A Concrete Approach to Abstract Algebra
From the Integers to the Insolvability of the Quintic
Published on 6. March 2010
Book
Hardback
720 pages
978-0-12-374941-3 (ISBN)
Description
A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra.
It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study.
This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus.
It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study.
This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus.
More details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Advanced undergraduate and graduate students taking a course in abstract algebra.
Product notice
Laminated cover
Dimensions
Height: 245 mm
Width: 200 mm
Thickness: 45 mm
Weight
1438 gr
ISBN-13
978-0-12-374941-3 (9780123749413)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Jeffrey Bergen
A Concrete Approach to Abstract Algebra
From the Integers to the Insolvability of the Quintic
Book
approx. 08/2029
2nd Edition
Academic Press
€141.50
Not yet published
Additional editions
Jeffrey Bergen
A Concrete Approach to Abstract Algebra
From the Integers to the Insolvability of the Quintic
E-Book
12/2009
Academic Press
€62.99
Available for download
Person
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.
Content
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