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Author : Joseph Landin
Publisher : Courier Corporation
Page : 275 pages
File Size : 55,9 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9780486150413
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 : Azriel Rosenfeld
Publisher : Unknown
Page : 312 pages
File Size : 50,8 Mb
Release : 1968
Category : Mathematics
ISBN : UOM:39015015626115
Author : F. J. Budden
Publisher : Unknown
Page : 136 pages
File Size : 54,6 Mb
Release : 1975
Category : Algebra
ISBN : 0582352185
Author : Palash B. Pal
Publisher : Cambridge University Press
Page : 717 pages
File Size : 42,7 Mb
Release : 2019-05-23
Category : Science
ISBN : 9781108492201
Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.
Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 41,8 Mb
Release : 2014-11-24
Category : Mathematics
ISBN : 9781118459829
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 : Bernard L. Johnston
Publisher : CRC Press
Page : 276 pages
File Size : 53,9 Mb
Release : 2020-07-25
Category : Mathematics
ISBN : 9781000153378
This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism. Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures. In terms of classical algebraic structures, the text divides roughly into three parts:
Author : Donald S. Passman
Publisher : Courier Corporation
Page : 754 pages
File Size : 44,8 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780486482064
"'Highly recommended' by the Bulletin of the London Mathematical Society, this book offers a comprehensive, self-contained treatment of group rings. The subject involves the intersection of two essentially different disciplines, group theory and ring theory. The Bulletin of the American Mathematical Society hailed this treatment as 'a majestic account,' proclaiming it "encyclopedic and lucid." 1985 edition"--
Author : Joseph H. Silverman
Publisher : American Mathematical Society
Page : 567 pages
File Size : 54,6 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9781470468606
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 : Marco Grandis
Publisher : World Scientific
Page : 393 pages
File Size : 40,6 Mb
Release : 2020-08-12
Category : Mathematics
ISBN : 9789811220333
'The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended.'CHOICESince the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from lattices to Boolean algebras, from metric spaces to topological spaces, from topological groups to Banach spaces.More recently, these structured sets and their transformations have been assembled in higher structures, called categories.We want to give a structural overview of these topics, where the basic facts of the different theories are unified through the 'universal properties' that they satisfy, and their particularities stand out, perhaps even more.This book can be used as a textbook for undergraduate studies and for self-study. It can provide students of Mathematics with a unified perspective of subjects which are often kept apart. It is also addressed to students and researchers of disciplines having strong interactions with Mathematics, like Physics and Chemistry, Statistics, Computer Science, Engineering.
Author : O. A. Laudal
Publisher : Springer
Page : 165 pages
File Size : 41,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385325
Author : Palash B. Pal
Publisher : Cambridge University Press
Page : 128 pages
File Size : 46,6 Mb
Release : 2019-06-30
Category : Science
ISBN : 1108729118
Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 254 pages
File Size : 47,9 Mb
Release : 2017-05-15
Category : Electronic
ISBN : 9781105618987
Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals. 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 : Minking Eie,Shou-Te Chang
Publisher : World Scientific Publishing Company
Page : 372 pages
File Size : 40,7 Mb
Release : 2010-02-26
Category : Mathematics
ISBN : 9789813107496
This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.
Author : T.S. Blyth
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 45,5 Mb
Release : 2005-04-18
Category : Mathematics
ISBN : 9781852339050
"The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS
Author : Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 634 pages
File Size : 51,7 Mb
Release : 2013-06-13
Category : Mathematics
ISBN : 9780821891322
Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr