Groups Rings And Fields
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Rings Fields And Groups
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Author : R. B. J. T. Allenby
language : en
Publisher: Butterworth-Heinemann
Release Date : 1991
Rings Fields And Groups written by R. B. J. T. Allenby and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses
Groups Rings And Fields
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Author : David A.R. Wallace
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-22
Groups Rings And Fields written by David A.R. Wallace and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-22 with Mathematics categories.
This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.
Algebra In Action A Course In Groups Rings And Fields
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Author : Shahriar Shahriar
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-16
Algebra In Action A Course In Groups Rings And Fields written by Shahriar Shahriar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-16 with Mathematics categories.
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.
Algebra 1
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Author : Ramji Lal
language : en
Publisher: Springer
Release Date : 2017-05-07
Algebra 1 written by Ramji Lal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-07 with Mathematics categories.
This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.
A First Course In Abstract Algebra
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Author : Marlow Anderson
language : en
Publisher: CRC Press
Release Date : 2005-01-27
A First Course In Abstract Algebra written by Marlow Anderson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-27 with Mathematics categories.
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
Basic Algebra
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Author : P.M. Cohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Basic Algebra written by P.M. Cohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic three-volume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two self-contained, companion volumes, covering advanced topics in algebra for second- and third-year undergraduate and postgraduate research students. In this first volume, the author covers the important results of algebra; the companion volume, Further Algebra and Applications, brings more advanced topics and focuses on the applications. Readers should have some knowledge of linear algebra and have met groups and fields before, although all the essential facts and definitions are recalled. The coverage is comprehensive and includes topics such as: - Groups - lattices and categories - rings, modules and algebras - fields The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks.
Lectures On Finite Fields And Galois Rings
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Author : Zhe-xian Wan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-08-12
Lectures On Finite Fields And Galois Rings written by Zhe-xian Wan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-12 with Mathematics categories.
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Applied Discrete Structures
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Author : Ken Levasseur
language : en
Publisher: Lulu.com
Release Date : 2012-02-25
Applied Discrete Structures written by Ken Levasseur and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-25 with Computers categories.
''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--
Introduction To Abstract Algebra
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Author : Benjamin Fine
language : en
Publisher: JHU Press
Release Date : 2014-07-01
Introduction To Abstract Algebra written by Benjamin Fine and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Mathematics categories.
A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic
Abstract Algebra
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Author : Gregory T. Lee
language : en
Publisher: Springer
Release Date : 2018-04-13
Abstract Algebra written by Gregory T. Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-13 with Mathematics categories.
This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.