The authors gradually introduce and develop concepts to help make the material more accessible. This text is intended for the introductory course in algebraic structures and covers groups before rings. This course often is used to bridge the gap from manipulative to theoretical mathematics and to help prepare secondary mathematics teachers for their careers. This text includes some optional sections to give instructors flexibility.
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)
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.
1. Fundamentals. 2. The Integers. 3. Groups. 4. More on Groups. 5. Rings, Integral Domains, and Fields. 6. More on Rings. 7. Real and Complex Numbers. 8. Polynomials. Appendix: The Basics of Logic. Bibliography. Answers to Selected Computational Exercises. Index.