Concrete Approach To Abstract Algebra
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Author | : W. W. Sawyer |
Publisher | : Courier Dover Publications |
Total Pages | : 241 |
Release | : 2018-08-15 |
Genre | : Mathematics |
ISBN | : 0486824616 |
Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.
Author | : Jeffrey Bergen |
Publisher | : Academic Press |
Total Pages | : 115 |
Release | : 2010-04-15 |
Genre | : Mathematics |
ISBN | : 0123846811 |
A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study.
Author | : Walter Warwick Sawyer |
Publisher | : |
Total Pages | : 234 |
Release | : 1978 |
Genre | : |
ISBN | : |
Author | : Niels Lauritzen |
Publisher | : Cambridge University Press |
Total Pages | : 258 |
Release | : 2003-10-16 |
Genre | : Mathematics |
ISBN | : 9780521534109 |
This book presents abstract algebra based on concrete examples and applications. All the traditional material with exciting directions.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 402 |
Release | : 2010-01-14 |
Genre | : Mathematics |
ISBN | : 0486474178 |
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 | : John A. Beachy |
Publisher | : |
Total Pages | : 325 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9780130044259 |
Textbook for undergraduate mathematics majors presumes basic knowledge of linear algebra. The "concrete" approach attempts to separate the problems of abstract mathematics from the problematic requirement that students produce proofs of their own devising. Annotation copyright Book News, Inc. Portland, Or.
Author | : Allan Clark |
Publisher | : Courier Corporation |
Total Pages | : 242 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486140350 |
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.
Author | : Walter Warwick Sawyer |
Publisher | : |
Total Pages | : 233 |
Release | : 1959 |
Genre | : |
ISBN | : |
Author | : Jonathan D. H. Smith |
Publisher | : CRC Press |
Total Pages | : 330 |
Release | : 2016-04-19 |
Genre | : Mathematics |
ISBN | : 1420063723 |
Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.
Author | : W. Keith Nicholson |
Publisher | : John Wiley & Sons |
Total Pages | : 560 |
Release | : 2012-03-20 |
Genre | : Mathematics |
ISBN | : 1118135350 |
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.