Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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1
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Front matter
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2
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Article: GEOMETRIC K-THEORY FOR LIE GROUPS AND FOLIATIONS
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3
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Chapter: 1. Introduction
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3
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Chapter: 2. Lie group actions
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4
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Chapter: 3. HOMOTOPY QUOTIENT
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8
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Chapter: 4. Solvable simply connected Lie groups
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11
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Chapter: 5. The geometric K-theory for $\pi_0G$ finite
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13
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Chapter: 6. Discrete groups : Chern character
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17
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Chapter: 7. Corollaries of the isomorphism conjecture
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20
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Chapter: 8. TWISTING BY A 2-COCYCLE
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22
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Chapter: 9. Foliations
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30
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Chapter: 10. FURTHER DEVELOPMENTS
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33
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Chapter: 11. ACKNOWLEDGEMENTS
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34
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Bibliography
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35
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Chapter: EDITORS' NOTE
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37
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Bibliography
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38
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Article: THE SATURATION CONJECTURE (AFTER A. KNUTSON AND T. TAO)
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43
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Chapter: 1. The hive model
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44
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Chapter: 2. Flatspaces
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47
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Chapter: 3. Small Flatspaces
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51
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Chapter: 4. Proof of the saturation conjecture
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53
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Chapter: 5. Remarks and questions
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54
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Appendix: Appendix. A bijection between hives and Littlewood-Richardson skew tableaux (by William FULTON)
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56
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Bibliography
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59
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Article: ARITHMETIC OF BINARY CUBIC FORMS
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61
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Abstract
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61
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Chapter: 1. Introduction
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61
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Abstract: Contents
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65
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Chapter: 2. Binary quadratic mappings
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65
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Chapter: 3. Cubic forms
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73
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Chapter: 4. A Lie algebra representation
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77
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Chapter: 5. Structure of the cubic C-forms
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81
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Chapter: 6. COHOMOLOGICAL INTERPRETATION
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89
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Chapter: 7. EXPLICIT COMPUTATIONS AND CUBIC TRACE FORMS
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91
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Bibliography
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93
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Article: ALMOST COMPLEX STRUCTURES ON 8-MANIFOLDS
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95
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Chapter: 1. Introduction
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95
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Chapter: 2. Stable almost complex structures
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100
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Chapter: 3. The top-dimensional obstruction
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100
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Chapter: 4. Existence of almost complex structures
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104
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Bibliography
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106
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Article: PREMIER NOMBRE DE BETTI ET SPECTRE DU LAPLACIEN DE CERTAINES VARIÉTÉS HYPERBOLIQUES
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109
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Abstract
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109
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Chapter: Introduction
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109
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Chapter: 1. Topologie des sous-groupes d'indice fini et groupes algébriques
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112
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Chapter: 2. Sur la topologie des cycles géodésiques
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114
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Chapter: 3. Extension au cas des cycles généralisés
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118
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Chapter: 4. Variétés hyperboliques isospectrales
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121
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Chapter: 5. Petites valeurs propres de certaines variétés hyperboliques
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128
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Appendix: Appendice : Spectre des variétés tubes
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132
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Bibliography
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136
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Article: TOPOLOGIE DES COURBES ALGÉBRIQUES RÉELLES : UNE QUESTION DE FELIX KLEIN
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139
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Abstract
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139
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Chapter: 1. Introduction
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139
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Chapter: 2. La classification topologique des surfaces symétriques
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140
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Chapter: 3. Les petites déformations des courbes planes nodales
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144
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Chapter: 4. Le théorème de Klein
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145
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Chapter: 5. Le problème de Klein: description des prohibitions
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147
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Chapter: 6. La génétique chez les courbes planes réelles
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148
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Chapter: 7. Le problème de Klein: construction de courbes
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149
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Chapter: 7.1 Les courbes de degré pair
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150
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Chapter: 7.2 Les courbes de degré impair
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157
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Chapter: 8. Remerciements
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160
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Bibliography
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160
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Article: HARTREE'S THEOREM ON EXISTENCE OF THE QUANTUM DEFECT
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162
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Chapter: Introduction
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163
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Appendix: Addendum
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202
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Bibliography
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206
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Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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209
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Chapter: DISCUSSION DOCUMENT FOR THE TWELFTH ICMI STUDY THE FUTURE OF THE TEACHING AND LEARNING OF ALGEBRA
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209
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Chapter: INTRODUCTION
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209
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Chapter: WHY ALGEBRA ?
