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Cover Art
PRINTED BOOKS
Author Duzhin, S. V. (Sergeĭ Vasilʹevich), 1956-

Title Transformation groups for beginners / S.V Duzhin, B.D. Chebotarevsky ; [translated from the Russian by S.V. Duzhin].

Published Providence, R.I. : American Mathematical Society, [2004]
©2004

Copies

Location Call No. Status
 UniM ERC  512.2 DUZH    AVAILABLE
Uniform title Ot ornamentov do different͡sialʹnykh uravneniĭ. English
Physical description x, 246 pages : illustrations ; 22 cm.
Series Student mathematical library ; v. 25.
Student mathematical library ; v. 25.
Notes Includes index.
Contents 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. General notion of a group 97 -- 2. Isomorphism 106 -- 3. 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. Bernoulli equation 203 -- 4. Point transformations 207 -- 5. One-parameter groups 214 -- 6. Symmetries of differential equations 216 -- 7. Solving equations by symmetries 220.
Other author Chebotarevskiĭ, B. D. (Boris Dmitrievich)
Subject Transformation groups -- Popular works.
Algebraic topology -- Popular works.
ISBN 0821836439 (paperback: alk. paper)