The role of mathematics in the rise of science:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton
Univ. Press
1969
|
| Ausgabe: | 2. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 386 S. |
Internformat
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Datensatz im Suchindex
| _version_ | 1804116366018478080 |
|---|---|
| adam_text | CONTENTS
PREFACE V
INTRODUCTION 3
PART I. ESSAYS 11
chapter 1. From Myth to Mathematics to
Knowledge 13
What is Mathematics? 13
Mathematics and Myths 14
Pre Greek Mathematics 20
What is in a Name? 22
Universality of Mathematics 28
Some Contrasts between Greek and Present Day
Mathematics 30
Euclid s Elements 33
Mathematics on the Rise 37
Prefabricated Mathematics 42
Relation between Mathematics and Science 45
The Abstractness of Mathematics 48
chapter 2. How History of Science Differs from
Other History 59
Slowness of the Rise of History of Science 63
Trends and Individuality 73
Relations to Source Works 83
Documentation of Greek Science 85
Limitations of Subject Matter 96
The Quest for Spectacularity 101
Medievalism 106
Progress and Continuity 113
Conventionalism 120
The Mathematization of Science 126
chapter 3. Revolutions in Physics and Crises
in Mathematics 131
The Thesis of T. S. Kuhn 131
The Role of Max Planck 133
Crises in Mathematics 138
[vii]
CONTENTS
chapter 4. Aristotle s Physics and Today s
Physics 143
Physics and Mathematical Physics 143
Physics and Philosophy 145
Time in Physics 147
Physics and Cosmology 148
Necessity and Chance 149
Chora ( Space ) and Topos ( Place ) 152
Space and Matter 156
Gravitational Space 158
The Void (Kenon) 160
Processes in Nature 160
The Scope of Processes in Nature 162
Opposites 165
Motion of Motion (kineseos kinesis) 166
Simple and Composite Changes 170
Aristotle s Theory of Topos 172
The Universe as One Physical System 175
Act and Potency 177
Conclusion 178
chapter 5. The Role of Mathematics in the Rise
of Mechanics 179
Before the 17th Century I80
The 17th Century 187
The 18th Century 193
The Principle of Least Action 203
chapter 6. The Significance of Some Basic
Mathematical Conceptions for
Physics 209
I. The Significance of Multiplication 210
Greek Magnitudes 210
Physical Dimensions 211
Proportions 213
The Fundamental Theorem of Prime Numbers 214
n. The Significance of Functions 216
The Rise of Functions 216
[viii]
CONTENTS
The First Occurrence of Functions 222
Equations of State 224
in. The Significance of Real Numbers 226
Quality and Quantity 226
Vectors and Tensors 229
Importance of Scalars 232
iv. The Significance of Complex Numbers 234
The Complexification of Physics 234
Complex Numbers in the 18th Century 237
Complex Numbers in Optics 240
v. The Significance of Mathematical Space 243
The Space Time Problem 243
Space before Aristotle 245
Space in Aristotle 246
Three Dimensionality of Space 248
Mathematical Schema of Time 250
The Future of the Space Time Problem 252
chapter 7. The Essence of Mathematics 255
Relation to Science 255
Creative Formulas 257
Foundations: Mathematical Logic 260
Counterexamples 264
Constructiveness: Approximations 267
Space in Mathematics 270
chapter 8. The Essence of Analysis 275
I. Meaning of Analysis 275
Relation to Science 275
Derivatives 276
Real Numbers 277
Magnitudes 278
II. Stages of Development 279
Irrational Numbers 279
Areas and Volumes 280
Set Theory 280
Analytic Geometry 281
19th Century 282
[ix]
CONTENTS
20th Century 282
in. Functions 283
Higher Derivatives 283
General Functions 284
Power Series 285
Piecewise Analytic Functions 287
Fourier Series 288
Analytic Theory of Numbers 291
Least Square Approximation 292
Functions of Real Variables 293
iv. Analysis and Space 295
Conformal Mapping 295
Degrees of Freedom 297
Tensorial Functions 299
PART II. BIOGRAPHICAL SKETCHES 301
INDEX 373
M
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| indexdate | 2024-07-09T15:37:22Z |
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| language | English |
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| spelling | Bochner, S. 1899-1982 Verfasser (DE-588)119439131 aut The role of mathematics in the rise of science 2. print. Princeton Univ. Press 1969 X, 386 S. txt rdacontent n rdamedia nc rdacarrier Naturwissenschaftler (DE-588)4041423-1 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Naturwissenschaftler (DE-588)4041423-1 s Geschichte (DE-588)4020517-4 s DE-604 Naturwissenschaften (DE-588)4041421-8 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001255922&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bochner, S. 1899-1982 The role of mathematics in the rise of science Naturwissenschaftler (DE-588)4041423-1 gnd Naturwissenschaften (DE-588)4041421-8 gnd Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4041423-1 (DE-588)4041421-8 (DE-588)4020517-4 (DE-588)4037944-9 |
| title | The role of mathematics in the rise of science |
| title_auth | The role of mathematics in the rise of science |
| title_exact_search | The role of mathematics in the rise of science |
| title_full | The role of mathematics in the rise of science |
| title_fullStr | The role of mathematics in the rise of science |
| title_full_unstemmed | The role of mathematics in the rise of science |
| title_short | The role of mathematics in the rise of science |
| title_sort | the role of mathematics in the rise of science |
| topic | Naturwissenschaftler (DE-588)4041423-1 gnd Naturwissenschaften (DE-588)4041421-8 gnd Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Naturwissenschaftler Naturwissenschaften Geschichte Mathematik |
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