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More About This Textbook
Overview
ELEMENTS OF MODERN ALGEBRA 7e, with its user-friendly format, provides you with the tools you need to get succeed in abstract algebra and develop mathematical maturity as a bridge to higher-level mathematics courses.. 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.
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Meet the Author
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.
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. Properties of Group Elements. 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). Cosets of a Subgroups. 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.