Elements of Modern Algebra / Edition 6

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Overview

Helping to make the study of modern algebra more accessible, this text gradually introduces and develops concepts through helpful features that provide guidance on the techniques of proof construction and logic analysis. The text develops mathematical maturity for students by presenting the material in a theorem-proof format, with definitions and major results easily located through a user-friendly format. The treatment is rigorous and self-contained, in keeping with the objectives of training the student in the techniques of algebra and of providing a bridge to higher-level mathematical courses.

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Editorial Reviews

Booknews
A text for an introductory course in algebraic structures. Some flexibility is provided by including more material than would normally be taught in one course. Material is presented in a theorem-proof format, with definitions and major results easily located. Learning features include many chapter problems, key terms, descriptive labels for definitions and theorems, strategy boxes on proofs, worked examples, and biographical sketches of key figures. This fifth edition contains an optional new section on cryptography, 122 new problems, and expanded material on mathematical induction and on Euclid's theorem on the infinitude of primes. The authors are affiliated with the University of South Carolina-Spartanburg. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780534402648
  • Publisher: Cengage Learning
  • Publication date: 8/10/2004
  • Edition description: REV
  • Edition number: 6
  • Pages: 456
  • Product dimensions: 7.42 (w) x 9.50 (h) x 0.85 (d)

Meet the Author

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 is Professor of Mathematics at the University of South Carolina, Upstate. She 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 and co-author 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. She and Jimmie have 6 children and 8 grandchildren. In her spare time, Linda enjoys salt-water fishing.

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Table of Contents

1. 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. 2. 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. 3. GROUPS. Definition of a Group. Subgroups. Cyclic Groups. Isomorphisms. Homomorphisms. Key Words and Phrases. A Pioneer in Mathematics: Niels Henrik Abel. 4. 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. 5. 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. 6. 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. 7. 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. 8. 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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