Abstract Algebra is a branch of mathematics that is concerned with the study of algebraic structures such as groups, rings, and fields. It is a fundamental subject that is essential for students who wish to pursue a career in mathematics, computer science, or any related field. The book “Abstract Algebra: Theory and Applications” by Thomas W. Judson is an excellent resource for students who wish to master the subject.
Thomas W. Judson is a well-respected mathematician and researcher with extensive experience in the field of abstract algebra. He has written a comprehensive guide to the subject that is both accessible and informative.
The book “Abstract Algebra: Theory and Applications” covers all the essential topics of abstract algebra, starting from the basics and progressing to more advanced topics. The author has used clear and concise language to explain complex mathematical concepts, making the book accessible to students of all levels. The book also includes numerous examples and exercises to help students understand and apply the concepts they learn.
Preliminaries
- A Short Note on Proof
- 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
Download Now Book in PDF
One of the key features of the book is its focus on applications. The author has included many real-world applications of abstract algebra, making the subject more accessible and relevant to students. This is an important aspect of the book, as it helps students understand how abstract algebra can be applied in a variety of fields.
In conclusion, the book “Abstract Algebra: Theory and Applications” by Thomas W. Judson is an excellent resource for students who wish to master the subject of abstract algebra. The author has done an excellent job of covering all the essential topics in a clear and concise manner, making the book accessible to students of all levels. We are pleased to inform students that this book is available in PDF format, making it easy for students to download and access.
