Synopses & Reviews
This text gives a basic introduction, and a unified approach, to algebra and geometry. Alan Beardon covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups, and various aspects of geometry including groups of isometries, rotations, and spherical geometry. The emphasis is on the interaction among these topics. The text is divided into short sections, with exercises at the end of each section.
Synopsis
This text gives a basic introduction and unified approach to algebra and geometry, two of the cornerstones of undergraduate mathematics. The emphasis is constantly on the interaction between these topics. For ease of use by students, the text is divided into short chapters, with exercises at the end of each.
Synopsis
Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. Each topic is used to describe and discuss the others, with many ideas developed gradually through the book. 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 Möbius group; 14. Group actions; 15. Hyperbolic geometry.