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### Abstract Algebra Theory and Applications by Thomas W. Judson

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books.

Abstract Algebra Theory and Applications written by Thomas W. Judson . This is an other great mathematics book cover the following topics of Problem Solving.

• Preliminaries
A Short Note on Proofs, Sets and Equivalence Relations

• The Integers
Mathematical Induction, The Division Algorithm

• Groups
Integer Equivalence Classes and Symmetries, Definitions and Examples, Subgroups

• Cyclic Groups
Cyclic Subgroups, Multiplicative Group of Complex Numbers, The Method of Repeated Squares

• Permutation Groups
Definitions and Notation, Dihedral Groups

• Cosets and Lagrange’s Theorem
Cosets, Lagrange’s Theorem, Fermat’s and Euler’s Theorems

• Introduction to Cryptography
Private Key Cryptography, Public Key Cryptography

• Algebraic Coding Theory
Error-Detecting and Correcting Codes, Linear Codes, Parity-Check and Generator Matrices, Efficient Decoding

• Isomorphisms
Definition and Examples, Direct Products

• Normal Subgroups and Factor Groups
Factor Groups and Normal Subgroups, The Simplicity of the Alternating Group

• Homomorphisms
Group Homomorphisms, The Isomorphism Theorems

• Matrix Groups and Symmetry
Matrix Groups, Symmetry

• The Structure of Groups
Finite Abelian Groups, Solvable Groups

• Group Actions
Groups Acting on Sets, The Class Equation, Burnside’s Counting Theorem

• The Sylow Theorems
The Sylow Theorems, Examples and Applications

• Rings
Rings, Integral Domains and Fields, Ring Homomorphisms and Ideals, Maximal and Prime Ideals, An Application to Software Design

• Polynomials
Polynomial Rings, The Division Algorithm, Irreducible Polynomials

• Integral Domains
Fields of Fractions, Factorization in Integral Domains

• Lattices and Boolean Algebras
Lattices, Boolean Algebras, The Algebra of Electrical Circuits

• Vector Spaces
Definitions and Examples, Subspaces, Linear Independence

• Fields
Extension Fields, Splitting Fields, Geometric Constructions

• Finite Fields
Structure of a Finite Field, Polynomial Codes

• Galois Theory
Field Automorphisms, The Fundamental Theorem, Applications

• ##### Math Books ABSTRACT ALGEBRA

• ###### Abstract Algebra (A Study Guide For Beginners) 2nd Edition by John A. Beachy

• 1. INTEGERS
• 2. FUNCTIONS
• 3. GROUPS
• 4. POLYNOMIALS
• 5. COMMUTATIVE RINGS
• 6. FIELDS
• ** SOLUTIONS of Review problems
• BIBLIOGRAPHY

• ###### Notes on Abstract Algebra by Scott M. LaLonde

• Introduction
• Group Theory
• Ring Theory
• Set Theory
• Techniques for Proof Writing

• ###### Abstract Algebra (Basics, Polynomials, Galois Theory Categorial and Commutative Algebra) by Andreas Hermann

• Introduction
• Groups and Rings
• Commutative Rings
• Modules
• Linear Algebra
• Structure Theorems
• Polynomial Rings
• Polynomials in One Variable
• Group Theory
• Multilinear Algebra

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