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Author: Thomas Judson Publisher: Orthogonal Publishing L3c ISBN: 9781944325190 Category : Languages : en Pages : 0
Book Description
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.
Author: Stephen Lovett Publisher: CRC Press ISBN: 1482248913 Category : Mathematics Languages : en Pages : 720
Book Description
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. "Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gröbner bases." Choice Reviewed: Recommended
Author: Charles C Pinter Publisher: Courier Corporation ISBN: 0486474178 Category : Mathematics Languages : en Pages : 402
Book Description
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: David R. Finston Publisher: Springer ISBN: 3319044982 Category : Mathematics Languages : en Pages : 194
Book Description
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.
Author: Richard Klima Publisher: CRC Press ISBN: 1482248255 Category : Mathematics Languages : en Pages : 556
Book Description
Applied Abstract Algebra with MapleTM and MATLAB provides an in-depth introduction to real-world abstract algebraic problems. This popular textbook covers a variety of topics including block designs, coding theory, cryptography, and counting techniques, including Polya's and Burnside's theorems. The book also includes a concise review of all prereq
Author: Derek J.S. Robinson Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110340879 Category : Mathematics Languages : en Pages : 347
Book Description
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe, and should ease the transition to (post)graduate studies.
Author: Richard Klima Publisher: CRC Press ISBN: 9781420049930 Category : Mathematics Languages : en Pages : 272
Book Description
The mathematical concepts of abstract algebra may indeed be considered abstract, but its utility is quite concrete and continues to grow in importance. Unfortunately, the practical application of abstract algebra typically involves extensive and cumbersome calculations-often frustrating even the most dedicated attempts to appreciate and employ its intricacies. Now, however, sophisticated mathematical software packages help obviate the need for heavy number-crunching and make fields dependent on the algebra more interesting-and more accessible. Applications of Abstract Algebra with Maple opens the door to cryptography, coding, Polya counting theory, and the many other areas dependent on abstract algebra. The authors have carefully integrated Maple V throughout the text, enabling readers to see realistic examples of the topics discussed without struggling with the computations. But the book stands well on its own if the reader does not have access to the software. The text includes a first-chapter review of the mathematics required-groups, rings, and finite fields-and a Maple tutorial in the appendix along with detailed treatments of coding, cryptography, and Polya theory applications. Applications of Abstract Algebra with Maple packs a double punch for those interested in beginning-or advancing-careers related to the applications of abstract algebra. It not only provides an in-depth introduction to the fascinating, real-world problems to which the algebra applies, it offers readers the opportunity to gain experience in using one of the leading and most respected mathematical software packages available.
Author: Audrey Terras
Author: Audrey Terras
Author: Thomas Judson
Author: Norman J. Bloch
Author: Stephen Lovett
Author: Charles C Pinter
Author: David R. Finston
Author: Richard Klima
Author: I. N. Herstein
Author: Derek J.S. Robinson
Author: Richard Klima