Contemporary Abstract Algebra 9th Edition by Joseph A Gallian is a widely recognized textbook in the field of abstract algebra. This book provides a thorough and accessible introduction to the fundamentals of abstract algebra, making it an ideal resource for students and instructors alike.
The 9th edition of this book has been updated to reflect the latest developments in the field and includes a wealth of new examples, exercises, and applications. The book begins with a discussion of basic algebraic structures, including groups, rings, and fields, before delving into more advanced topics like Galois theory, factorization in algebraic number fields, and the theory of finitely generated modules over a principal ideal domain.
One of the strengths of this book is its clear and concise writing style, which makes the material accessible to students of all levels. The book is also well-organized, with each chapter building upon the material covered in previous chapters to ensure a comprehensive understanding of the subject matter.
TABLE OF CONTENTS
1 Introduction to Groups
- Symmetries of a Square
- The Dihedral Groups
- Biography of Niels Abe
2 Groups
- Definition and Examples of Groups
- Elementary
- Properties of Groups
- Historical Note
3 Finite Groups; Subgroups
- Terminology and Notation
- Subgroup Tests
- Examples of Subgroups
4 Cyclic Groups
- Properties of Cyclic Groups
- Classification of Subgroups of Cyclic Groups
- Biography of James Joseph Sylvester
5 Permutation Groups
- Definition and Notation
- Cycle Notation
- Properties of Permutations
- A Check-Digit Scheme Based on D5
- Biography of Augustin Cauchy
- Biography of Alan Turing
6 Isomorphisms
- Motivation
- Definition and Examples
- Cayley’s Theorem
- Properties of Isomorphisms
- Automorphisms
- Biography of Arthur Cayley
7 Cosets and Lagrange’s Theorem
- Properties of Cosets
- Lagrange’s Theorem and Consequences
- An Application of Cosets to Permutation Groups
- The Rotation Group of a Cube and a Soccer Ball
- An Application of Cosets to the Rubik’s Cube
- Biography of Joseph Lagrange
8 External Direct Products
- Definition and Examples
- Properties of External Direct Products
- The Group of Units Modulo n as an External Direct Product
- Applications
- Biography of Leonard Adleman
9 Normal Subgroups and Factor Groups
- Normal Subgroups
- Factor Groups
- Applications of Factor Groups
- Internal Direct Products
- Biography of Évariste Galois
10 Group Homomorphisms
- Definition and Examples
- Properties of Homomorphisms
- The First Isomorphism Theorem
- Biography of Camille Jordan
11 Fundamental Theorem of Finite
- Abelian Groups
- The Fundamental Theorem
- The Isomorphism Classes of Abelian Groups
- Proof of the Fundamental Theorem
12 Introduction to Rings
- Motivation and Definition
- Examples of Rings
- Properties of Rings
- Subrings
- Biography of I. N. Herstein
13 Integral Domains
- Definition and Examples
- Fields
- Characteristic of a Ring
- Biography of Nathan Jacobson
14 Ideals and Factor Rings
- Ideals
- Factor Rings
- Prime Ideals and Maximal Ideals
- Biography of Richard Dedekind
- Biography of Emmy Noether
15 Ring Homomorphisms
- Definition and Examples
- Properties of Ring Homomorphisms
- The Field of Quotients
- Biography of Irving Kaplansky
16 Polynomial Rings
- Notation and Terminology
- The Division Algorithm and Consequences
- Biography of Saunders Mac Lane
17 Factorization of Polynomials
- Reducibility Tests
- Irreducibility Tests
- Unique Factorization in Z[x]
- Weird Dice: An Application of Unique Factorization
- Biography of Serge Lang
18 Divisibility in Integral Domains
- Irreducibles, Primes
- Historical Discussion of Fermat’s Last Theorem
- Unique Factorization Domains
- Euclidean Domains
- Biography of Sophie Germain
- Biography of Andrew Wiles
- Biography of Pierre de Fermat
19 Vector Spaces
- Definition and Examples
- Subspaces
- Linear Independence
