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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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Front matter
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Index
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Front matter
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Front matter
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1
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Article
SUR LA FONCTION: NOMBRE DE FACTEURS PREMIERS DE N
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3
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Abstract
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3
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Chapter
Introduction
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3
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Chapter
§1. DÉMONSTRATION DU THÉORÈME 1
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6
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Chapter
§2. DÉMONSTRATION DU THÉORÈME 2
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10
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Chapter
§3. Valeurs extrêmes de f(n) + f(n +1)
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12
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Chapter
§4. Nombres ω-intéressants
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17
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Chapter
§5. DÉMONSTRATION DU THÉORÈME 4
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19
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Bibliography
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25
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Article
THE HYPER-KLOOSTERMAN SUM
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29
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Chapter
1. Introduction
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29
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Chapter
2. Lemmas
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30
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Chapter
3. Proof of Theorems 1 and 2
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32
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Bibliography
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40
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Article
THÉORÈMES DE GAUSS-BONNET, DE HOPF, ET RÉSIDUS DES CONNEXIONS MÉTRIQUES A SINGULARITÉS
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41
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Chapter
1. Introduction
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41
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Chapter
2. Connexions métriques sur une surface (Rappels)
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43
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Chapter
3. Résidus et formule locale de Gauss-Bonnet
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45
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Chapter
4. Théorème des résidus
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47
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Chapter
5. Connexions métriques sans singularités
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48
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Chapter
6. Connexions métriques plates a singularités isolées
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50
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Bibliography
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55
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Article
SCHUBERT CALCULUS OF A COXETER GROUP
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57
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Chapter
Introduction
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57
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Chapter
1. Coxeter groups
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59
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Chapter
2. Demazure's basis theorem
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63
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Chapter
3. GIAMBELLI FORMULA
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66
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Chapter
4. Pieri formula
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71
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Chapter
5. $H_w$ AS A AND PARABOLICS
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74
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Chapter
6. Application: The combinatorics of the classical Pieri formula
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76
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Bibliography
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83
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Article
SPECKER'S MATHEMATICAL WORK FROM 1949 TO 1979
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85
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Chapter
From doctorate to professorship
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87
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Chapter
Enjoyment of interaction
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88
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Chapter
Topology and recursive analysis
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88
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Chapter
An example of beginning with concrete problems
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89
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Chapter
Logic and quantum mechanics
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90
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Chapter
Typical ambiguity and model theory
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92
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Chapter
Complexity of algorithms
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94
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Chapter
Specker's Mathematical Publications (1949-79)
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96
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Article
TOWARDS A COMPLEXITY THEORY OF SYNCHRONOUS PARALLEL COMPUTATION
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99
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Abstract
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99
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Chapter
1. Introduction
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99
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Chapter
2. Circuits and Alternating Turing Machines
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102
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Chapter
3. Log Depth vs Log Space
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109
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Chapter
4. Conglomerates and Aggregates
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111
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Chapter
5. Hardware Modification Machines
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116
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Chapter
6. Other Modifiable Models
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117
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Chapter
7. Simultaneous Resource Bounds
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118
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Chapter
8. Open Questions
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122
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Bibliography
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123
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Article
ZUR AXIOMATISIERUNG GEWISSER AFFINER GEOMETRIEN
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125
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Chapter
1. EINFÜHRUNG UND PROBLEMSTELLUNG
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125
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Chapter
2. Beweis der Charakterisierungslemmas
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128
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Chapter
3. Die Nicht-Charakterisierbarkeit
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132
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Chapter
4. SCHLUSSBEMERKUNGEN
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134
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Bibliography
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135
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Article
ALTERNATION AND THE ACKERMANN CASE OF THE DECISION PROBLEM
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137
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Abstract
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137
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Chapter
1. Introduction and historical background
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137
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Chapter
2. Some notions from logic
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141
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Chapter
3. Some notions from computational complexity
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142
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Chapter
4. Alternating Turing machines
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144
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Chapter
5. Upper bounds
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147
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Chapter
6. Lower bounds
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154
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Chapter
Conclusions
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159
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Chapter
Acknowledgment
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160
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Bibliography
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160
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Article
PROBLEMS AND RESULTS ON FINITE AND INFINITE COMBINATORIAL ANALYSIS II
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163
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Article
