A Course On Abstract Algebra

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A Course on Abstract Algebra

Author : Minking Eie
Publisher : World Scientific Publishing Company
ISBN 13 : 9813229640
Total Pages : 432 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis A Course on Abstract Algebra by : Minking Eie

Download or read book A Course on Abstract Algebra written by Minking Eie and published by World Scientific Publishing Company. This book was released on 2017-09-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the 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. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials. Three whole new chapters are added to this second edition. Group action is introduced to give a more in-depth discussion on Sylow's theorems. We also provide a formula in solving combinatorial problems as an application. We devote two chapters to module theory, which is a natural generalization of the theory of the vector spaces. Readers will see the similarity and subtle differences between the two. In particular, determinant is formally defined and its properties rigorously proved. The 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.

A First Course in Abstract Algebra

Author : John B. Fraleigh
Publisher : Pearson
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis A First Course in Abstract Algebra by : John B. Fraleigh

Download or read book A First Course in Abstract Algebra written by John B. Fraleigh and published by Pearson. This book was released on 2003 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

A First Graduate Course in Abstract Algebra

Author : William Jennings Wickless
Publisher : CRC Press
ISBN 13 : 0824757181
Total Pages : 232 pages
Book Rating : 4.8/5 (247 download)

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Book Synopsis A First Graduate Course in Abstract Algebra by : William Jennings Wickless

Download or read book A First Graduate Course in Abstract Algebra written by William Jennings Wickless and published by CRC Press. This book was released on 2019-09-27 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Realizing the specific needs of first-year graduate students, this reference allows readers to grasp and master fundamental concepts in abstract algebra-establishing a clear understanding of basic linear algebra and number, group, and commutative ring theory and progressing to sophisticated discussions on Galois and Sylow theory, the structure of abelian groups, the Jordan canonical form, and linear transformations and their matrix representations.

A First Course in Abstract Algebra

Author : Joseph J. Rotman
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis A First Course in Abstract Algebra by : Joseph J. Rotman

Download or read book A First Course in Abstract Algebra written by Joseph J. Rotman and published by . This book was released on 2000 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: For one-semester or two-semester undergraduate courses in Abstract Algebra. This new edition has been completely rewritten. The four chapters from the first edition are expanded, from 257 pages in first edition to 384 in the second. Two new chapters have been added: the first 3 chapters are a text for a one-semester course; the last 3 chapters are a text for a second semester. The new Chapter 5, Groups II, contains the fundamental theorem of finite abelian groups, the Sylow theorems, the Jordan-Holder theorem and solvable groups, and presentations of groups (including a careful construction of free groups). The new Chapter 6, Commutative Rings II, introduces prime and maximal ideals, unique factorization in polynomial rings in several variables, noetherian rings and the Hilbert basis theorem, affine varieties (including a proof of Hilbert's Nullstellensatz over the complex numbers and irreducible components), and Grobner bases, including the generalized division algorithm and Buchberger's algorithm.

A Course in Abstract Algebra, 4th Edition

Author : V.K. Khanna & S.K Bhamri
Publisher : Vikas Publishing House
ISBN 13 : 9325969009
Total Pages : pages
Book Rating : 4.3/5 (259 download)

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Book Synopsis A Course in Abstract Algebra, 4th Edition by : V.K. Khanna & S.K Bhamri

Download or read book A Course in Abstract Algebra, 4th Edition written by V.K. Khanna & S.K Bhamri and published by Vikas Publishing House. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduate and postgraduate students of mathematics the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from set theory and number theory. It then goes on to cover groups, rings, vector spaces (Linear Algebra) and fields. The topics under Groups include subgroups, permutation groups, finite abelian groups, Sylow theorems, direct products, group actions, solvable and nilpotent groups. The course in Ring theory covers ideals, embedding of rings, euclidean domains, PIDs, UFDs, polynomial rings, irreducibility criteria, Noetherian rings. The section on vector spaces deals with linear transformations, inner product spaces, dual spaces, eigen spaces, diagonalizable operators etc. Under fields, algebraic extensions, splitting fields, normal and separable extensions, algebraically closed fields, Galois extensions and construction by ruler and compass are discussed. The theory has been strongly supported by numerous examples and worked out problems. There is also plenty of scope for the readers to try and solve problems on their own. NEW IN THIS EDITION • Learning Objectives and Summary with each chapter • A large number of additional worked-out problems and examples • Alternate proofs of some theorems and lemmas • Reshuffling/Rewriting of certain portions to make them more reader friendly

A Course on Abstract Algebra

Author : Minking Eie
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813229624
Total Pages : 417 pages
Book Rating : 4.2/5 (296 download)

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Book Synopsis A Course on Abstract Algebra by : Minking Eie

Download or read book A Course on Abstract Algebra written by Minking Eie and published by World Scientific Publishing Company. This book was released on 2017-09-15 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the 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. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials. Three whole new chapters are added to this second edition. Group action is introduced to give a more in-depth discussion on Sylow's theorems. We also provide a formula in solving combinatorial problems as an application. We devote two chapters to module theory, which is a natural generalization of the theory of the vector spaces. Readers will see the similarity and subtle differences between the two. In particular, determinant is formally defined and its properties rigorously proved. The 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.

Abstract Algebra

Author : Dan Saracino
Publisher : Waveland Press
ISBN 13 : 1478610131
Total Pages : 320 pages
Book Rating : 4.4/5 (786 download)

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Book Synopsis Abstract Algebra by : Dan Saracino

Download or read book Abstract Algebra written by Dan Saracino and published by Waveland Press. This book was released on 2008-09-02 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.

