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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010144585 | QA155 B42 2005 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Reviews 1
Choice Review
Beardon has prepared a book that this reviewer will keep on his shelf as a reference. The author takes a grand tour of many topics in algebra and shows their connections to geometry. When he uses the word "algebra" as he does in the title, he means algebra of the type one might see in calculus, linear algebra, and modern or abstract algebra. This assemblage of topics results in an interesting and useful collection of subjects, which is why, at the least, the book makes a great reference; at best, it would make a great course resource for upper-level undergraduates or beginning graduate students, to show them the connections between academic courses that have, due to our manner of teaching, become so compartmentalized. Beardon starts off with a necessary discussion of groups, and leads into real numbers and complex numbers; then he makes a natural jump to vectors, vector spaces, and linear algebra topics, eventually coming back to groups and group actions. Along the way, he does some spherical and hyperbolic geometry. This reviewer likes the book and hopes to find a good way to put it to use in teaching. ^BSumming Up: Highly recommended. Upper-division undergraduates through professionals. M. D. Sanford Felician College
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 M�s transformations |
| 14 Group actions |
| 15 Hyperbolic geometry |
| Index |
