Elements of Modern Algebra

ISBN-10: 0495561363

ISBN-13: 9780495561361

Edition: 7th 2009

List price: $303.95
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Book details

List price: $303.95
Edition: 7th
Copyright year: 2009
Publisher: Brooks/Cole
Publication date: 10/20/2008
Binding: Hardcover
Pages: 456
Size: 7.50" wide x 9.25" long x 1.00" tall
Weight: 2.442
Language: English

Jimmie Gilbert was Professor of Mathematics at the University of South Carolina, Upstate. He received his Ph.D from Auburn University with a specialty in Linear and Abstract Algebras. He authored the first edition of Elements of Modern Algebra in 1970, joined on subsequent editions by his wife and longtime co-author Linda Gilbert. Together they have published titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, Intermediate Algebra, and another Cengage Learning title, Linear Algebra and Matrix Theory, now in its second edition. He and Linda have 6 children and 8 grandchildren. In his leisure time Jimmie enjoyed the outdoors, fishing, and gardening.

Linda Gilbert received her Ph.D. from Louisiana Tech University with a specialty in Linear and Abstract Algebras. She has been writing textbooks since 1981 with her husband Jimmie Gilbert, including ELEMENTS OF MODERN ALGEBRA and LINEAR ALGEBRA and MATRIX THEORY (now in its second edition) with Cengage Learning, plus titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, and Intermediate Algebra.

Preface
Fundamentals
Sets
Mappings
Properties of Composite Mappings (Optional)
Binary Operations
Permutations and Inverses
Matrices
Relations
Key Words and Phrases
A Pioneer in Mathematics: Arthur Cayley
The Integers
Postulates for the Integers (Optional)
Mathematical Induction
Divisibility
Prime Factors and Greatest Common Divisor
Congruence of Integers
Congruence Classes
Introduction to Coding Theory (Optional)
Introduction to Cryptography (Optional)
Key Words and Phrases
A Pioneer in Mathematics: Blaise Pascal
Groups
Definition of a Group
Properties of Group Elements
Subgroups
Cyclic Groups
Isomorphisms
Homomorphisms
Key Words and Phrases
A Pioneer in Mathematics: Niels Henrik Abel
More on Groups
Finite Permutation Groups
Cayley's Theorem
Permutation Groups in Science and Art (Optional)
Cosets of a Subgroup
Normal Subgroups
Quotient Groups
Direct Sums (Optional)
Some Results on Finite Abelian Groups (Optional)
Key Words and Phrases
A Pioneer in Mathematics: Augustin Louis Cauchy
Rings, Integral Domains, and Fields
Definition of a Ring
Integral Domains and Fields
The Field of Quotients of an Integral Domain
Ordered Integral Domains
Key Words and Phrases
A Pioneer in Mathematics: Richard Dedekind
More on Rings
Ideals and Quotient Rings
Ring Homomorphisms
The Characteristic of a Ring
Maximal Ideals (Optional)
Key Words and Phrases
A Pioneer in Mathematics: Amalie Emmy Noether
Real and Complex Numbers
The Field of Real Numbers
Complex Numbers and Quaternions
De Moivre's Theorem and Roots of Complex Numbers
Key Words and Phrases
A Pioneer in Mathematics: William Rowan Hamilton
Polynomials
Polynomials over a Ring
Divisibility and Greatest Common Divisor
Factorization in F[x]
Zeros of a Polynomial
Solution of Cubic and Quartic Equations by Formulas (Optional)
Algebraic Extensions of a Field
Key Words and Phrases
A Pioneer in Mathematics: Carl Friedrich Gauss
The Basics of Logic
Answers to True/False and Selected Computational Exercises
Bibliography
Index
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