Provides an introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by ...Show synopsisProvides an introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. This text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings.Hide synopsis
Description:New. CONTEMPORARY ABSTRACT ALGEBRA, 8E, provides a solid...New. CONTEMPORARY ABSTRACT ALGEBRA, 8E, provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. "Why Is Abstract Algebra Useful? " essay on the author`s website shows students the importance of studying abstract algebra and its applicability to everyday life. This motivational essay can be incorporated into a lesson on the first day of class, or can serve as a motivational tool further along in the course. Coverage of proof writing is provided on the instructor`s website in the updated essay "Advice for students learning proofs." This essay provides basic guidance for students encountering proof writing for the first time or needing to freshen their skills. This text focuses on abstract algebra as a contemporary subject, with concepts and methodologies currently being used by computer scientists, physics, and chemists. Extensive coverage of groups, rings, and fields, plus a variety of non-traditional special topics. A good mixture of now more that 1750 computational and theoretical exercises appearing in each chapter and in Supplementary Exercise sets that synthesize concepts from multiple chapters. Emphasis on computation and proof writing, with an abundance of exercises to help students develop both skills. Lines from popular songs, poems, and quotations give the text a fresh, contemporary feel and keep students engaged. Over 200 new exercises! New Examples! Refreshed quotations, historical notes, and biographies! PART I: INTEGERS AND EQUIVALENCE RELATIONS. Preliminaries. Properties of Integers. Complex Numbers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises. PART I: GROUPS. 1. Introduction to Groups. Symmetries of a Square. The Dihedral Groups. Exercises. Biography of Neils Abel 2. Groups. Definition and Examples of Groups. Elementary Properties of Groups. Historical Note. Exercises. 3. Finite Groups Subgroups. Terminology and Notation. Subgroup Tests. Examples of Subgroups. Exercises. 4. Cyclic Groups. Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups. Exercises. Biography of J. J. Sylvester. Supplementary Exercises for Chapters 1-4. 5. Permutation Groups. Definition and Notation. Cycle Notation. Properties of Permutations. A Check-Digit Scheme Based on D5. Exercises. Biography of Augustin Cauchy. 6. Isomorphisms. Motivation. Definition and Examples. Cayley`s Theorem. Properties of Isomorphisms. Automorphisms. Exercises. Biography of Arthur Cayley. 7. Cosets and Lagrange`s Theorem. Properties of Cosets. Lagrange`s Theorem and Consequences. An Application of Cosets to Permutation Groups. The Rotation Group of a Cube and a Soccer Ball. Exercises. Biography of Joseph Lagrange. 8. External Direct Products. Definition and Examples. Properties of External Direct Products. The Group of Units Modulo n as an External Direct Product. Applications. Exercises. Biography of Leonard Adleman. Supplementary Exercises for Chapters 5-8 9. Normal Subgroups and Factor Groups. Normal Subgroups. Factor Groups. Applications of Factor Groups. Internal Direct Products. Exercises. Biography of Évariste Galois 10. Group Homomorphisms. Definition and Examples. Properties of Homomorphisms. The First Isomorphism Theorem. Exercises. Biography of Camille Jordan. 11. Fundamental Theorem of Finite Abelian Groups. The Fundamental Theorem. The Isomorphism Classes of Abelian Groups. Proof of the Fundamental Theorem. Exercises. Supplementary Exercises for Chapters 9-11. PART III: RINGS. Printed Pages: 652..
This book is very well written, but I advise you that it is not for the weak brained! I am taking this class as an independent study, so I am working almost enturely independently, and it is very hard. Great book though
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