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Author : Fernando Q. Gouvêa
Publisher : MAA
Page : 329 pages
File Size : 48,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780883853559
Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.
Author : Fernando Quadros Gouvêa
Publisher : Unknown
Page : 0 pages
File Size : 55,6 Mb
Release : 2012
Category : MATHEMATICS
ISBN : OCLC:1335926822
Author : Fernando Q. Gouvêa
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 42,9 Mb
Release : 2012-12-31
Category : Mathematics
ISBN : 9781614442110
Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.
Author : Shahriar Shahriar
Publisher : American Mathematical Soc.
Page : 675 pages
File Size : 43,7 Mb
Release : 2017-08-16
Category : Algebra
ISBN : 9781470428495
This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Author : Marlow Anderson,Todd Feil
Publisher : CRC Press
Page : 684 pages
File Size : 53,9 Mb
Release : 2005-01-27
Category : Mathematics
ISBN : 9781420057119
Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
Author : Steve Warner
Publisher : Unknown
Page : 346 pages
File Size : 47,7 Mb
Release : 2019-07-28
Category : Mathematics
ISBN : 0999811789
"This book [provides] a basic but rigorous introduction to abstract algebra." --
Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 574 pages
File Size : 45,8 Mb
Release : 2012-02-25
Category : Applied mathematics
ISBN : 9781105559297
Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 46,6 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175
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 : Robert Lockhart
Publisher : Springer Nature
Page : 555 pages
File Size : 44,7 Mb
Release : 2021-11-14
Category : Mathematics
ISBN : 9783030817558
This book offers an original account of the theory of near-rings, with a considerable amount of material which has not previously been available in book form, some of it completely new. The book begins with an introduction to the subject and goes on to consider the theory of near-fields, transformation near-rings and near-rings hosted by a group. The bulk of the chapter on near-fields has not previously been available in English. The transformation near-rings chapters considerably augment existing knowledge and the chapters on product hosting are essentially new. Other chapters contain original material on new classes of near-rings and non-abelian group cohomology. The Theory of Near-Rings will be of interest to researchers in the subject and, more broadly, ring and representation theorists. The presentation is elementary and self-contained, with the necessary background in group and ring theory available in standard references.
Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 54,9 Mb
Release : 2021-06-08
Category : Education
ISBN : 9781470464332
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 : D. J. H. Garling
Publisher : Cambridge University Press
Page : 207 pages
File Size : 42,8 Mb
Release : 2021-07-22
Category : MATHEMATICS
ISBN : 9781108838924
This textbook contains a full account of Galois Theory and the algebra that it needs, with exercises, examples and applications.
Author : David M. Evans
Publisher : Cambridge University Press
Page : 232 pages
File Size : 45,6 Mb
Release : 1997-07-10
Category : Mathematics
ISBN : 9780521589550
Surveys recent interactions between model theory and other branches of mathematics, notably group theory.
Author : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 55,6 Mb
Release : 2003
Category : Algebra
ISBN : 9780821833186
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 : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 46,6 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : Audrey Terras
Publisher : Cambridge University Press
Page : 331 pages
File Size : 49,5 Mb
Release : 2018-12-20
Category : Mathematics
ISBN : 9781107164079
This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.