Synopses & Reviews
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.
Review
"Beardon has written a fine introductory text...[he] outlines a beautiful course."
MAA Reviews, Stephen Ahearn
Review
Beardon has prepared a book that this reviewer will keep on his shelf as a reference. Highly recommended.
Choice
Synopsis
Unified introduction to algebra and geometry, emphasising links between the topics. It is ideal for self-study.
Synopsis
This text gives a basic introduction, and a unified approach algebra and geometry, two of the cornerstones of undergraduate mathematics. The emphasis is always on the interaction between these topics, and each topic is constantly illustrated by using it to describe and discuss the other topics. Many of the ideas are developed gradually throughout the book. For ease of use by students, the text is divided into short sections, with exercises at the end of each section.
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
Preface; 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. Linear maps of Euclidean space; 12. Groups; 13. Möbius transformations; 14. Group actions; 15. Hyperbolic geometry; Index.