Includes bibliographical references (p. [185]-186) and index.
Contents:
1. Divisibility in the Integers
2. Rings and Fields
3. Vector Spaces
4. Field Extensions
5. Polynomials
6. The Field Generated by an Element
7. Straightedge and Compass Constructions.
Summary:
Using the proof of the nontrisectibility of an arbitrary angle as a final goal, the author develops, in an easy conversational style, the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition, on conveying mathematical insight to an audience that is as yet unaccustomed to abstraction. Familiarity with the material is developed by exposing the students to a large number of examples, and the text is peppered liberally with questions intended to encourage the students to think through the material themselves.