Transformation groups for beginners:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2004]
|
| Series: | Student mathematical library
volume 25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 246 Seiten Illustrationen, Diagramme |
| ISBN: | 0821836439 9780821836439 |
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MARC
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| 240 | 1 | 0 | |a Ot ornamentov do differencial′nych uravnenij |
| 245 | 1 | 0 | |a Transformation groups for beginners |c S. V. Duzhin ; B. D. Chebotarevsky. Translated from the Russian by S. V. Duzhin |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2004] | |
| 264 | 4 | |c © 2004 | |
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Record in the Search Index
| _version_ | 1804132845278461952 |
|---|---|
| adam_text | Contents
Preface ix
Introduction 1
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
v
§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
Answers, Hints and Solutions to Exercises 229
Index 245
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| indexdate | 2024-07-09T19:59:17Z |
| institution | BVB |
| isbn | 0821836439 9780821836439 |
| language | English |
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| series | Student mathematical library |
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| spelling | Dužin, Sergej V. 1956- Verfasser (DE-588)1023516128 aut Ot ornamentov do differencial′nych uravnenij Transformation groups for beginners S. V. Duzhin ; B. D. Chebotarevsky. Translated from the Russian by S. V. Duzhin Providence, Rhode Island American Mathematical Society [2004] © 2004 x, 246 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 25 Transformation groups Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Transformationsgruppe (DE-588)4127386-2 s DE-604 Algebraische Topologie (DE-588)4120861-4 s Čebotarevskij, Boris Dmitrievič Verfasser (DE-588)1159143153 aut Erscheint auch als Online-Ausgabe 978-1-4704-2137-3 Student mathematical library volume 25 (DE-604)BV013184751 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012856978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dužin, Sergej V. 1956- Čebotarevskij, Boris Dmitrievič Transformation groups for beginners Student mathematical library Transformation groups Algebraische Topologie (DE-588)4120861-4 gnd Transformationsgruppe (DE-588)4127386-2 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4127386-2 (DE-588)4151278-9 |
| title | Transformation groups for beginners |
| title_alt | Ot ornamentov do differencial′nych uravnenij |
| title_auth | Transformation groups for beginners |
| title_exact_search | Transformation groups for beginners |
| title_full | Transformation groups for beginners S. V. Duzhin ; B. D. Chebotarevsky. Translated from the Russian by S. V. Duzhin |
| title_fullStr | Transformation groups for beginners S. V. Duzhin ; B. D. Chebotarevsky. Translated from the Russian by S. V. Duzhin |
| title_full_unstemmed | Transformation groups for beginners S. V. Duzhin ; B. D. Chebotarevsky. Translated from the Russian by S. V. Duzhin |
| title_short | Transformation groups for beginners |
| title_sort | transformation groups for beginners |
| topic | Transformation groups Algebraische Topologie (DE-588)4120861-4 gnd Transformationsgruppe (DE-588)4127386-2 gnd |
| topic_facet | Transformation groups Algebraische Topologie Transformationsgruppe Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012856978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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