HOMÉOMORPHIE DES ROTATIONS DE $S^m$ ÉVOLUTION D'UN PROBLÈME, SOUVENIRS
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177
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Bibliography
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183
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Article
THE RIEMANN-ROCH THEOREM FOR COMPACT RIEMANN SURFACES
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185
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Chapter
§1. Introduction
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185
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Chapter
§2. Line bundles and vector bundles. Sheaf theoretic preliminaries
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185
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Chapter
§3. RIEMANN-ROCH THEOREM (PRELIMINARY FORM)
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189
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Chapter
§4. The degree of the canonical line bundle
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191
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Chapter
§5. RIEMANN-ROCH THEOREM (FINAL FORM). SERRE DUALITY
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193
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Bibliography
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196
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Article
IDENTITIES FOR PRODUCTS OF GAUSS SUMS OVER FINITE FIELDS
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197
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Chapter
1. Introduction
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197
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Chapter
2. Notation and the identities
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198
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Chapter
3. Theorems of Stickelberger and Davenport-Hasse
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200
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Chapter
4. Proof of (2)
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200
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Chapter
5. Proof of (3)
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201
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Chapter
6. Proof of (4)
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204
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Chapter
7. Proof of (5)
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206
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Chapter
8. Character sum analogues of (1), (1a) and (1b)
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207
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Bibliography
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209
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Article
ON THE GENUS OF GENERALIZED FLAG MANIFOLDS
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211
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Chapter
Introduction
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211
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Chapter
§1. Genus and self maps
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213
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Chapter
§2. The case of generalized flag manifolds
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216
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Bibliography
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219
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Article
SUR L'USAGE DE CRITÈRES POUR RECONNAÎTRE UN GROUPE LIBRE, UN PRODUIT AMALGAMÉ OU UNE HNN-EXTENSION
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221
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Chapter
Introduction
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221
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Chapter
2. DÉFINITIONS ET GÉNÉRALITÉS SUR LES ACTIONS DE GROUPES ET LES GRAPHES
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222
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Chapter
3. Critère pour groupes libres
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225
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Chapter
4. Critères pour produits amalgamés
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230
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Chapter
5. Critère pour les HNN-extensions
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232
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Chapter
6. Structures bipolaires
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236
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Bibliography
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242
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Article
LOCALLY HOMOGENEOUS VARIATIONS OF HODGE STRUCTURE
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243
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Chapter
Introduction
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243
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Abstract
TABLE OF CONTENTS
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246
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Chapter
§1. Preliminaries
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246
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Chapter
§2. Vector bundles on Γ\M
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250
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Chapter
§3. The cohomology groups $H^n(\Gamma; \rho, V)$
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254
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Chapter
§4. The variation of Hodge structure associated to (ρ, V)
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261
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Chapter
§5. Hodge theory for $H^n(\Gamma; \rho, V)$, FROM THE VARIATION OF HODGE STRUCTURE
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264
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Bibliography
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276
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Article
APPLICATION OF TOPOLOGY TO PROBLEMS ON SUMS OF SQUARES
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277
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Bibliography
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283
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Article
FINITENESS THEOREMS IN GEOMETRIC CLASSFIELD THEORY
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285
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Chapter
0. Introduction
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285
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Chapter
II. Preliminaries
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288
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Chapter
II. The Main theorem
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294
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Chapter
III. A VARIANT
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306
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Chapter
IV. Absolute Finiteness theorems
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311
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Chapter
V. Application to l-adic representations
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312
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Bibliography
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314
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Article
APPENDIX: TORSION POINTS OF ABELIAN VARIETIES IN CYCLOTOMIC EXTENSIONS
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315
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Bibliography
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319
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Article
ON COUSIN-I COMPLEX SPACES
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321
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Abstract
Summary
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321
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Rubric
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322
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Bibliography
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325
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Article
DESCARTES, EULER, POINCARÉ, PÓLYA—AND POLYHEDRA
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327
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Chapter
1. Introduction
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327
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Chapter
2. Pólya's proof of Descartes' theorem
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331
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Chapter
3. The angular defect in higher dimensions
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335
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Chapter
3. Historical comment and summary
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342
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Bibliography
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343
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE
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345
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Chapter
FIFTH INTERNATIONAL CONGRESS ON MATHEMATICS EDUCATION
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345
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Article
INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION, 1980-81
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347
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Chapter
1. THE PRESIDENT'S REPORT
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347
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Chapter
2. ICME iv
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348
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Chapter
3. BULLETIN OF ICMI
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350
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Chapter
4. FUTURE ACTIVITIES
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350
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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57
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Back matter
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