A Concrete Approach to Abstract Algebra - 1st Edition - ISBN: 9780123749413, 9780080958620

A Concrete Approach to Abstract Algebra

1st Edition

From the Integers to the Insolvability of the Quintic

Authors: Jeffrey Bergen
Paperback ISBN: 9780123749413
eBook ISBN: 9780080958620
Imprint: Academic Press
Published Date: 28th January 2010
Page Count: 720
109.99 + applicable tax
78.95 + applicable tax
66.99 + applicable tax
Unavailable
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access


Description

A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus.  The final four chapters present the more theoretical material needed for graduate study.

Ancillary list:
Online ISM- http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123749413
Online SSM- http://www.elsevierdirect.com/product.jsp?isbn=9780123749413
* Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749413

Key Features

  • Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra
  • Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems
  • Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms
  • Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices


Readership

Advanced undergraduate and graduate students studying mathematics, education, biology, chemistry, economics, environmental sciences, physics, computer science and engineering taking a course in abstract algebra.

Table of Contents

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

Details

No. of pages:
720
Language:
English
Copyright:
© Academic Press 2010
Published:
Imprint:
Academic Press
eBook ISBN:
9780080958620
Paperback ISBN:
9780123749413

About the Author

Jeffrey Bergen

Affiliations and Expertise

DePaul University, Chicago, USA