Mathematics - the music of reason:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1998
|
| Ausgabe: | Corr. 2nd print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 287 S. graph. Darst. |
| ISBN: | 354053346X 038753346X |
Internformat
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Datensatz im Suchindex
| _version_ | 1804126892254560256 |
|---|---|
| adam_text | JEAN DIEUDONNE MATHEMATICS - THE MUSIC OF REASON TRANSLATED BY H.G. AND
J.C. DALES WITH 41 FIGURES SPRINGER CONTENTS INTRODUCTION 1 I
MATHEMATICS AND MATHEMATICIANS 7 1. THE CONCEPT OF MATHEMATICS 7 2. A
MATHEMATICIAN S LIFE 8 3. THE WORK OF MATHEMATICIANS AND THE
MATHEMATICAL COMMUNITY 12 4. MASTERS AND SCHOOLS 14 II THE NATURE OF
MATHEMATICAL PROBLEMS 19 1. PURE MATHEMATICS AND APPLIED MATHEMATICS
19 2. THEORETICAL PHYSICS AND MATHEMATICS 21 3. APPLICATIONS OF
MATHEMATICS IN THE CLASSICAL ERA 21 4. THE UTILITARIAN ATTACKS 25 5.
FASHIONABLE DOGMAS 26 6. CONCLUSIONS 28 III OBJECTS AND METHODS IN
CLASSICAL MATHEMATICS 29 1. THE BIRTH OF PRE-MATHEMATICAL IDEAS 31 2.
THE IDEA OF PROOF 33 3. AXIOMS AND DEFINITIONS 35 4. GEOMETRY, FROM
EUCLID TO HILBERT 37 5. NUMBERS AND MAGNITUDES 41 6. THE IDEA OF
APPROXIMATION 45 7. THE EVOLUTION OF ALGEBRA 49 8. THE METHOD OF
COORDINATES 51 9. THE CONCEPT OF LIMIT AND THE INFINITESIMAL CALCULUS 56
APPENDIX 1. CALCULATION OF RATIOS IN EUCLID S BOOK V 64 2. THE AXIOMATIC
THEORY OF REAL NUMBERS 65 3. APPROXIMATION OF THE REAL ROOTS OF A
POLYNOMIAL 68 4. ARGUMENTS BY EXHAUSTION 70 5. APPLICATIONS OF
ELEMENTARY ALGORITHMS OF THE INTEGRAL CALCULUS 72 VIII CONTENTS IV SOME
PROBLEMS OF CLASSICAL-MATHEMATICS 77 1. INTRACTABLE PROBLEMS AND STERILE
PROBLEMS 77 A. PERFECT NUMBERS 77 B. FERMAT NUMBERS 78 C. THE
FOUR-COLOUR PROBLEM 79 D. PROBLEMS OF ELEMENTARY GEOMETRY 80 2. PROLIFIC
PROBLEMS 82 A. THE SUMS OF SQUARES 82 B. THE PROPERTIES OF PRIME NUMBERS
86 C. THE BEGINNINGS OF ALGEBRAIC GEOMETRY 91 APPENDIX 93 1. PRIME
NUMBERS OF THE FORM 4K-L OR 6K-L 93 2. THE DECOMPOSITION OF (S) AS A
EULERIAN PRODUCT 93 3. LAGRANGE S METHOD FOR THE SOLUTION OF AX 2 + BXY
+ Q/ 2 = N IN INTEGERS 95 4. BERNOULLI NUMBERS AND THE ZETA FUNCTION 98
V NEW OBJECTS AND NEW METHODS 103 1. NEW CALCULATIONS 105 A. COMPLEX
NUMBERS 105 B. VECTORS 108 C. ALGEBRAIC CALCULATION ON FUNCTIONS ILL D.
PERMUTATIONS AND SUBSTITUTIONS 113 E. DISPLACEMENTS AND AFFINITIES *..
118 F. CALCULATION OF CONGRUENCES OF NATURAL NUMBERS 119 G. THE
CALCULATION OF CLASSES OF QUADRATIC FORMS 120 2. THE FIRST STRUCTURES
121 A. THE PRINCIPAL PROPERTIES OF THE LAWS OF COMPOSITION 121 B. GROUPS
OF TRANSFORMATIONS 124 C. ABSTRACT GROUPS 128 D. QUATERNIONS AND
ALGEBRAS 129 3. THE LANGUAGE OF SETS AND GENERAL STRUCTURES 133 A. THE
CONCEPT OF SET 133 B. THE LANGUAGE OF SETS 134 C. ALGEBRAIC STRUCTURES
136 D. ORDER STRUCTURES 139 E. METRIC SPACES AND TOPOLOGICAL CONCEPTS
141 F. SUPERPOSITION AND DISSOCIATION OF STRUCTURES 142 4. ISOMORPHISMS
AND CLASSIFICATIONS 146 A. ISOMORPHISMS 146 B. PROBLEMS OF
CLASSIFICATION 149 C. THE INVENTION OF FUNCTORS AND OF STRUCTURES 150
CONTENTS IX 5. MATHEMATICS OF OUR DAY 152 A. A PANORAMA OF MATHEMATICS
152 B. SPECIALISTS AND GENERALISTS 161 C. THE EVOLUTION OF MATHEMATICAL
THEORIES 161 6. INTUITION AND STRUCTURES 163 APPENDIX 167 1. THE
RESOLUTION OF QUARTIC EQUATIONS 167 2. ADDITIONAL REMARKS ON GROUPS AND
ON THE RESOLUTION OF ALGEBRAIC EQUATIONS 168 A. THE SYMMETRIC GROUP S N
168 B. THE GALOIS GROUP OF AN EQUATION 168 C. GALOIS GROUPS AND GROUPS
OF AUTOMORPHISMS 169 D. NORMAL SUBGROUPS AND SIMPLE GROUPS 170 E.