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210
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Chapter: APPROACHES TO ALGEBRA
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211
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Chapter: LANGUAGE ASPECTS OF ALGEBRA
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212
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Chapter: TEACHING AND LEARNING WITH COMPUTER ALGEBRA SYSTEMS
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212
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Chapter: TECHNOLOGICAL ENVIRONMENTS
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213
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Chapter: ALGEBRA WITH REAL DATA
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214
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Chapter: USING THE HISTORY OF ALGEBRA
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214
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Chapter: EARLY ALGEBRA EDUCATION
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215
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Chapter: TERTIARY ALGEBRA
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215
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Chapter: HOW TO PARTICIPATE
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216
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Chapter: INTERNATIONAL SYMPOSIUM «One Hundred Years of L'Enseignement Mathématique: Moments of Mathematics Education in the 20th Century»
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219
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Chapter: BACKGROUND
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219
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Chapter: PRESENTATION OF THE SYMPOSIUM
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220
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Chapter: PROGRAMME
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221
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Chapter: ORGANIZATION
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222
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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1
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Chapter: Génélités
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1
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Chapter: Histoire
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6
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Chapter: Logique et fondements
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7
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Chapter: Théorie des ensembles
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8
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Chapter: Analyse combinatoire
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9
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Chapter: Ordre,treillis
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10
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Chapter: Théorie des nombres
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10
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Chapter: Corps et polynômes
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12
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Chapter: Géométrie algébrique
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12
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Chapter: Algébre linéaire et multilinéaire,théorie des matrices
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13
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Chapter: Anneaux et algébres
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13
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Chapter: Catégories, algébre homologique,cohomologie des groupes
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14
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Chapter: Théorie des groupes et généralisation
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14
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Chapter: Groupes topologiques;groupes et algébres de Lie
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15
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Chapter: Mesure et intégration
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15
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Chapter: Fonctions d'une variable complexe
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16
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Chapter: Fonctions de plusieurs variables complexes
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16
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Chapter: Equations différentielles ordinaires
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17
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Chapter: Equations aux dérivées partielles
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17
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Chapter: Systèmes dynamiques et théorie ergodique
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19
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Chapter: Analyse de Fourier, analyse harmonique abstraite
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19
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Chapter: Equations intégrales
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20
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Chapter: Analyse fonctionnelle et théorie des opérateurs
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20
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Chapter: Géométrie
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21
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Chapter: Géométrie différentielle
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22
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Chapter: Topologie algébrique
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23
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Chapter: Topologie des variétés,analyse globale et analyse des variétés
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24
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Chapter: Probabilités et processus stochastiques
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25
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Chapter: Statistique
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28
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Chapter: Analyse numérique
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29
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Chapter: Informatique
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30
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Chapter: Mécanique des solides,élasticité et plasticité
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31
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Chapter: Mécanique des fluides, acoustique
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31
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Chapter: Thermodynamique classique ,propagation de la chaleur
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32
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Chapter: Mécanique quantique
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32
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Chapter: Economie, recherche opérationnelle,jeux
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33
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Chapter: Systèmes,contrôle optimal
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33
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Chapter: Information,communication ,circuits
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34
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Back matter
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Back matter
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Issue 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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223
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Front matter
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224
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Article: p-ADIC L-FUNCTION OF TWO VARIABLES
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225
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Abstract
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225
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Chapter: 1. Introduction
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225
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Chapter: 2. Preliminaries
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233
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Chapter: 2.1 Dirichlet characters
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234
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Chapter: 2.2 Generalized Bernoulli polynomials
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235
