Structuralism and structures: a mathematical perspective
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Singapore <<[u.a.]>>
World Scientific
1995
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| Series: | Series in pure mathematics
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 219 S. graph. Darst. |
| ISBN: | 9810218605 |
Staff View
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Record in the Search Index
| _version_ | 1804144613226708992 |
|---|---|
| adam_text | CONTENTS
PREFACE v
I. INTRODUCTION
1. The Structuralist Approach 1
2. The Special Role of Mathematics 7
3. Plato s Lecture on The Good 8
II. GENERAL STRUCTURE CONCEPTS
4. The Definition Problem 11
5. Structuralist Notions of Structure 11
6. A Simple Example 15
7. The Basic Definitions 17
8. Isomorphisms of Structures 21
9. Analogies and Isomorphisms 23
10. An Analysis of Point-Line Structures 27
11. Special Kinds of Relations 29
12. Structural Stability 30
13. Structural Information 33
14. On Abstract Structures 35
III. SOME EXAMPLES OF STRUCTURES
15. Introduction 39
16. Atoms and Machines 40
17. Line Drawings by Josef Albers 42
18. Configurations 44
19. The Pascal Configuration 46
20. The Triangle Group 48
21. Group Structures 50
22. The Real Number System 54
IV. MANAGEMENT OF COMPLEX STRUCTURES
23. The Analysis of Structures 57
24. The Approximation of Structures 58
25. Axiomatics and Approximation 58
26. Structural Determinism and Reductionism 60
27. Contractions 65
28. Contraction of Group Structures 71
xi
xii CONTENTS
V. LANGUAGE AND STRUCTURE
29. The Role of Language 73
30. Simple Communication 75
31. Structural Linguistics 77
32. Semiotics 82
33. The Language Faculty 88
VI. STRUCTURES IN MENTAL PHENOMENA
34. Introduction 93
35. The Central Role of Structures 94
36. The Drive for Intelligibility 97
37. Philosophical Questions 100
38. The Background Structure and Understanding 105
39. Teaching and Learning 108
VII. MATHEMATICAL STRUCTURES
40. Introduction 115
41. Mathematical Language 116
42. How to Recognize a Mathematical Structure 119
43. Research and Development of Mathematics 120
44. The Role of Insight in Research 122
45. A Structural Interpretation of Creativity 128
46. How Mathematics is Applied 131
47. The Effectiveness of Mathematics in Physics 133
48. Other Applications of Mathematics 138
VIII. BIOLOGICAL STRUCTURES
49. Introduction 145
50. Classification of Organisms 146
51. The Genetic Structure 14g
52. The Environment of a Structure 152
53. The Evolutionary Process 153
54. Complexity in Evolution 157
55. Multiple Function 163
56. Biological Catastrophes 168
57. Determining Structures 173
58. Convergent Evolution I74
59. Anthropomorphism 175
CONTENTS xiii
IX. SPACE STRUCTURES AND STABILITY
60. Introduction 179
61. Euclidean Spaces 180
62. Substructures of Euclidean Space 181
63. The Conic Sections 182
64. Stability in a Family of Conies 186
65. Catastrophe Theory 188
66. Zeeman s Catastrophe Machine 190
67. A Mathematical Example 191
68. Attack or Retreat 196
69. Metric Spaces 199
70. Stability of Point-Line Structures 201
BIBLIOGRAPHY 207
INDEX 211
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| id | DE-604.BV026161256 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:06:20Z |
| institution | BVB |
| isbn | 9810218605 |
| language | Undetermined |
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| owner | DE-188 |
| owner_facet | DE-188 |
| physical | XIII, 219 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Rickart, Charles E. 1913-2002 Verfasser (DE-588)108983803 aut Structuralism and structures a mathematical perspective Charles E. Rickart Singapore <<[u.a.]>> World Scientific 1995 XIII, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 21 Mathematik (DE-588)4037944-9 gnd rswk-swf Strukturalismus (DE-588)4058129-9 gnd rswk-swf Strukturalismus (DE-588)4058129-9 s Mathematik (DE-588)4037944-9 s DE-188 Series in pure mathematics 21 (DE-604)BV000016845 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021747729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rickart, Charles E. 1913-2002 Structuralism and structures a mathematical perspective Series in pure mathematics Mathematik (DE-588)4037944-9 gnd Strukturalismus (DE-588)4058129-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4058129-9 |
| title | Structuralism and structures a mathematical perspective |
| title_auth | Structuralism and structures a mathematical perspective |
| title_exact_search | Structuralism and structures a mathematical perspective |
| title_full | Structuralism and structures a mathematical perspective Charles E. Rickart |
| title_fullStr | Structuralism and structures a mathematical perspective Charles E. Rickart |
| title_full_unstemmed | Structuralism and structures a mathematical perspective Charles E. Rickart |
| title_short | Structuralism and structures |
| title_sort | structuralism and structures a mathematical perspective |
| title_sub | a mathematical perspective |
| topic | Mathematik (DE-588)4037944-9 gnd Strukturalismus (DE-588)4058129-9 gnd |
| topic_facet | Mathematik Strukturalismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021747729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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