First Course in Abstract Algebra With Applications

ISBN-10: 0131862677

ISBN-13: 9780131862678

Edition: 3rd 2006 (Revised)

Authors: Joseph J. Rotman
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Book details

List price: $117.80
Edition: 3rd
Copyright year: 2006
Publisher: Prentice Hall PTR
Publication date: 9/28/2005
Binding: Paperback
Pages: 640
Size: 7.25" wide x 9.75" long x 1.00" tall
Weight: 2.552
Language: English

Preface to the Third Edition
Suggested Syllabi
To the Reader
Number Theory
Induction
Binomial Theorem and Complex Numbers
Greatest Common Divisors
The Fundamental Theorem of Arithmetic
Congruences
Dates and Days
Groups I
Some Set Theory
Functions
Equivalence Relations
Permutations
Groups
Symmetry
Subgroups and Lagrange's Theorem
Homomorphisms
Quotient Groups
Group Actions
Counting with Groups
Commutative Rings I
First Properties
Fields
Polynomials
Homomorphisms
From Numbers to Polynomials
Euclidean Rings
Unique Factorization
Irreducibility
Quotient Rings and Finite Fields
A Mathematical Odyssey
Latin Squares
Magic Squares
Design of Experiments
Projective Planes
Linear Algebra
Vector Spaces
Gaussian Elimination
Euclidean Constructions
Linear Transformations
Eigenvalues
Codes
Block Codes
Linear Codes
Decoding
Fields
Classical Formulas
Viete's Cubic Formula
Insolvability of the General Quintic
Formulas and Solvability by Radicals
Quadratics
Cubics
Quartics
Translation into Group Theory
Epilog
Groups II
Finite Abelian Groups
The Sylow Theorems
Ornamental Symmetry
Commutative Rings II
Prime Ideals and Maximal Ideals
Unique Factorization
Noetherian Rings
Varieties
Generalized Divison Algorithm
Monomial Orders
Division Algorithm
Grobner Bases
Inequalities
Pseudocodes
Hints for Selected Exercises
Bibliography
Index
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