Contemporary Abstract Algebra 9th Edition by Joseph Gallian – Ebook PDF Instant Download/Delivery: 1305657969 ,9781305657960
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ISBN 10: 1305657969
ISBN 13: 9781305657960
Author: Joseph Gallian
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian�s text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.
Contemporary Abstract Algebra 9th Edition Table of contents:
Chapter 1: Groups
- 1.1 Introduction to Groups
- 1.2 Examples of Groups
- 1.3 Properties of Groups
- 1.4 Subgroups
- 1.5 Cyclic Groups
- 1.6 Permutation Groups
- 1.7 Cosets and Lagrange’s Theorem
- 1.8 Group Homomorphisms
- 1.9 Isomorphisms
- 1.10 The Fundamental Theorem of Finite Abelian Groups
- 1.11 Group Actions
- 1.12 Sylow’s Theorems
Chapter 2: Rings
- 2.1 Introduction to Rings
- 2.2 Examples of Rings
- 2.3 Subrings and Ideals
- 2.4 Ring Homomorphisms
- 2.5 Quotient Rings
- 2.6 Division Rings and Fields
- 2.7 The Ring of Polynomials
- 2.8 The Structure of Fields
- 2.9 Field Extensions
Chapter 3: Polynomials
- 3.1 Polynomial Rings
- 3.2 The Division Algorithm
- 3.3 Roots of Polynomials
- 3.4 Factorization of Polynomials
- 3.5 The Field of Complex Numbers
- 3.6 The Fundamental Theorem of Algebra
- 3.7 Eisenstein’s Criterion
Chapter 4: Vector Spaces
- 4.1 Introduction to Vector Spaces
- 4.2 Subspaces
- 4.3 Linear Independence and Basis
- 4.4 Dimension and Rank
- 4.5 Linear Transformations
- 4.6 Eigenvalues and Eigenvectors
- 4.7 The Characteristic Polynomial
Chapter 5: Linear Transformations and Matrices
- 5.1 Introduction to Matrices
- 5.2 Matrix Operations
- 5.3 Matrix Rank
- 5.4 The Inverse of a Matrix
- 5.5 Eigenvalues and Eigenvectors
- 5.6 Diagonalization
- 5.7 Jordan Canonical Form
Chapter 6: Groups and Rings in Action
- 6.1 Applications to Geometry
- 6.2 Symmetry Groups in Geometry
- 6.3 Applications to Coding Theory
- 6.4 The Chinese Remainder Theorem
- 6.5 Applications to Cryptography
Chapter 7: Number Theory
- 7.1 Divisibility and Primes
- 7.2 Euclidean Algorithm
- 7.3 Modular Arithmetic
- 7.4 The Chinese Remainder Theorem
- 7.5 Fermat’s Little Theorem
- 7.6 The Fundamental Theorem of Arithmetic
- 7.7 Diophantine Equations
Chapter 8: Galois Theory
- 8.1 Introduction to Galois Theory
- 8.2 Field Extensions
- 8.3 The Galois Group of a Polynomial
- 8.4 Solvability by Radicals
- 8.5 The Fundamental Theorem of Galois Theory
- 8.6 Applications of Galois Theory
Chapter 9: Advanced Topics in Group Theory
- 9.1 Simple Groups
- 9.2 Solvable Groups
- 9.3 Nilpotent Groups
- 9.4 The Sylow Theorems Revisited
- 9.5 The Classification of Finite Simple Groups
Chapter 10: Introduction to Homological Algebra
- 10.1 Chain Complexes
- 10.2 Exact Sequences
- 10.3 Homology and Cohomology Groups
- 10.4 Applications to Group and Ring Theory
Appendices
- A. Review of Set Theory
- B. Review of Number Systems
- C. Solutions to Selected Exercises
- D. Index
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