Algebra I: A Basic Course in Abstract Algebra

Author : Rajendra Kumar Sharma
Publisher : Pearson Education India
ISBN 13 : 8131797627
Total Pages : 781 pages
Book Rating : 4.1/5 (317 download)

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Book Synopsis Algebra I: A Basic Course in Abstract Algebra by : Rajendra Kumar Sharma

Download or read book Algebra I: A Basic Course in Abstract Algebra written by Rajendra Kumar Sharma and published by Pearson Education India. This book was released on 2011 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra is a compulsory paper offered to the undergraduate students of Mathematics. The majority of universities offer the subject as a two /three year paper or in two/three semesters. Algebra I: A Basic Course in Abstract Algebra covers the topic required for a basic course.

Algebra

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
ISBN 13 : 0821847996
Total Pages : 516 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebra by : I. Martin Isaacs

Download or read book Algebra written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2009 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: as a student." --Book Jacket.

A Course in Abstract Algebra, 5th Edition

Author : Khanna V.K. & Bhamri S.K
Publisher : Vikas Publishing House
ISBN 13 : 9352593200
Total Pages : 869 pages
Book Rating : 4.3/5 (525 download)

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Book Synopsis A Course in Abstract Algebra, 5th Edition by : Khanna V.K. & Bhamri S.K

Download or read book A Course in Abstract Algebra, 5th Edition written by Khanna V.K. & Bhamri S.K and published by Vikas Publishing House. This book was released on 2016 with total page 869 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduate and postgraduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set theory and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. The topics under groups include subgroups, finitely generated abelian groups, group actions, solvable and nilpotent groups. The course in ring theory covers ideals, embedding of rings, Euclidean domains, PIDs, UFDs, polynomial rings, Noetherian (Artinian) rings. Topics of field include algebraic extensions, splitting fields, normal extensions, separable extensions, algebraically closed fields, Galois extensions, and construction by ruler and compass. The portion on linear algebra deals with vector spaces, linear transformations, Eigen spaces, diagonalizable operators, inner product spaces, dual spaces, operators on inner product spaces etc. The theory has been strongly supported by numerous examples and worked-out problems. There is also plenty of scope for the readers to try and solve problems on their own.New in this Edition• A full section on operators in inner product spaces.• Complete survey of finite groups of order up to 15 and Wedderburn theorem on finite division rings.• Addition of around one hundred new worked-out problems and examples.• Alternate and simpler proofs of some results.• A new section on quick recall of various useful results at the end of the book to facilitate the reader to get instant answers to tricky questions.

A Course in Algebra

Author : Yun Fan
Publisher : World Scientific
ISBN 13 : 9789810240615
Total Pages : 268 pages
Book Rating : 4.2/5 (46 download)

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Book Synopsis A Course in Algebra by : Yun Fan

Download or read book A Course in Algebra written by Yun Fan and published by World Scientific. This book was released on 2000 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lectures given by the authors at Wuhan University and Hubei University in courses on abstract algebra. It presents the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them and other mathematical branches and applied aspects.

Abstract Algebra

Author : Gary L. Mullen
Publisher : CRC Press
ISBN 13 : 1482250071
Total Pages : 204 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Abstract Algebra by : Gary L. Mullen

Download or read book Abstract Algebra written by Gary L. Mullen and published by CRC Press. This book was released on 2016-12-19 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual

A First Course In Apstract Algebra

Author : John B. Fraleigh
Publisher :
ISBN 13 : 9788185015705
Total Pages : 478 pages
Book Rating : 4.0/5 (157 download)

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Book Synopsis A First Course In Apstract Algebra by : John B. Fraleigh

Download or read book A First Course In Apstract Algebra written by John B. Fraleigh and published by . This book was released on 1982 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to MATLAB with Applications for Chemical and Mechanical Engineers

Author : Daniel G. Coronell
Publisher : CRC Press
ISBN 13 : 1584885157
Total Pages : 693 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Introduction to MATLAB with Applications for Chemical and Mechanical Engineers by : Daniel G. Coronell

Download or read book Introduction to MATLAB with Applications for Chemical and Mechanical Engineers written by Daniel G. Coronell and published by CRC Press. This book was released on 2015-10-15 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to MATLAB with Applications for Chemical and Mechanical Engineers provides applications from chemical engineering and biotechnology, such as thermodynamics, heat transfer, fluid mechanics, and mass transfer. The book features a section on input, output, and storage of data as well as a section on data analysis and parameter estimation that contains statistical analysis, curve fitting optimization, and error analysis. Many applied case studies are included from the engineering disciplines. It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.

ISM to First Course in Abstract Algebra

Author : John B. Fraleigh
Publisher : Addison-Wesley Longman
ISBN 13 : 9780201437188
Total Pages : 320 pages
Book Rating : 4.4/5 (371 download)

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Book Synopsis ISM to First Course in Abstract Algebra by : John B. Fraleigh

Download or read book ISM to First Course in Abstract Algebra written by John B. Fraleigh and published by Addison-Wesley Longman. This book was released on 1998-11 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A History of Abstract Algebra

Author : Israel Kleiner
Publisher : Springer Science & Business Media
ISBN 13 : 081764685X
Total Pages : 175 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A History of Abstract Algebra by : Israel Kleiner

Download or read book A History of Abstract Algebra written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2007-09-20 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.

Learning Abstract Algebra with ISETL

Author : Ed Dubinsky
Publisher : Springer Science & Business Media
ISBN 13 : 1461226023
Total Pages : 264 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Learning Abstract Algebra with ISETL by : Ed Dubinsky

Download or read book Learning Abstract Algebra with ISETL written by Ed Dubinsky and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture.