Jeffrey Bergen (DePaul University, Chicago, USA)

Concrete Approach to Abstract Algebra

From the Integers to the Insolvability of the Quintic

• Gebundenes Buch

Produktbeschreibung

Examines familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials. This title shows how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems. It builds on relatively familiar material (Integers and polynomials).

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Produktdetails

• Verlag: Academic Press
• Seitenzahl: 720
• Erscheinungstermin: März 2010
• Englisch
• Abmessung: 235mm
• Gewicht: 1390g
• ISBN-13: 9780123749413
• ISBN-10: 0123749417
• Artikelnr.: 28436959

Autorenporträt

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.

Inhaltsangabe

Introduction; What This Book Is about and Who This Book Is for; Proof and Intuition; The Integers; Rational Numbers and the Real Numbers; The Complex Numbers; The fundamental Theorem of Algebra; The Integers Modulo n; Group Theory; Polynomials over the Integers and Rationals; Roots of Polynomials of Degree Less than 5; Rational Values of Trigonometric Functions; Polynomials over Arbitrary Fields; Difference Functions and Partial Fractions; An Introduction to Linear Algebra and Vector Spaces; Degrees and Galois Groups of Field Extensions; Geometric Constructions; The Insolvability of the Quintic; Bibliography; Index