Contemporary Abstract Algebra PDF by Joseph Gallian Download 2022

Download the Latest Contemporary Abstract Algebra 9th edition PDF book by Joseph A Gallian . This book is specially Designed for undergraduate and postgraduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a short introduction to results from pure mathematics and variety theory.

Comtemporary Abstract Algebra by Joseph A. Gallian Book Pdf DOWNLOAD for IIT JAM, JEST, TIFR, UOH etc.


Changes in this Edition of Contemporary Abstract Algebra PDF by Joseph Gallian


Changes for the ninth edition include new exercises, new examples, new  biographies, new quotes, new applications, and a freshening of the historical notes and biographies from the 8th edition. These changes accentuate and enhance the hallmark features that have made previous editions of the book a comprehensive, lively, and engaging introduction to the subject:

  • Extensive coverage of groups, rings, and fields, plus a variety of non-traditional special topics
  • A good mixture of more nearly 1700 computational and theoretical  exercises appearing in each chapter that synthesize concepts from  multiple chapters
  • Back-of-the-book skeleton solutions and hints to the odd-numbered exercises
  • Worked-out examples– totaling more than 300–ranging from routine  computations to quite challenging
  • Computer exercises that utilize interactive software available on my  website that stress guessing and making conjectures
  • A large number of applications from scientific and computing fields, as well as from everyday life
  • Numerous historical notes and biographies that spotlight the people and events behind the mathematics
  • Motivational and humorous quotations.
  • More than 275 figures, photographs, tables, and reproductions of currency that honor mathematicians
  • Annotated suggested readings for interesting further exploration of topics.

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Download Contemporary Abstract Algebra PDF by Joseph Gallian


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Contemporary Abstract Algebra PDF by Joseph Gallian: Table of Contents


  • PART 1 : INTEGERS AND EQUIVALENCE RELATIONS
Chapter 0 : PreliminariesProperties of Integers | Modular Arithmetic Complex Numbers  | Mathematical Induction  | Equivalence Relations  | Functions (Mappings)
Exercises
  • PART 2 : GROUPS
Chapter 1 : Introduction to GroupsSymmetries of a Square | The Dihedral Groups
Exercises
Biography of Niels Abel
Chapter 2 : GroupsDefinition and Examples of Groups | Elementary Properties of Groups | Historical Note
Exercises
Chapter 3 : Finite Groups; SubgroupsTerminology and Notation  | Subgroup Tests | Examples of Subgroups 
Exercises
Chapter 4 : Cyclic GroupsProperties of Cyclic Groups | Classification of Subgroups of Cyclic Groups
Exercises
Biography of James Joseph Sylvester
Chapter 5 : Permutation GroupsDefinition and Notation | Cycle Notation  | Properties of Permutations | A Check-Digit Scheme Based on D5
Exercises
Biography of Augustin Cauchy
Biography of Alan Turing
Chapter 6 : IsomorphismsMotivation | Definition and Examples | Cayley’s Theorem  | Properties of Isomorphisms | Automorphisms
Exercises
Biography of Arthur Cayley
Chapter 7 : Cosets and Lagrange’s TheoremProperties 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
Exercises
Biography of Joseph Lagrange
Chapter 8 :  External Direct ProductsDefinition and Examples | Properties of External Direct Products  | The Group of Units Modulo n as an External Direct Product  | Applications
Exercises
Biography of Leonard Adleman
Chapter 9 :  Normal Subgroups and Factor GroupsNormal Subgroups | Factor Groups | Applications of Factor Groups  | Internal Direct Products  Exercises
Biography of Évariste Galois
Chapter 10 : Group HomomorphismsDefinition and Examples | Properties of Homomorphisms | The First Isomorphism Theorem
Exercises
Biography of Camille Jodan
Chapter 11 : Fundamental Theorem of FiniteAbelian Groups  | The Fundamental Theorem | The Isomorphism Classes of Abelian Groups  | Proof of the Fundamental Theorem
Exercises
  • PART 3 : RINGS
Chapter 12 :  Introduction to RingsMotivation and Definition | Examples of Rings | Properties of Rings | Subrings |
Exercises
Biography of I. N. Herstein
Chapter 13 : Integral DomainsDefinition and Examples | Fields | Characteristic of a Ring
Exercises
Biography of Nathan Jacobson
Chapter 14 :  Ideals and Factor RingsIdeals | Factor Rings | Prime Ideals and Maximal | Ideals
Exercises
Biography of Richard Dedekind
Biography of Emmy Noether
Chapter 15 : Ring HomomorphismsDefinition and Examples | Properties of Ring | Homomorphisms | The Field of Quotients
Exercises
Biography of Irving Kaplansky
Chapter 16 : Polynomial RingsNotation and Terminology | The Division Algorithm and Consequences
Exercises
Biography of Saunders Mac Lane
Chapter 17 : Factorization of  PolynomialsReducibility Tests  | Irreducibility Tests | Unique Factorization in Z[x]  | Weird Dice : An Application of Unique | Factorization
Exercises
Biography of Serge Lang
Chapter 18 : Divisibility in Integral DomainsIrreducibles, Primes  | Historical Discussion of Fermat’s Last Theorem  | Unique Factorization Domains  | Euclidean Domains
Exercises
Biography of Sophie Germain
Biography of Andrew Wiles
Biography of Pierre de Fermat
  • PART 4 : FIELDS
Chapter 19 :  Vector SpacesDefinition and Examples  | Subspaces | Linear | Independence
Exercises
Biography of Emil Artin
Biography of Olga Taussky-Todd
Chapter 20 : Extension FieldsThe Fundamental Theorem of Field Theory | Splitting Fields  | Zeros of an Irreducible Polynomial
Exercises
Biography of Leopold Kronecker
Chapter 21 :  Algebraic ExtensionsCharacterization of Extensions | Finite Extensions | Properties of Algebraic Extensions
Exercises
Biography of Ernst Steinitz
Structure of Finite Fields
Chapter 22 :  Finite FieldsClassification of Finite Fields | Subfields of a Finite Field
Exercises
Biography of L. E. Dickson
Chapter 23 Geometric ConstructionsHistorical Discussion of Geometric Constructions | Constructible Numbers  | Angle-Trisectors and Circle-Squarers
Exercises