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Chapter: 2.3 Dirichlet L-functions
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238
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Chapter: 2.4 The p-adic number field
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239
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Chapter: 2.5 p-ADIC FUNCTIONS
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241
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Chapter: 3. The p-adic L-function $L_p(s,t,\lambda)$
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245
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Chapter: 3.1 $L_p(s,\tau;\lambda)$ FOR $\tau \in \bar{Q}_p$, $|\tau|_p \leq 1$
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245
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Chapter: 3.2 $L_p(s,\tau;\lambda)$ FOR $\tau \in C_p$, $|\tau|_p \leq 1$
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250
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Chapter: 4. Properties of $L_p(s,t;\lambda)$
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258
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Chapter: 4.1 A SYMMETRY PROPERTY IN t
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258
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Chapter: 4.2 $L_p(s,t;\lambda)$ AS A POWER SERIES IN $t – \alpha, \quad \alpha \in C_p, \quad $|\alpha|_p \leq 1$
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260
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Chapter: 4.3 Relating $L_p(s, t; \lambda)$ to some finite sums
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266
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Chapter: 4.4 Generalized Bernoulli power series
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273
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Bibliography
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277
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Article: ORDERINGS OF MAPPING CLASS GROUPS AFTER THURSTON
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279
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Abstract
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279
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Chapter: 1. Orderable groups
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280
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Chapter: 2. Orderings of mapping class groups using hyperbolic geometry
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282
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Chapter: 3. Main results
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287
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Chapter: 4. Orderings of mapping class groups using curve diagrams
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Chapter: 5. Which pairs of curve diagrams determine the same ordering?
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293
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Chapter: 6. Replacing finite type geodesics by curve diagrams
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Chapter: 7. Orderings associated to geodesics of infinite type
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304
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Bibliography
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Article: IDEAL SOLUTIONS OF THE TARRY-ESCOTT PROBLEM OF DEGREE FOUR AND A RELATED DIOPHANTINE SYSTEM
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Abstract
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313
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Chapter: 1. Introduction
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313
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Chapter: 2. The complete ideal symmetric solution of the Tarry-Escott problem of degree four
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315
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Chapter: 3. A parametric ideal non-symmetric solution of the Tarry-Escott problem of degree four
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Chapter: 4. The diophantine system $\sum_{i=1}^5 a_i^r = \sum_{i=1}^5 b_i^5, \quad r=1,2,3,4,6$
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321
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Bibliography
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Article: ÉCHELLES DE SOBOLEV D'ORIGINE ARBITRAIRE
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Abstract
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325
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Abstract
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325
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Chapter: 1. Introduction
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Chapter: 2. Les espaces de Banach de distributions
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Chapter: 2.1 DÉFINITION ET PREMIÈRES PROPRIÉTÉS
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Chapter: 2.2 Échelles de régularité
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Chapter: 2.3 Dualité de l'échelle de Sobolev
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329
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Chapter: 2.4 Les $D(R^n)$ -modules invariants par translation
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330
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Chapter: 3. RÉSULTATS POSITIFS EN DIMENSION UN
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Chapter: 4. RÉSULTATS NÉGATIFS EN DIMENSIONS SUPÉRIEURES
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Chapter: 4.1 La propriété de Mitiagin-Ornstein
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332
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Chapter: 4.2 Preuve du théorème 1
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Chapter: 4.3 Contre-exemples explicites
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Chapter: 4.4 Les plongements de Sobolev sous-jacents
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Chapter: 5. Pour aller plus loin
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335
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Chapter: 6. Questions ouvertes
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337
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Bibliography
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Article: REMARKS ON THE HAUSDORFF-YOUNG INEQUALITY
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Chapter: §1. Introduction
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Chapter: §2. Notations and some known facts
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Chapter: §3. Main theorems
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Chapter: §4. HISTORICAL REMARKS
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Appendix: §5. Appendix
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346
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Bibliography
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Article: THE SPECTRAL MAPPING THEOREM, NORMS ON RINGS, AND RESULTANTS
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349
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Abstract
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349
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Chapter: 1. Introduction
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349
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Chapter: 2. The Spectral Mapping Theorem
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Chapter: 3. A REDUCTION
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Chapter: 4. The proof
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Chapter: 5. Norms on algebras
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Chapter: 6. NORMS AND RESULTANTS
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Chapter: 7. Uniqueness of norms and the Spectral Mapping Theorem
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Chapter: 8. The discriminant
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Bibliography
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Article: NOTE OF THE EDITORS
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Article: THE WITT GROUP OF LAURENT POLYNOMIALS
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Abstract
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361
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Chapter: 1. Introduction
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Chapter: 2.K-theoretic PRELIMINARIES
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Chapter: 3. The Witt group of polynomial rings
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Chapter: 4. The Witt group of torsion modules
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Chapter: 5. The Witt group of extended spaces
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Chapter: 6. The residue
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Chapter: 7. The Witt group of Laurent polynomials
