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Abstract Algebra: A Concrete Introduction

Abstract Algebra: A Concrete Introduction


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About the Book

This is a new text for the Abstract Algebra course. The author has written this text with a unique, yet historical, approach: solvability by radicals. This approach depends on a fields-first organization. However, professors wishing to commence their course with group theory will find that the Table of Contents is highly flexible, and contains a generous amount of group coverage. *Fields-first approach. Unique approach to subject matters, allows instructor to cover groups, rings and fields in one semester. *Flexible Table of Contents. Allows professors to teach the material in a traditional way, Groups-first. *Proof Technique Appendix. Offers tips and techniques to students to improve their proof writing skills. *Exercise sets. Large quantity of exercises for professors to choose from, with a varying degree of difficulty. *Historical perspective. Interesting, timely biographies of mathematicians.

Table of Contents:
Introduction, Biography: Al-Kwharizmi. I. PRELIMINARIES.  1. Properties of the Integers, Biography: Augustus de Morgan.  2. Solving Cubic and Quartic Polynomial Equations, Historical Note: How the Cubic and Quartic Equations were Solved.  3. Complex Numbers. Historical Note: Highlights in the Development of the Complex Numbers.  4. Some Other Examples, Biography: William Rowan Hamilton. II. ALGEBRAIC EXTENSION FIELDS.  5. Fields.  6. Solvability by Radicals, Biography: Niels Henrik Abel.  7. Rings.  8. Ways in Which Polynomials Are Like the Integers, Biography: Julia Robinson.  9. Principal Ideals, Biography: Emmy Noether. 10. Algebraic Elements. 11. Eisenstein's Irreducibility Criterion, Biography: Gotthold Eisenstein. 12. Extension Fields as Vector Spaces. 13. Automorphisms of Fields, Biography: Evariste Galois. 14. Counting Automorphisms, Biography: Richard Dedekind. III. ELEMENTARY GROUP THEORY. 15. Groups, Biography: Walther von Dyck. 16. Permutation Groups. 17. Group Homomorphisms, Biography: Arthur Cayley. 18. Subgroups. 19. Subgroups Generated by Subsets. 20. Cosets. 21. Finite Groups and Lagrange's Theorem, Biography: Joseph Louis Lagrange. 22. Equivalence Relations and Cauchy's Theorem, Biography: Augustin-Louis Cauchy. 23. Normal Subgroups and Quotient Groups, Biography: Otto Hölder. 24. The Homomorphism Theorem for Groups, Biography: B. L. van derWaerden. IV. POLYNOMIAL EQUATIONS NOT SOLVABLE BY RADICALS. 25. Galois Groups of Radical Extensions. 26. Solvable Groups and Commutator Subgroups, Biography: William Burnside. 27. Solvable Galois Groups. 28. Polynomial Equations Not Solvable by Radicals, Biography: Paolo Ruffini. V. FINITE GROUPS. 29. Finite External Direct Products of Groups, Biography: J. H. M. Wedderburn. 30. Finite Internal Direct Products of Groups. 31. Abelian Groups with Prime Power Order. 32. The Fundamental Theorem of Finite Abelian Groups, Biography: Leopold Kronecker. 33. Dihedral Groups, Biography: Felix Klein. 34. Cauchy's Theorem. 35. The Sylow Theorems, Biography: Peter Ludvig Sylow. 36. Groups of Order Less than 16. 37. Groups of Even Permuatations, Biography: Camille Jordan. 38. Semidirect Products. APPENDICES. A. The Greek Alphabet. B. Proving Theorems, Biography: George Boole. C. Vector Spaces over Fields. D. Constructions with Straightedge and Compass.


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Product Details
  • ISBN-13: 9780201437218
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Height: 195 mm
  • No of Pages: 480
  • Sub Title: A Concrete Introduction
  • Width: 238 mm
  • ISBN-10: 020143721X
  • Publisher Date: 02 Mar 2001
  • Binding: Hardback
  • Language: English
  • Spine Width: 22 mm
  • Weight: 803 gr


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