankar Pdf

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.

Author : Thomas Judson
Publisher : Orthogonal Publishing L3c
Page : 0 pages
File Size : 50,6 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 : Nathan Carter
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 50,7 Mb
Release : 2021-06-08
Category : Education
ISBN : 9781470464332

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Visual Group Theory by Nathan Carter Pdf

Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

Author : Anonim
Publisher : Unknown
Page : 217 pages
File Size : 42,9 Mb
Release : 1951
Category : Electronic
ISBN : OCLC:465113485

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Lectures in abstract algebra. Vol. 1 by Anonim Pdf

Author : Robert B. Ash
Publisher : Courier Corporation
Page : 432 pages
File Size : 41,6 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 : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 50,9 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 : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 47,6 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 : N. Jacobson
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461298724

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Lectures in Abstract Algebra by N. Jacobson Pdf

The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are of interest in number theory. A second objective of our ac count has been to indicate the links between the present theory of fields and the classical problems which led to its development.

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
Page : 713 pages
File Size : 40,7 Mb
Release : 2021-11-09
Category : Education
ISBN : 9781470465711

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Algebra: Chapter 0 by Paolo Aluffi Pdf

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Author : Nathan Jacobson
Publisher : Unknown
Page : 217 pages
File Size : 40,7 Mb
Release : 1965
Category : Electronic
ISBN : OCLC:749605214

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Lectures in Abstract Algebra by Nathan Jacobson Pdf

Author : N. Jacobson
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468473018

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Lectures in Abstract Algebra I by N. Jacobson Pdf

The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under standing of a few topics is to be preferred to a superficial under standing of many. The second and third volumes of this work will be more special ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP. -a. ces. . . . . Volume III, The Theory of Fields and Galois Theory, will be con cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses.