Abstract Algebra: Theory and Applications

Abstract Algebra: Theory and Applications

Download Abstract Algebra: Theory and Applications, by Thomas W. Judson, in pdf format.

Description

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and elds. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown signi cantly.

Table of Contents

  • The Integers
  • Groups
  • Cyclic Groups
  • Permutation Groups
  • Cosets and Lagrange’s Theorem
  • Introduction to Cryptography
  • Algebraic Coding Theory
  • Isomorphisms
  • Normal Subgroups and Factor Groups
  • Homomorphisms
  • Matrix Groups and Symmetry
  • The Structure of Groups
  • Group Actions
  • The Sylow Theorems
  • Rings
  • Polynomials
  • Integral Domains
  • Lattices and Boolean Algebras
  • Vector Spaces
  • Fields
  • Finite Fields
  • Galois Theory
  • Hints and Solutions

Book Details

Author(s): Thomas W. Judson
Publisher: –
Format(s): PDF
File size: 2.33 MB
Number of pages: 442
Link: Download.







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