- Biography of Emil Artin
- Biography of Olga Taussky-Todd
20 Extension Fields
- The Fundamental Theorem of Field Theory
- Splitting Fields
- Zeros of an Irreducible Polynomial
- Biography of Leopold Kronecker
21 Algebraic Extensions
- Characterization of Extensions
- Finite Extensions
- Properties of Algebraic Extensions
- Biography of Ernst Steinitz
22 Finite Fields
- Classification of Finite Fields
- Structure of Finite Fields
- Subfields of a Finite Field
- Biography of L. E. Dickson
23 Geometric Constructions
- Historical Discussion of Geometric Constructions
- Constructible Numbers
- Angle-Trisectors and
- Circle-Squarers
24 Sylow Theorems
- Conjugacy Classes
- The Class Equation
- The Sylow Theorems
- Applications of Sylow Theorems
- Biography of Oslo Ludwig Sylow
- Historical Background
- Nonsimplicity Tests
- The Simplicity of A5
- The Fields Medal
25 The Cole Prize
- Biography of Michael Aschbacher
- Biography of Daniel Gorenstein
- Biography of John Thompson
26 Generators and Relations
- Motivation
- Definitions and Notation
- Free Group
- Generators and Relations
- Classification of Groups of Order Up to 15
- Characterization of Dihedral Groups
- Realizing the Dihedral Groups with Mirrors
- Biography of Marshall Hall, Jr.
27 Symmetry Groups
- Isometries
- Classification of Finite Plane Symmetry
- Groups
- Classification of Finite Groups of Rotations in R3
28 Frieze Groups and Crystallographic Groups
- The Frieze Groups
- The Crystallographic Groups
- Identification of Plane Periodic Patterns
- Biography of M. C. Escher
- Biography of George Pólya
- Biography of John H. Conway
29 Symmetry and Counting
- Motivation
- Burnside’s Theorem
- Applications
- Group Action
- Biography of William Burnside
30 Cayley Digraphs of Groups
- Motivation
- The Cayley Digraph of a Group
- Hamiltonian Circuits and Paths
- Some Applications
- Biography of William Rowan Hamilton
- Biography of Paul Erdó ́s
31 Introduction to Algebraic Coding Theory
- Motivation
- Linear Codes
- Parity-Check Matrix
- Decoding
- Coset Decoding
- Historical Note: The Ubiquitous Reed–Solomon Codes
- Biography of Richard W. Hamming
- Biography of Jessie MacWilliams
- Biography of Vera Pless
32 An Introduction to Galois Theory
- Fundamental Theorem of Galois Theory
- Solvability of Polynomials by Radicals
- Insolvability of a Quintic
- Biography of Philip Hall
33 Cyclotomic Extensions
- Motivation
- Cyclotomic Polynomials
- The Constructible Regular n-gons
- Biography of Carl Friedrich Gauss
- Biography of Manjul Bhargava
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Another standout feature of this book is its use of real-world examples and applications. These examples help to bring the abstract concepts of algebra to life for the reader and demonstrate the practical applications of the theory. The book also includes numerous exercises and review questions, which provide opportunities for students to test their understanding of the material.
In addition to its comprehensive coverage of the subject matter, Contemporary Abstract Algebra 9th Edition also includes a number of helpful features, such as a glossary of terms, an index, and a solutions manual. These resources make the book an ideal tool for students who are studying abstract algebra on their own or for instructors who are teaching a course in the subject.
In conclusion, Contemporary Abstract Algebra 9th Edition by Joseph A Gallian is an essential resource for anyone studying abstract algebra. With its clear writing style, comprehensive coverage of the subject matter, and real-world examples and applications, this book is sure to help students and instructors alike gain a deep understanding of the fundamentals of abstract algebra.
We are proud to announce that we have this book in PDF format available for download. So, students can easily access this valuable resource from the comfort of their own homes.