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Chapter: 8. TWO COUNTEREXAMPLES
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380
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Bibliography
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383
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Article: THE SIXTH FERMAT NUMBER AND PALINDROMIC CONTINUED FRACTIONS
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385
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Abstract
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385
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Rubric
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Bibliography
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Article: THREE REMARKS ON GEODESIC DYNAMICS AND FUNDAMENTAL GROUP
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Chapter: §1. HOMOTOPIC STABILITY
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391
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Chapter: §2. Entropy
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Chapter: §3. Periodic orbits
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395
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Bibliography
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Appendix: Why the Appendices were not written : author's apologies to the readers
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399
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Bibliography
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Bibliography
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Article: FINITE GROUP ACTIONS ON THE 7-SPHERE
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Bibliography
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409
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Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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411
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Article: REPORT ON THE ICMI STUDY : «PERSPECTIVES ON THE TEACHING OF GEOMETRY FOR THE 21ST CENTURY»
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411
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Bibliography
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415
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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35
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Chapter: Généralités
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35
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Chapter: Histoire
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42
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Chapter: Logique et fondements
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44
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Chapter: Analyse combinatoire
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45
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Chapter: Théorie des nombres
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46
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Chapter: Corps et polynômes
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48
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Chapter: Géométrie algébrique
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48
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Chapter: Algèbre linéaire et multilinéaire, théorie des matrices
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50
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Chapter: Anneaux et algèbres
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51
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Chapter: Catégories, algèbre homologique, cohomologie des groupes
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52
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Chapter: K théorie
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52
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Chapter: Théorie des groupes et généralisations
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53
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Chapter: Groupes topologiques; groupes et algèbres de Lie
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56
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Chapter: Fonctions de variables réelles
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56
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Chapter: Mesure et intégration
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57
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Chapter: Fonctions d'une variable complexe
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57
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Chapter: Fonctions de plusieurs variables complexes
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57
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Chapter: Equations différentielles ordinaires
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58
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Chapter: Equations aux dérivées partielles
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59
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Chapter: Systèmes dynamiques et théorie ergodique
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61
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Chapter: Equations aux différences finies, équations fonctionnelles
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63
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Chapter: Approximations et développements en série
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63
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Chapter: Analyse de Fourier, analyse harmonique abstraite
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63
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Chapter: Transformations intégrales, calcul opérationnel
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64
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Chapter: Equations intégrales
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64
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Chapter: Analyse fonctionnelle
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64
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Chapter: Théorie des opérateurs
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66
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Chapter: Calcul des variations
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69
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Chapter: Géométrie
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69
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Chapter: Géométrie différentielle
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70
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Chapter: Topologie algébrique
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71
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Chapter: Topologie des variétés, analyse globale et analyse des variétés
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71
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Chapter: Probabiltés et processus stochastiques
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73
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Chapter: Statistique
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73
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Chapter: Analyse numérique
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74
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Chapter: Informatique
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75
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Chapter: Mécanique des particules et systèmes
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77
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Chapter: Mécanique des solides, élasticité et plasticité
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77
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Chapter: Mécanique des fluides, acoustique
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77
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Chapter: Mécanique quantique
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79
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Chapter: Economie, recherche opérationnelle, jeux
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79
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Chapter: Biologie et sciences du comportement
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79
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Chapter: Systèmes, contrôle optimal
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80
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Chapter: Information, communication, circuits
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81
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Back matter
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Index
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Back matter
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