Modern algebra with applications 1st Edition by John Wiley, Sons ISBN 0471298913 9780471298915

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Product details:
ISBN 10: 0471298913
ISBN 13: 9780471298915
Author: John Wiley, Sons

This book blends the theoretical with the practical in the instruction of modern algebra. Modern algebra is usually taught from the point of view of its intrinsic interest, without using applications. Many readers lose interest when they do not see the relevance of the subject and often become skeptical of the explanation that the material will be used later. The author believes by providing interesting and nontrivial applications, the student will better appreciate and understand the subject.

Modern algebra with applications 1st Edition Table of contents:

• Introduction to Algebra

  • The Nature of Algebra
  • Key Concepts in Algebraic Structures
  • Historical Development and Applications of Algebra

• Basic Set Theory and Logic

  • Sets, Relations, and Functions
  • Logical Connectives and Proof Techniques
  • Applications of Set Theory in Algebraic Structures

• Groups and Group Theory

  • Definition of Groups
  • Properties of Group Operations
  • Subgroups, Cyclic Groups, and Group Homomorphisms
  • Applications of Group Theory in Symmetry and Cryptography

• Rings and Ring Theory

  • Definition and Properties of Rings
  • Subrings, Ideals, and Quotient Rings
  • Ring Homomorphisms and Ring Isomorphisms
  • Applications of Ring Theory in Coding and Error Detection

• Fields and Field Theory

  • Definition and Properties of Fields
  • Field Extensions and Galois Theory
  • Applications of Field Theory in Coding Theory and Cryptography

• Vector Spaces and Linear Algebra

  • Definition of Vector Spaces
  • Basis, Dimension, and Linear Transformations
  • Eigenvalues, Eigenvectors, and Diagonalization
  • Applications of Linear Algebra in Computer Graphics and Engineering

• Polynomials and Polynomial Rings

  • Polynomial Operations and Factorization
  • Polynomial Rings and Divisibility
  • Applications of Polynomials in Computational Algebra

• Modules and Algebras

  • Definition and Properties of Modules
  • Algebras and Their Applications
  • Advanced Topics in Module Theory
  • Use of Modules in Structural Analysis

• Applications of Algebra in Coding Theory

  • Error Detection and Correction Codes
  • Linear Block Codes and Cyclic Codes
  • Applications in Data Transmission and Security

• Applications of Algebra in Cryptography

  • Classical Cryptographic Systems
  • Modern Cryptographic Algorithms
  • Algebraic Structures in Secure Communication

• Advanced Topics in Algebraic Structures

  • Lattices, Boolean Algebras, and Applications
  • Advanced Group Theory Topics
  • Applications of Algebra in Network Theory

• Algebra in Computational Mathematics

  • Algebraic Algorithms and Complexity
  • Computational Tools for Algebraic Calculations
  • Practical Applications in Engineering and Technology

• Conclusion and Future Trends in Algebra

  • Emerging Areas in Modern Algebra
  • Interdisciplinary Applications of Algebra
  • Future Directions in Algebraic Research and Development

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