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Rubric
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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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1
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Front matter
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2
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Article
PARAMETRIZED PLANE CURVES, MINKOWSKI CAUSTICS, MINKOWSKI VERTICES AND CONSERVATIVE LINE FIELDS
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3
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Chapter
0. Introduction
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3
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Chapter
1. Finsler metric from the contact geometrical viewpoint
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4
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Chapter
2. Minkowski geometry associated with a parametrized curve
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7
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Chapter
3. Osculating indicatrices and Minkowski caustic
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10
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Chapter
4. Minkowski vertices and Chebyshev Systems
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16
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Chapter
5. Conservative transverse line fields
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20
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Bibliography
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25
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Article
EVEN NON-SPIN MANIFOLDS, SPINc STRUCTURES, AND DUALITY
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27
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Abstract
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27
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Rubric
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28
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Bibliography
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32
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Article
BOTT-CHERN FORMS AND ARITHMETIC INTERSECTIONS
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33
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Abstract
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33
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Chapter
1. Introduction
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33
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Chapter
2. Invariant and symmetric functions
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35
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Chapter
3. Hermitian differential geometry
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36
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Chapter
4. Calculating Bott-Chern Forms
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39
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Chapter
5. $0 \rightarrow \bar{S} \rightarrow \bar{E} \rightarrow \bar{Q} \rightarrow 0$ WITH $\bar{E}$ FLAT
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42
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Chapter
6. Calculations when $\bar{E}$ is projectively flat
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44
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Chapter
7. Arithmetic intersection theory
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48
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Chapter
8. Arakelov Chow rings of grassmannians
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51
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Bibliography
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53
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Article
ATKIN-LEHNER EIGENFORMS AND STRONGLY MODULAR LATTICES
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55
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Abstract
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55
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Chapter
Introduction
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55
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Chapter
1. Standard involutions on lattices
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56
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Chapter
2. ATKIN-LEHNER ACTION ON THETA FUNCTIONS
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59
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Chapter
3. Some use of modular forms
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61
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Bibliography
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65
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Article
THE NORMALISER ACTION AND STRONGLY MODULAR LATTICES
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67
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Abstract
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67
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Chapter
1. Introduction
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67
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Chapter
2. PRELIMINAIRES AND NOTATION
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68
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Chapter
3. Similarities Normalise
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69
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Chapter
4. Obtaining Elements of N
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70
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Chapter
5. Proof of the Theorem
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73
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Bibliography
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75
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Article
SUR LA LOI DE RÉCIPROCITÉ DE KATO POUR LES ANNEAUX LOCAUX DE DIMENSION 2
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77
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Chapter
1. ÉNONCÉS
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77
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Chapter
2. Préparation
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79
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Chapter
3. Toujours préparation, mais à la Weierstrass
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82
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Chapter
4. RÉDUCTIONS
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84
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Chapter
5. Conclusion
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87
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Bibliography
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90
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Article
LA SOMMATION DE RAMANUJAN
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93
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Abstract
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93
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Chapter
1. Introduction
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93
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Chapter
2. DÉVELOPPEMENTS D'EULER-MACLAURIN FORMELS
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94
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Chapter
3. Sommation de Ramanujan et transformation de Laplace-Borel
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96
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Chapter
3.1. Sommation de Ramanujan
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96
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Chapter
3.2. Liens avec la sommation de Cauchy
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102
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Chapter
4. Propriétés de la sommation
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104
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Chapter
4.1. Linéarité
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104
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Chapter
4.2. Translation
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104
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Chapter
4.3. Dérivation
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105
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Chapter
4.4. Sommation par parties
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105
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Chapter
4.5. SÉPARATION DES TERMES PAIRS ET IMPAIRS
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108
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Chapter
4.6. Utilisations de développements en série entière
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109
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Chapter
4.7. DÉPENDANCE ANALYTIQUE PAR RAPPORT À UN PARAMÈTRE
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112
