A Concrete Approach to Abstract Algebra

From the Integers to the Insolvability of the Quintic
2. Auflage 2018
ISBN: 978-0-12-805148-1
Verlag: Elsevier Science

Buch, Englisch, 976 Seiten, Format (B × H): 191 mm x 235 mm

A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability of the Quintic, Second Edition provides a primer and reference on abstract algebra for readers whose interests lie in mathematics and information and physical sciences. Adopting the unique 'rings first' approach, the work provides a gentle transition into abstract structures that will make abstract algebra more natural to interested readers.

In addition to introducing the major concepts of modern algebra, the book covers numerous applications which are intended to illustrate the concepts and convince the reader of the utility and relevance of algebra today. This Second Edition features 40% new or revised content, including complete and self-contained proofs of the fundamental theorems of algebra and the Insolvability of the Quintic, and new coverage of commutative rings and linear transformations.

Zielgruppe

<p>(senior) Undergraduate students in algebraic and discrete mathematics seeking to move to graduate studies or into teaching who use the work as a foundational reference. Readers from across the physical sciences seeking to use algebraic structures with exact proofs. Application specialists routinely called on to use integers, group theory and complex algebraic structures. </p>

Autoren/Hrsg.

Bergen, Jeffrey

Inhaltsverzeichnis

1. What this book is about and who this book is for2. Proof and Intuition3. The Integers4. The Rational Numbers and the Real Numbers5. The Complex Numbers6. The Integers7. Group Theory: A First Look8. Roots and Factorization of Polynomials over the integrals9. Polynomials over arbitrary fields10. Difference Functions and Partial Fractions11. An Introduction to Linear Algebra and Vector Spaces12. Degrees and Galois Groups of Field Extensions13. Geometric Constructions14. Group Theory: Solvable and Symmetric Groups15. Insolvability of the Quintic16. Values of Trigonometric Functions17. Additional Topics

Über Autor(innen)

Bergen, Jeffrey
Jeffrey Bergen (DePaul, Chicago), received his B.S. in Mathematics from Brooklyn College in 1976. He received his M.S. in 1977 and Ph.D. in 1981 from the University of Chicago. His DePaul career began in 1981, where he continues to do research in the branch of abstract algebra known as noncommutative ring theory. His research has received external support from the English Speaking Union, the National Science Foundation, and the National Security Agency. He has given lectures in 7 countries and co-authored papers with 16 mathematicians around the world. In 2001, he received the Excellence in Teaching Award from the College of Liberal Arts and Sciences and, in 2007, received their Cortelyou-Lowery Award for Excellence.