PART 5 : SPECIAL TOPICS

Chapter 24 :  Sylow TheoremsConjugacy Classes | The Class Equation  | The Sylow Theorems  | Applications of Sylow Theorems
Exercises
Biography of Oslo Ludwig Sylow
Chapter 25 : Finite Simple GroupsHistorical Background | Nonsimplicity Tests | The Simplicity of A5 | The Fields Medal | The Cole Prize
Exercises
Biography of Michael Aschbacher
Biography of Daniel Gorenstein
Biography of John Thompson
Chapter 26 : Generators and RelationsMotivation | 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
Exercises
Biography of Marshall Hall, Jr.
Chapter 27 :  Symmetry GroupsIsometries  | Classification of Finite Plane Symmetry Groups | Classification of Finite Groups of Rotations in R3
Exercises
Chapter 28 :  Frieze Groups and Crystallographic GroupsThe Frieze Groups | The Crystallographic Groups  | Identification of Plane Periodic Patterns
Exercises
Biography of M. C. Escher
Biography of George Pólya
Biography of John H. Conway
Chapter 29 :  Symmetry and CountingMotivation  | Burnside’s Theorem  | Applications | Group Action
Exercises
Biography of William Burnside
Chapter 30 :  Cayley Digraphs of GroupsMotivation | The Cayley Digraph of a Group | Hamiltonian Circuits and Paths  | Some Applications
Exercises
Biography of William Rowan Hamilton
Biography of Paul Erdős
Chapter 31 :  Introduction to Algebraic Coding TheoryMotivation  | Linear Codes  | Parity-Check Matrix | Decoding  | Coset Decoding  | Historical Note: The Ubiquitous Reed-Solomon Codes
Exercises
Biography of Richard W. Hamming
Biography of Jessie MacWilliams
Biography of Vera Pless
Chapter 32 : An Introduction to Galois TheoryFundamental Theorem of Galois Theory | Solvability of Polynomials by Radicals  | Insolvability of a Quintic
Exercises
Biography of Philip Hall
Chapter 33 : Cyclotomic ExtensionsMotivation | Cyclotomic Polynomials | The Constructible Regular n-gons
Exercises
Biography of Carl Friedrich Gauss
Biography of Manjul Bhargava
Selected Answers A1
Index of Mathematicians A33
Index of Terms A37

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