A Course in Abstract Algebra 4th Edition by Vijay K. Khanna is a comprehensive and well-written textbook that covers the essential concepts of abstract algebra. This book is designed for students of mathematics who are interested in learning about the fundamental theories and applications of abstract algebra. The book provides a clear and in-depth explanation of the concepts, making it an ideal resource for students at all levels of mathematical proficiency.
The author has included numerous examples and exercises throughout the text to help students understand and apply the concepts they are learning. Additionally, the book is well-organized and easy to navigate, making it a great resource for students who are studying on their own.
One of the key strengths of A Course in Abstract Algebra is its clarity. The author has made every effort to ensure that the language used in the book is clear and concise, making it easy for students to understand the material. The book also provides a logical and systematic approach to the subject, building upon the concepts as the book progresses.
TABLE OF CONTENTS
Preliminaries
- Sets
- Subsets
- Relations
- Equivalence Classes
- Mappings or Functions
- Equality of Mappings
- Composition of Mappings
- Binary Compositions
- Permutations
- Cyclic Permutations
- Cycles of a Permutation
- Disjoint Permutations
- Some Results From Number Theory
- The Greatest Common Divisor
- Prime Numbers
- Composite Numbers
- Congruences
- Chinese Remainder Theorem
Groups
- Subgroups
- Cyclic Groups
Normal Subgroups, Homomorphisms Permutation Groups
- Quotient Groups
- Homomorphisms – Isomorphisms
- The Diedral Group
- Generators of a Subgroup
- Cummutator
.
Automorphisms and Conjugate Elements
- Inner Automorphism
- Characteristic Subgroups
- Conjugate Elements
- Similar Permutations
- Partition of Integer
Sylow Theorems and Direct Problems
- Sylow p-groups
- Double Cosets
- Sylow Groups in Spk
- Direct Products
- Finite Abelian Groups
Group Actions, Solvable and Nilpotent Groups
- Group Actions
- Normal Series
- Solvable Groups
- Nilpotent Groups
Rings
- Subrings
- Sum of two Subrings
- Characteristics of a Ring
- Product of Rings
- Ideals
- Sum of Ideals
- Product of Ideals
Homomorpisms and Embedding of Rings
- Quotient Rings
- Homomorphisms
- Embedding of Rings
- More on Ideals
Maximal Ideals
Euclidean and Factorization Domains
- Euclidean Domains
- Prime and Irreducible Elements
- Polynomial Rings
- Greatest Common Divisor
- Unique Factorization Domains
- Noetherian Rings
Vector Spaces
- Subspaces
- Sum of Subspaces
- Quotient Spaces
- Homomorphisms or Linear Transformations
- Linear Span
- Linear Dependence and Independence
- Inner Product Spaces
- Norm of a Vector
- Orthogonality
- Orthonormal Set
Linear Transformations
- Algebra of Linear Transformations
- Invertible Linear Transformations
- Matrix of a Linear Transformation
- Dual Spaces
- Transpose of a Linear Transformation
Eigen Values and Eigen Vectors
- Characteristic Polynomials
- Characteristic Polynomial of a Linear Operator
- Minimal Polynomials
- Diagonalizable Operators
- Primary Decomposition Theorem
- Invariant Subspaces
- Cyclic Subspaces
- Projections
Fields
- Algebraic Expressions
- Roots of Polynomials
- Splitting Fields
More on Fields
- Prime Subfields
- Seperable Extensions
- Normal Extensions
- Algebraically Closed Fields and Algebraic Closure
- Automorphisms of Field Extensions
- Galois Extensions
- Roots of Unity
- Finite Fields
- Ruler and Compass Constructions
Download Now Book in PDF
The book is also available in PDF format, allowing students to easily access and study the material from their computer or mobile device. This is especially useful for students who are unable to attend physical classes or who prefer to study at their own pace. With the PDF format, students can easily search for specific information, make notes, and highlight important sections of the text.
In conclusion, A Course in Abstract Algebra 4th Edition by Vijay K. Khanna is an excellent resource for students who are interested in learning about abstract algebra. The book provides a clear and comprehensive overview of the subject, making it an ideal resource for students at all levels of mathematical proficiency. And with the availability of the book in PDF format, students can easily access and study the material at their convenience.
