Algebra and Geometry

by Alan F. Beardon

• ISBN13: 9780521890496
• ISBN10: 0521890497
• Format: Paperback
• Copyright: 2005-06-20
• Publisher: Cambridge University Press

Summary

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

Table of Contents

1. Groups and permutations

2. The real numbers

3. The complex plane

4. Vectors in three-dimensional space

5. Spherical geometry

6. Quaternions and isometries

7. Vector spaces

8. Linear equations

9. Matrices

10. Eigenvectors

11. Orthonormal bases of Euclidean space

12. Groups

13. The Mö

bius group

14. Group actions

15. Hyperbolic geometry.