Contemporary abstract algebra
Author(s)
Bibliographic Information
Contemporary abstract algebra
Brooks/Cole, c2010
7th ed., International ed
Available at 1 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references and indexes
Description and Table of Contents
Description
Contemporary Abstract Algebra, 7e, International Edition 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.
Table of Contents
- PART I. INTEGERS AND EQUIVALENCE RELATIONS. Preliminaries. Properties of Integers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises. Computer Exercises. PART II. 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. Computer Exercises. 3. Finite Groups
- Subgroups. Terminology and Notation. Subgroup Tests. Examples of Subgroups. Exercises. Computer Exercises. 4. Cyclic Groups. Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups. Exercises. Computer 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. Computer Exercises. Biography of Augustin Cauchy. 6. Isomorphisms. Motivation. Definition and Examples. Cayley's Theorem. Properties of Isomorphisms Automorphisms. Exercises. Computer 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 Computer 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. Computer 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 +variste Galois 10. Group Homomorphisms. Definition and Examples. Properties of Homomorphisms. The First Isomorphism Theorem. Exercises. Computer 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. Computer Exercises. Supplementary Exercises for Chapters 9-11. PART III. RINGS. 12. Introduction to Rings. Motivation and Definition. Examples of Rings. Properties of Rings. Subrings. Exercises. Computer Exercises. Biography of I. N. Herstein. 13. Integral Domains. Definition and Examples. Fields. Characteristic of a Ring. Exercises. Computer Exercises. Biography of Nathan Jacobson. 14. Ideals and Factor Rings. Ideals. Factor Rings. Prime Ideals and Maximal Ideals. Exercises. Computer Exercises Biography of Richard Dedekind. Biography of Emmy Noether. Supplementary Exercises for Chapters 12-14. 15. Ring Homomorphisms. Definition and Examples. Properties of Ring Homomorphisms. The Field of Quotients Exercises. 16. Polynomial Rings. Notation and Terminology. The Division Algorithm and Consequences. Exercises Biography of Saunders Mac Lane. 17. Factorization of Polynomials. Reducibility Tests. Irreducibility Tests. Unique Factorization in Z[x]. Weird Dice: An Application of Unique Factorization. Exercises. Computer Exercises. Biography of Serge Lang. 18. Divisibility in Integral Domains. Irreducibles, Primes. Historical Discussion of Fermat's Last Theorem. Unique Factorization Domains. Euclidean Domains. Exercises. Computer Exercises Biography of Sophie Germain. Biography of Andrew Wiles. Supplementary Exercises for Chapters 15-18. PART IV. FIELDS. 19. Vector Spaces Definition and Examples. Subspaces. Linear Independence. Exercises. Biography of Emil Artin. Biography of Olga Taussky-Todd. 20. Extension Fields. The Fundamental Theorem of Field Theory. Splitting Fields. Zeros of an Irreducible Polynomial. Exercises. Biography of Leopold Kronecker. 21. Algebraic Extensions. Characterization of Extensions. Finite Extensions. Properties of Algebraic Extensions Exercises. Biography of Irving Kaplansky. 22. Finite Fields. Classification of Finite Fields. Structure of Finite Fields. Subfields of a Finite Field Exercises. Computer Exercises. Biography of L. E. Dickson. 23. Geometric Constructions. Historical Discussion of Geometric Constructions. Constructible Numbers. Angle-Trisectors and Circle-Squarers. Exercises. Supplementary Exercises for Chapters 19-23. PART V. SPECIAL TOPICS. 24. Sylow Theorems. Conjugacy Classes. The Class Equation. The Probability That Two Elements Commute. The Sylow Theorems. Applications of Sylow Theorems. Exercises. Computer Exercises. Biography of Ludvig Sylow. 25. Finite Simple Groups. Historical Background. Nonsimplicity Tests. The Simplicity of A5. The Fields Medal. The Cole Prize. Exercises. Computer Exercises. Biography of Michael Aschbacher. Biography of Daniel Gorenstein. Biography of John Thompson. 26. Generators and Relations. Motivation. Definitions and Notation. Free Group. Generators and Relations. Classification of Groups of Order up to 15. Characterization of Dihedral Groups. Realizing the Dihedral Groups with Mirrors. Exercises. Biography of Marshall Hall, Jr. 27. Symmetry Groups. Isometries. Classification of Finite Plane Symmetry Groups. Classification of Finite Group of Rotations in R . Exercises. 28. Frieze Groups and Crystallographic Groups. The Frieze Groups. The Crystallographic Groups. Identification of Plane Periodic Patterns. Exercises. Biography of M. C. Escher. Biography of George P lya. Biography of John H. Conway. 29. Symmetry and Counting. Motivation. Burnside's Theorem. Applications. Group Action. Exercises. Biography of William Burnside. 30. Cayley Digraphs of Groups. Motivation. The Cayley Digraph of a Group. Hamiltonian Circuits and Paths. Some Applications. Exercises. Biography of William-Rowan Hamilton. Biography of Paul Erd/s. 31. Introduction to Algebraic Coding Theory. Motivation. Linear Codes. Parity-Check Matrix Decoding. Coset Decoding. Historical Note: The Ubiquitous Reed-Solomon Codes. Exercises. Biography of Richard W. Hamming. Biography of Jessie MacWilliams. Biography of Vera Pless. 32. An Introduction to Galois Theory. Fundamental Theorem of Galois Theory. Solvability of Polynomials by Radicals. Insolvability of a Quintic. Exercises. Biography of Philip Hall. 33. Cyclotomic Extensions. Motivation. Cyclotomic Polynomials. The Constructible Regular n-gons. Exercises. Computer Exercises. Biography of Carl Friedrich Gauss. Biography of Manjul Bhargava. Supplementary Exercises for Chapters 24-33.
by "Nielsen BookData"