Compactness and contradiction:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2013]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 249 - 253 |
| Beschreibung: | xii, 256 Seiten |
| ISBN: | 9780821894927 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804150456093507584 |
|---|---|
| adam_text | Titel: Compactness and contradiction
Autor: Tao, Terence
Jahr: 2013
Contents
Preface xi
A remark on notation xi
Acknowledgments xii
Chapter 1. Logic and foundations 1
§1.1. Material implication 1
§1.2. Errors in mathematical proofs 2
§1.3. Mathematical strength 4
§1.4. Stable implications 6
§1.5. Notational Conventions 8
§1.6. Abstraction 9
§1.7. Circular arguments 11
§1.8. The classical number Systems 12
§1.9. Round numbers 15
§1.10. The no-self-defeating object argument, revisited 16
§1.11. The no-self-defeating object argument, and the vagueness
paradox 28
§1.12. A computational perspective on set theory 35
Chapter 2. Group theory 51
§2.1. Torsors 51
§2.2. Active and passive transformations 54
§2.3. Cayley graphs and the geometry of groups 56
§2.4. Group extensions 62
vii
viii Contents
§2.5. A proof of Gromov s theorem 69
Chapter 3. Analysis 79
§3.1. Orders of magnitude, and tropical geometry 79
§3.2. Descriptive set theory vs. Lebesgue set theory 81
§3.3. Complex analysis vs. real analysis 82
§3.4. Sharp inequalities 85
§3.5. Implied constants and asymptotic notation 87
§3.6. Brownian snowflakes 88
§3.7. The Euler-Maclaurin formula, Bernoulli numbers, the zeta
function, and real-variable analytic continuation 88
§3.8. Finitary consequences of the invariant subspace problem 104
§3.9. The Guth-Katz result on the Erdös distance problem 110
§3.10. The Bourgain-Guth method for proving restriction theorems 123
Chapter 4. Non- Standard analysis 133
§4.1. Real numbers, non-standard real numbers, and finite precision
arithmetic 133
§4.2. Non-Standard analysis as algebraic analysis 136
§4.3. Compactness and contradiction: the correspondence principle
in ergodic theory 137
§4.4. Non-Standard analysis as a completion of Standard analysis 150
§4.5. Concentration compactness via non-standard analysis 168
Chapter 5. Partial differential equations 181
§5.1. Quasilinear well-posedness 181
§5.2. A type diagram for function Spaces 189
§5.3. Amplitude-frequency dynamics for semilinear dispersive
equations 194
§5.4. The Euler-Arnold equation 203
Chapter 6. Miscellaneous 217
§6.1. Multiplicity of perspective 217
§6.2. Memorisation vs. derivation 220
§6.3. Coordinates 222
§6.4. Spatial scales 227
§6.5. Averaging 228
^6.6. What colour is the sun? 231
Contents ix
§6.7. Zeno s paradoxes and induction 232
§6.8. Jevons paradox 233
§6.9. Bayesian probability 236
§6.10. Best, worst, and average-case analysis 242
§6.11. Duality 244
§6.12. Open and closed conditions 246
Bibliography 249
Index 255
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut Compactness and contradiction Terence Tao Providence, Rhode Island American Mathematical Society [2013] © 2013 xii, 256 Seiten txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite 249 - 253 Mathematical analysis Proof theory Beweistheorie (DE-588)4145177-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Gruppentheorie (DE-588)4072157-7 s Beweistheorie (DE-588)4145177-6 s Analysis (DE-588)4001865-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1611-9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026060254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tao, Terence 1975- Compactness and contradiction Mathematical analysis Proof theory Beweistheorie (DE-588)4145177-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Analysis (DE-588)4001865-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4072157-7 (DE-588)4001865-9 (DE-588)4037951-6 |
| title | Compactness and contradiction |
| title_auth | Compactness and contradiction |
| title_exact_search | Compactness and contradiction |
| title_full | Compactness and contradiction Terence Tao |
| title_fullStr | Compactness and contradiction Terence Tao |
| title_full_unstemmed | Compactness and contradiction Terence Tao |
| title_short | Compactness and contradiction |
| title_sort | compactness and contradiction |
| topic | Mathematical analysis Proof theory Beweistheorie (DE-588)4145177-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Analysis (DE-588)4001865-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematical analysis Proof theory Beweistheorie Gruppentheorie Analysis Mathematische Logik |
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