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Chapter
5. Exemples d'utilisation
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113
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Chapter
5.1. DÉVELOPPEMENT EN SÉRIE DE LA FONCTION Ψ
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113
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Chapter
5.2. Calcul de $\sum_{n \geq 1}^R n^{2q} \ln(n)$
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114
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Chapter
5.3. Une solution de l'équation de la chaleur
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116
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Chapter
6. Interpolation de Newton et sommation de Ramanujan
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117
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Appendix
7. Appendice: Transformation de Laplace-Borel
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121
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Chapter
7.1. Notations
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121
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Chapter
7.2. Transformation de Borel
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121
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Chapter
7.3. Transformation de Laplace
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124
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Chapter
7.4. Le cas intégrable
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128
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Chapter
7.5. Quelques propriétés
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131
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Bibliography
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131
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Article
THE LOCAL LINEARIZATION PROBLEM FOR SMOOTH SL(n) -ACTIONS
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133
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Abstract
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133
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Abstract
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133
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Chapter
1. Introduction
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133
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Chapter
2. Background and Motivation
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136
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Chapter
3. Preparatory results
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142
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Chapter
4. SL(n,R)-ACTIONS ON $R^n$ FOR n ≥ 3
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149
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Chapter
5. The adjoint representation of SL(2,R)
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151
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Chapter
6. SL(2,R) -actions on $R^2$
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153
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Chapter
7. Examples of $C^0$-actions of SL(2,R) on $R^m$
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157
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Chapter
8. A $C^\infty$ -action of SL(2,R) which is not linearizable
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159
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Chapter
9. A $C^\infty$ -ACTION OF SL(3,R) WHICH IS NOT LINEARIZABLE
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161
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Chapter
10. LINEARIZABILITY OF SL(n,Z)-ACTIONS
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164
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Bibliography
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168
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Article
POLYGON SPACES AND GRASSMANNIANS
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173
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Abstract
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173
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Chapter
1. Introduction
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173
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Chapter
2. The polygon spaces
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175
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Chapter
3. Quaternions, Grassmannians and structures on the full polygon spaces
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178
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Chapter
4. POLYGONS WITH GIVEN SIDES – KÄHLER STRUCTURES
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183
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Chapter
5. The Gel'fand-Cetlin action
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187
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Chapter
6. Toric manifold structures on $mP_+^3(\alpha)(a)$ for m = 4,5,6
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191
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Chapter
7. Remarks and open problems
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196
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Bibliography
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197
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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199
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Chapter
THE ROLE OF THE HISTORY OF MATHEMATICS IN THE TEACHING AND LEARNING OF MATHEMATICS DISCUSSION DOCUMENT FOR AN ICMI STUDY (1997-2000)
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199
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Chapter
Some research questions
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199
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Chapter
Call for contributions
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202
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Back matter
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44
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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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205
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Front matter
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206
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Article
AN ALGORITHM FOR CELLULAR MAPS OF CLOSED SURFACES
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207
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Abstract
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207
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Chapter
1. Introduction
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207
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Chapter
2. DIAGRAMS OF CELLULAR SURFACE MAPS
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212
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Chapter
3. The algorithm
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222
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Chapter
4. HOMOMORPHISMS OF SURFACE GROUPS
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237
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Chapter
5. A WORKED EXAMPLE
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247
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Bibliography
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251
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Article
QUATERNARY CUBIC FORMS AND PROJECTIVE ALGEBRAIC THREEFOLDS
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253
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Chapter
Introduction
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253
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Chapter
I. Quaternary Cubic Forms
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255
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Chapter
1. Normal Forms for Quaternary Cubic Forms
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256
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Chapter
2. The Invariant Theory of Quaternary Cubic Forms
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260
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Chapter
II. Cubic Forms of Projective Threefolds
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262
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Chapter
1. Preliminaries
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262
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Chapter
2. A Projective Threefold with a Nodal Cubic as Cup Form
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263
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Chapter
3. Quaternary Cubic Forms that are Cup Forms of Projective Algebraic Manifolds
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264
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Chapter
4. Real Cubic Forms which are not Cup Forms of Projective Algebraic Manifolds
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268
