abstract algebra structures and applications

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Abstract Algebra

Author : Stephen Lovett
ISBN : 1482248905
Genre : Mathematics
File Size : 61. 61 MB
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A Discovery-Based Approach to Learning about Algebraic Structures Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure Motivation Examples General properties Important objects Description Subobjects Morphisms Subclasses Quotient objects Action structures Applications The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics.

Abstract Algebra

Author : David R. Finston
ISBN : 9783319044989
Genre : Mathematics
File Size : 34. 58 MB
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This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.

Abstract Algebra

Author : Thomas W. Judson
ISBN : 1944325050
Genre : Mathematics
File Size : 25. 46 MB
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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.

Abstract Algebra

Author : Celine Carstensen
ISBN : 9783110250084
Genre : Mathematics
File Size : 88. 93 MB
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A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics."

A Book Of Abstract Algebra

Author : Charles C Pinter
ISBN : 9780486474175
Genre : Mathematics
File Size : 40. 73 MB
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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.

Algebra And Number Theory

Author : Martyn R. Dixon
ISBN : 0470640537
Genre : Mathematics
File Size : 74. 32 MB
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Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.

Post Modern Algebra

Author : Jonathan D. H. Smith
ISBN : 0471127388
Genre : Mathematics
File Size : 68. 69 MB
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Advanced algebra in the service of contemporary mathematical research–– a unique introduction. This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden′s Modern Algebra––a book that has dominated the field for nearly seventy years. Post–Modern Algebra offers a truly up–to–date alternative to the standard approach, explaining topics from an applications–based perspective rather than by abstract principles alone. The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory. Classical algebraic areas of groups, rings, fields, and vector spaces are bolstered by such topics as ordered sets, monoids, monoid actions, quasigroups, loops, lattices, Boolean algebras, categories, and Heyting algebras. The text features: ∗ A clear and concise treatment at an introductory level, tested in university courses. ∗ A wealth of exercises illustrating concepts and their practical application. ∗ Effective techniques for solving research problems in the real world. ∗ Flexibility of presentation, making it easy to tailor material to specific needs. ∗ Help with elementary proofs and algebraic notations for students of varying abilities. Post–Modern Algebra is an excellent primary or supplementary text for graduate–level algebra courses. It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.

Basic Abstract Algebra

Author : Robert B. Ash
ISBN : 9780486318110
Genre : Mathematics
File Size : 81. 37 MB
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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.

Ordered Algebraic Structures

Author : Jorge Martínez
ISBN : 1402007523
Genre : Mathematics
File Size : 66. 96 MB
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This publication surveys some of the disciplines within ordered algebraic structures and also contains chapters highlighting a broad spectrum of research interests. In all, this book represents a reasonably accurate cross-section of the state of the art in ordered algebraic structures.

Elements Of Abstract Algebra

Author : Allan Clark
ISBN : 9780486140353
Genre : Mathematics
File Size : 78. 65 MB
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Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

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