Transformation groups for beginners /
"This book is intended for undergraduate students and all those interested in mathematics. Its goal is to give an easy introduction to the concept of a transformation group using examples from different areas of mathematics. The book contains plenty of figures, as well as many exercises with hi...
| Main Authors: | , |
|---|---|
| Other Authors: | , |
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, R.I. :
American Mathematical Society,
[2004], ©2004
Providence, R.I. : c2004 Providence, R.I. : ©2004 Providence, RI : c2004 Providence, R.I. : [2004] |
| Series: | Student mathematical library ;
v. 25 Student mathematical library, v. 25 Student mathematical library ; v. 25 Student mathematical library v. 25 |
| Subjects: |
Table of Contents:
- Ch. 1 Algebra of points
- Ch. 2. Plane movements
- Ch. 3. Transformation groups
- Ch. 4. Arbitrary groups
- Ch. 5. Orbits and ornaments
- Ch. 6. Other types of transformations
- Ch. 7. Symmetries of differential equations.
- Ch. 1 Algebra of points
- Ch. 2. Plane movements
- Ch. 3. Transformation groups
- Ch. 4. Arbitrary groups
- Ch. 5. Orbits and ornaments
- Ch. 6. Other types of transformations
- Ch. 7. Symmetries of differential equations.
- Chapter 1 Algebra of Points 7
- 1. Checkered plane 7
- 2. Point addition 10
- 3. Multiplying points by numbers 14
- 4. Centre of gravity 17
- 5. Coordinates 20
- 6. Point multiplication 24
- 7. Complex numbers 30
- Chapter 2. Plane Movements 41
- 1. Parallel translations 41
- 2. Reflections 44
- 3. Rotations 47
- 4. Functions of a complex variable 50
- 5. Composition of movements 55
- 6. Glide reflections 61
- 7. Classification of movements 63
- 8. Orientation 66
- 9. Calculus of involutions 68
- Chapter 3. Transformation Groups 73
- 1. A rolling triangle 73
- 2. Transformation groups 76
- 3. Classification of finite groups of movements 78
- 4. Conjugate transformations 80
- 5. Cyclic groups 86
- 6. Generators and relations 90
- Chapter 4. Arbitrary Groups 97
- 1. The general notion of a group 97
- 2. Isomorphism 106
- 3. The Lagrange theorem 118
- Chapter 5. Orbits and Ornaments 127
- 1. Homomorphism 127
- 2. Quotient group 131
- 3. Groups presented by generators and relations 136
- 4. Group actions and orbits 137
- 5. Enumeration of orbits 141
- 6. Invariants 148
- 7. Crystallographic groups 151
- Chapter 6. Other Types of Transformations 165
- 1. Affine transformations 165
- 2. Projective transformations 169
- 3. Similitudes 175
- 4. Inversions 182
- 5. Circular transformations 187
- 6. Hyperbolic geometry 191
- Chapter 7. Symmetries of Differential Equations 197
- 1. Ordinary differential equations 197
- 2. Change of variables 202
- 3. The Bernoulli equation 203
- 4. Point transformations 207
- 5. One-parameter groups 214
- 6. Symmetries of differential equations 216
- 7. Solving equations by symmetries 220.