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Friday 10 August 2012

A First Course in Abstract Algebra by John B. Fraleigh

Buy A First Course in Abstract Algebra: Book Price Rs 475/=

Book Summary of A First Course in Abstract Algebra

Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

Features
  • This classical approach to abstract algebra focuses on applications.
  • The text is geared toward high-level courses at schools with strong mathematics programs.
  • Accessible pedagogy includes historical notes written by Victor Katz, an authority on the history of math.
  • By opening with a study of group theory, this text provides students with an easy transition to axiomatic mathematics.

Table Of Contents
GROUPS AND SUBGROUPS.
  • Introduction and Examples.
  • Binary Operations.
  • Isomorphic Binary Structures.
  • Groups.
  • Subgroups.
  • Cyclic Groups.
  • Generators and Cayley Digraphs.
PERMUTATIONS, COSETS, AND DIRECT PRODUCTS.
  • Groups of Permutations.
  • Orbits, Cycles, and the Alternating Groups.
  • Cosets and the Theorem of Lagrange.
  • Direct Products and Finitely Generated Abelian Groups.
  • Plane Isometries.
HOMOMORPHISMS AND FACTOR GROUPS.
  • Homomorphisms.
  • Factor Groups.
  • Factor-Group Computations and Simple Groups.
  • Group Action on a Set.
  • Applications of G-Sets to Counting.
RINGS AND FIELDS.
  • Rings and Fields.
  • Integral Domains.
  • Fermat's and Euler's Theorems.
  • The Field of Quotients of an Integral Domain.
  • Rings of Polynomials.
  • Factorization of Polynomials over a Field.
  • Noncommutative Examples.
  • Ordered Rings and Fields.
IDEALS AND FACTOR RINGS.
  • Homomorphisms and Factor Rings.
  • Prime and Maximal Ideas.
  • Gröbner Bases for Ideals.
EXTENSION FIELDS.
  • Introduction to Extension Fields.
  • Vector Spaces.
  • Algebraic Extensions.
  • Geometric Constructions.
  • Finite Fields.
ADVANCED GROUP THEORY.
  • Isomorphism Theorems.
  • Series of Groups.
  • Sylow Theorems.
  • Applications of the Sylow Theory.
  • Free Abelian Groups.
  • Free Groups.
  • Group Presentations.
GROUPS IN TOPOLOGY.
  • Simplicial Complexes and Homology Groups.
  • Computations of Homology Groups.
  • More Homology Computations and Applications.
  • Homological Algebra.
FACTORIZATION.
  • Unique Factorization Domains.
  • Euclidean Domains.
  • Gaussian Integers and Multiplicative Norms.
MORPHISMS AND GALOIS THEORY.
  • Automorphisms of Fields.
  • The Isomorphism Extension Theorem.
  • Splitting Fields.
  • Separable Extensions.
  • Totally Inseparable Extensions.
  • Galois Theory.
  • Illustrations of Galois Theory.
  • Cyclotomic Extensions.
  • Insolvability of the Quintic.

Details of Book: A First Course in Abstract Algebra

Book:A First Course in Abstract Algebra
Author:John B. Fraleigh
ISBN:8177589008
ISBN-13:

9788177589009

978-8177589009

Binding:Paperback
Publishing Date:2003
Publisher:Pearson Education
Edition:7thEdition
Number of Pages:530
Language:English
Dimensions:9.13 x 7.48 x 0.94 inches
Weight:821 grams

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