ROTATIONS OF THE CUBE 172 3. ADDITIONAL REMARKS ON RINGS AND FIELDS 174
A. CONGRUENCES MODULO A PRIME NUMBER 174 B. THE RING L[I] OF GAUSSIAN
INTEGERS 176 C. CONGRUENCES MODULO A POLYNOMIAL 179 D. THE FIELD OF
ALGEBRAIC FUNCTIONS 181 E. REMARKS ON ORDERED FIELDS 183 4. EXAMPLES OF
DISTANCES 184 A. DISTANCES ON THE SPACE OF CONTINUOUS FUNCTIONS 184 B.
PREHILBERT SPACES 187 C. HILBERT SPACES 190 D. P-ADIC DISTANCES 191 5.
FOURIER SERIES 192 A. TRIGONOMETRIC SERIES AND FOURIER COEFFICIENTS 192
B. THE CONVERGENCE OF FOURIER SERIES 195 C. FOURIER SERIES OF BERNOULLI
POLYNOMIALS 199 D. CANTOR S PROBLEMS 200 VI PROBLEMS AND PSEUDO-PROBLEMS
ABOUT FOUNDATIONS ... 203 1. NON-EUCLIDEAN GEOMETRIES 204 A. THE
PARALLEL POSTULATE 204 B. GEOMETRY ON A SURFACE 207 C. MODELS OF
NON-EUCLIDEAN GEOMETRY 208 2. THE DEEPENING OF THE CONCEPT OF NUMBER 213
A. IRRATIONAL NUMBERS 213 B. MONSTERS 215 C. THE AXIOMATIZATION OF
ARITHMETIC 216 3. INFINITE SETS 218 A. INFINITE SETS AND NATURAL NUMBERS
218 B. THE COMPARISON OF INFINITE SETS 220 CONTENTS 4. PARADOXES AND
THEIR CONSEQUENCES 222 A. EXISTENCE AND CONSTRUCTIONS 222 B. THE MIXED
FORTUNES OF THE CONCEPT OF SET AND THE AXIOM OF CHOICE 224 C. PARADOXES
AND FORMALIZATION 226 5. THE RISE OF MATHEMATICAL LOGIC 228 A. THE
FORMALIZATION OF LOGIC 228 B. METAMATHEMATICS 229 C. THE TRIUMPHS OF
MATHEMATICAL LOGIC 230 D. MATHEMATICIANS REACTIONS 233 E. RELATIONS
BETWEEN MATHEMATICS AND LOGIC 234 6. THE CONCEPT OF RIGOROUS PROOF 235
APPENDIX 23 9 1. GEOMETRY ON A SURFACE 239 A. SKEW CURVES 239 B. CURVES
ON A SURFACE 239 C. POINCARE S HALF-PLANE 241 2. MODELS OF THE REAL
NUMBERS 245 A. THE THEORY OF RATIONAL NUMBERS 245 B. THE MODEL OF
DEDEKIND (SIMPLIFIED ACCOUNT) 246 C. THE MODEL OF MERAY-CANTOR
(SIMPLIFIED ACCOUNT) 246 3. THEOREMS OF CANTOR AND OF HIS SCHOOL 247 A.
THE SET OF REAL NUMBERS IS NOT COUNTABLE 247 B. THE ORDER RELATION AMONG
CARDINALS 248 C. THE EQUIPOTENCE OF 1R AND IR 2 = IR X ET 250 D. THE
CARDINAL OF THE SET OF SUBSETS 253 INDEX 255 1. HISTORICAL INDEX 255 2.
STANDARD NOTATION 281 3. INDEX OF TERMINOLOGY 282
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| spelling | Dieudonné, Jean Alexandre 1906-1992 Verfasser (DE-588)119320738 aut Pour l'honneur de l'esprit humain Mathematics - the music of reason Jean Dieudonné Corr. 2nd print. Berlin u.a. Springer 1998 X, 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Mathematics Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Mathematik (DE-588)4037944-9 s Geschichte (DE-588)4020517-4 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008317495&sequence=000001&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 | Dieudonné, Jean Alexandre 1906-1992 Mathematics - the music of reason Mathematik Mathematics Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4037944-9 (DE-588)4143413-4 |
| title | Mathematics - the music of reason |
| title_alt | Pour l'honneur de l'esprit humain |
| title_auth | Mathematics - the music of reason |
| title_exact_search | Mathematics - the music of reason |
| title_full | Mathematics - the music of reason Jean Dieudonné |
| title_fullStr | Mathematics - the music of reason Jean Dieudonné |
| title_full_unstemmed | Mathematics - the music of reason Jean Dieudonné |
| title_short | Mathematics - the music of reason |
| title_sort | mathematics the music of reason |
| topic | Mathematik Mathematics Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Mathematics Geschichte Aufsatzsammlung |
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