Algebra and Geometry [Paperback]

Unified introduction to algebra and geometry, emphasising links between the topics. It is ideal for self-study.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.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.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.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. M?bius transformations; 14. Group actions; 15. Hyperbolic geometry; Index. Beardon has written a fine introductory text...[he] outlines a beautiful course.
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