Elements of Modern Algebra

ISBN-10: 053440264X
ISBN-13: 9780534402648
Edition: 6th 2005 (Revised)
List price: $304.95
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Description: Succeed in modern algebra with ELEMENTS OF MODERN ALGEBRA! With a user-friendly format, this mathematics text provides you with the tools you need to get a good grade. Strategy boxes give you guidance and explanations about techniques and enable you  More...

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Book details

List price: $304.95
Edition: 6th
Copyright year: 2005
Publisher: Brooks/Cole
Publication date: 8/10/2004
Binding: Hardcover
Pages: 394
Size: 7.25" wide x 9.25" long x 0.75" tall
Weight: 1.892

Succeed in modern algebra with ELEMENTS OF MODERN ALGEBRA! With a user-friendly format, this mathematics text provides you with the tools you need to get a good grade. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem solving skills.

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.

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.

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
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)
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
Solutions of Cubic and Quartic Equations by Formulas (Optional)
Algebraic Extensions of a Field
Key Words and Phrases
A Pioneer in Mathematics: Carl Friedrich Gauss
Appendix: The Basics Of Logic
Bibliography
Answers to Selected Computational Exercises
Index

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