Abstract algebra
Subtitle: an interactive approach
By: William Paulsen
Series: Textbooks in mathematics; Textbooks in mathematics (Boca Raton, Fla.)
Publisher: CRC Press
Published: 2010
Place of publication: Boca Raton, Fla
Language: eng
Number of pages: 525
ISBN-13: 9781420094534
Subjects: Textbooks; Abstract Algebra
Description: Understanding the Group Concept Introduction to Groups Modular Arithmetic Prime Factorizations The Definition of a Group The Structure within a Group Generators of Groups Defining Finite Groups in Mathematica and GAP Subgroups Patterns within the Cosets of Groups Left and Right Cosets How to Write a Secret Message Normal Subgroups Quotient Groups Mappings between Groups Isomorphisms Homomorphisms The Three Isomorphism Theorems Permutation Groups Symmetric Groups Cycles Cayley's Theorem Numbering the PermutationsBuilding Larger Groups from Smaller Groups The Direct Product The Fundamental Theor.
Notes: Includes bibliographical references and index.
Table of contents: title: 1. Understanding the group concept; title: 2. The structure within a group; title: 3. Patterns within the cosets of groups; title: 4. Mappings between groups; title: 5. Permutation groups; title: 6. Building larger groups from smaller groups; title: 7. The search for normal subgroups; title: 8. Solvable and insoluble groups; title: 9. Introduction to rings; title: 10. The structure within rings; title: 11. Integral domains and fields; title: 12. Unique factorization; title: 13. Finite division rings; title: 14. The theory of fields; title: 15. Galois theory.