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Bibliography
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269
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Article
4-MANIFOLDS, GROUP INVARIANTS, AND $l_2$-BETTI NUMBERS
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271
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Chapter
1. A BASIC CONSTRUCTION
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271
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Chapter
2. The Hausmann-Weinberger invariant
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272
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Chapter
3. The (λ+σ) -invariant
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273
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Chapter
4. Deus ex machina: $l_2$-cohomology
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275
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Chapter
5. The vanishing of q(G)
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278
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Bibliography
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279
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Article
THEOREM OF INGHAM IMPLYING THAT DIRICHLET'S L-FUNCTIONS HAVE NO ZEROS WITH REAL PART ONE
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281
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Chapter
§1. Introduction
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281
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Chapter
§2. Proof of Ingham's Theorem
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283
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Bibliography
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284
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Article
SUR LES TRANSFORMATIONS DE CREMONA DE BIDEGRÉ (3,3)
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285
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Abstract
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285
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Chapter
Introduction
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285
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Chapter
1. Le résultat principal
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286
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Chapter
2. Exemples
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287
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Chapter
3. Preuve du théorème
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289
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Chapter
4. Un corollaire et plus d'exemples
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293
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Chapter
5. Comparaison avec les résultats classiques
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295
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Bibliography
|
297
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Article
NONMINIMAL RATIONAL CURVES ON K3 SURFACES
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299
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Chapter
Introduction
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299
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Chapter
1. About finiteness
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303
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Chapter
2. About existence
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304
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Chapter
3. Rational curves on quartics in $P^3$
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310
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Chapter
4. Rational curves on K3 surfaces in $P^4$
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313
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Bibliography
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316
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Article
ON CYCLOTOMIC POLYNOMIALS, POWER RESIDUES, AND RECIPROCITY LAWS
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319
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Abstract
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319
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Chapter
1. Introduction
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319
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Chapter
2. Statement of results
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320
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Chapter
3. Background
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322
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Chapter
4. The odd case
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325
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Chapter
5. Homogeneous polynomials
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328
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Chapter
6. WHAT ABOUT q?
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329
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Chapter
7. The even case
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330
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Chapter
8. The second proof
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333
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Bibliography
|
335
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Article
AMENABILITY AND GROWTH OF ONE-RELATOR GROUPS
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337
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Abstract
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337
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Chapter
0. Introduction
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337
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Chapter
1. An algorithm for checking amenability
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339
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Chapter
2. Two-generated one-relator groups
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342
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Chapter
3. Uniformly exponential growth and growth of graded algebras
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346
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Chapter
4. More on uniformly exponential growth of one-relator groups
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349
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Bibliography
|
352
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Article
ÉQUISINGULARITÉ DANS LES PINCEAUX DE GERMES DE COURBES PLANES ET $C^0$-SUFFISANCE
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355
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Chapter
§1. Introduction
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355
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Chapter
§2. ÉLIMINATION DE L'INDÉTERMINATION LOCALE D'UNE FONCTION MÉROMORPHE À DEUX VARIABLES
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357
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Chapter
§3. Valeurs spéciales d'un pinceau de germes de courbes planes
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360
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Chapter
§4. L'OUVERT D'ÉQUISINGULARITÉ D'UN PINCEAU LOCAL
|
363
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Chapter
§5. Bonnes composantes dicritiques
|
369
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Chapter
§6. Étude d'un cas particulier
|
371
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Chapter
§7. Le calcul du degré de $C^0$ -suffisance
|
372
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Chapter
§8. Un petit historique de la $C^0$-suffisance
|
377
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Bibliography
|
379
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
|
381
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Chapter
ICMI STUDY ON THE TEACHING AND LEARNING OF MATHEMATICS AT UNIVERSITY LEVEL DISCUSSION DOCUMENT
|
381
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Chapter
1. WHY A STUDY ON THE TEACHING AND LEARNING OF MATHEMATICS AT UNIVERSITY LEVEL ?
|
382
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Chapter
2. THEMES AND ISSUES PERTAINING TO RESEARCH ON THE TEACHING AND LEARNING OF MATHEMATICS AT UNIVERSITY LEVEL
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384
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Chapter
3. THEMES AND ISSUES PERTAINING TO PRACTICE
|
385
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Chapter
4. THEMES AND ISSUES RELATING TO POLICY
|
387
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Chapter
5. Call for reactions
|
388
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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45
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Back matter
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Index
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Back matter
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