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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
UNE REMARQUE SUR LE SPECTRE DES SOLUTIONS MATRICIELLES DE L'ÉQUATION DE RICCATI
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3
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Bibliography
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11
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Article
THE MEAN SQUARE OF THE RIEMANN ZETA-FUNCTION ON THE LINE σ = 1
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13
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Abstract
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13
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Rubric
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14
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Bibliography
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25
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Article
THE CATEGORY OF NILMANIFOLDS
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27
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Abstract
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27
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Chapter
Introduction
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27
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Chapter
§1. Category
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28
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Chapter
§2. Rational homotopy and category
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30
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Chapter
§3. NILMANIFOLDS
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34
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Chapter
§4. Category of nilmanifolds
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36
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Chapter
§5. HIGHER DEGREE ANALOGUES
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37
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Chapter
§6. Ganea's conjecture
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38
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Bibliography
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39
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Article
PERMUTATION GROUPS GENERATED BY A TRANSPOSITION AND ANOTHER ELEMENT
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41
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Abstract
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41
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Chapter
1. A GRAPH FOR A SUBGROUP CONTAINING A TRANSPOSITION
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42
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Chapter
2. An application to Galois theory
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46
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Chapter
3. TWO GENERATOR SUBGROUPS OF Sym(n)
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46
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Bibliography
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53
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Article
ACTIONS QUASI-LINÉAIRES SUR LES SPHÈRES
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55
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Chapter
Introduction
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55
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Chapter
2. G-COBORDISMES D'ACTIONS
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56
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Chapter
3. Actions libres – Résultats généraux
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59
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Chapter
4. Actions libres d'un groupe cyclique fini
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62
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Chapter
5. Actions libres de $S^1$
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64
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Chapter
6. Actions libres de $S^3$
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67
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Chapter
7. Exemples d'actions quasi linéaires
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68
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Bibliography
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70
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Article
POLYÈDRES ET RÉSEAUX
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71
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Chapter
0. Introduction
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71
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Chapter
1. Fonctions caractéristiques
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72
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Chapter
1.1. Polynômes et séries de Laurent
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72
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Chapter
1.2. Fonctions caractéristiques de cônes et polyèdres
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73
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Chapter
2. Identités entre fonctions caractéristiques
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75
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Chapter
2.1 Un propriété d'additivité
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75
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Chapter
2.2. Polyèdres et fonctions d'appui
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77
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Chapter
2.3. Fonctions caractéristiques de polyèdres ouverts
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78
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Chapter
2.4. Fonctions caractéristiques pondérées
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80
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Chapter
3. Propriétés énumératives des polytopes convexes entiers
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83
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Chapter
3.1. Comportement polynomial de fonctions de comptage
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83
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Chapter
3.2. Loi de réciprocité
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84
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Chapter
3.3. Le cas d'un polytope rationnel
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86
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Bibliography
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87
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Article
LA NON-DÉRIVABILITÉ DE LA FONCTION DE WEIERSTRASS
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89
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Chapter
1. Propriétés de Lipschitz de la fonction de Weierstrass
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89
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Chapter
2. Cas où b est un entier impair
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91
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Chapter
3. Cas général
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92
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Chapter
4. Conclusion
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94
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Bibliography
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94
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Article
COMPLEX GROWTH SERIES OF COXETER SYSTEMS
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95
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Chapter
1. Introduction
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95
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Chapter
2. Complex growth series
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97
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Bibliography
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102
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Article
EMMY NOETHER: HIGHLIGHTS OF HER LIFE AND WORK
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103
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Chapter
A. Her life
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103
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Chapter
B. Her work
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109
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Chapter
Invariant theory
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110
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Chapter
Commutative algebra
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113
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Chapter
Noncommutative algebra and representation theory
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117
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Chapter
Applications of noncommutative to commutative algebra
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119
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Chapter
C. Her legacy
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120
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Bibliography
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122
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Article
SIMPLE PROOF OF A THEOREM OF THUE ON THE MAXIMAL DENSITY OF CIRCLE PACKINGS IN $E^2$
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125
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Chapter
Introduction
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125
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Chapter
Local cell and local density
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125
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Chapter
Remark on the uniqueness of the finite packings of maximal density
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130
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Bibliography
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131
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Article
AN ANALOGUE OF HUBER'S FORMULA FOR RIEMANN'S ZETA FUNCTION
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133
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Chapter
1. Introduction
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133
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Chapter
2. OUTLINE OF THE LECTURE
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134
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Bibliography
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148
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Article
REAL NUMBERS WITH BOUNDED PARTIAL QUOTIENTS: A SURVEY
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151
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Abstract
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151
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Chapter
1. Introduction and Definitions
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151
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Chapter
2. Numbers of Constant Type
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152
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Chapter
3. The Metric Theory of Continued Fractions
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154
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Chapter
4. Continued Fractions for Algebraic Numbers
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156
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Chapter
5. Certain Sums in Diophantine Approximation
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158
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Chapter
6. Fractal Geometry
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159
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Chapter
7. Schmidt's Game
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160
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Chapter
8. Hall's theorem
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160
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Chapter
9. EXPLICIT EXAMPLES OF TRANSCENDENTAL NUMBERS WITH BOUNDED PARTIAL QUOTIENTS
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161
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Chapter
10. "Quasi-Monte-Carlo" Methods and Zaremba's Conjecture
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164
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Chapter
11. Properties of the sequence nθ (mod 1)
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166
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Chapter
12. Discrepancy and Dispersion
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167
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Chapter
13. Connections with Ergodic Theory
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168
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Chapter
14. PSEUDO-RANDOM NUMBER GENERATION
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169
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Chapter
15. FORMAL LANGUAGE THEORY
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169
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Chapter
16. Other Results
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170
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Chapter
17. Related Results
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171
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Chapter
18. ACKNOWLEDGMENTS
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171
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Bibliography
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172
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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189
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Chapter
GENDER AND MATHEMATICS EDUCATION Key issues and questions Discussion Document for an ICMI Study
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189
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Chapter
1. Rationale for the study
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189
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Chapter
2. Factors generating gender inequities in mathematics
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191
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Chapter
3. Manifestations of gender inequities
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193
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Chapter
4. FOCI FOR CHANGE
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194
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Chapter
5. Call for papers
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197
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Bibliography
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198
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Back matter
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Back matter
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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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199
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Front matter
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200
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Article
KREISPACKUNGEN UND TRIANGULIERUNGEN
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201
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Preface
1. EINLEITUNG
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201
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Chapter
2. VORBEREITUNGEN
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202
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Chapter
3. Die funktion L: W → R
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207
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Chapter
4. IMMERSIERTE KREISPACKUNGEN
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211
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Chapter
5. Randwinkel
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216
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Bibliography
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217
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Article
POLYNÔMES HOMOGÈNES RÉELS AVEC GRADIENT À SINGULARITÉ ISOLÉE
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219
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Abstract
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219
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Chapter
1. Introduction
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219
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Chapter
2. Exemples et cas particuliers
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220
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Chapter
3. Enoncés des résultats
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224
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Chapter
4. Preuves
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225
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Bibliography
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231
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Article
NOTES SUR L'INVARIANT DE CASSON DES SPHÈRES D'HOMOLOGIE DE DIMENSION TROIS
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233
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Chapter
1. Enoncé des résultats
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234
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Chapter
2. DÉMONSTRATION DE LA PROPOSITION (1.3)
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238
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Chapter
3. Construction de l'invariant de Casson
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244
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Chapter
4. DÉMONSTRATION DES PROPRIÉTÉS 1) ET 2) DE L'INVARIANT DE CASSON
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256
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Appendix
Appendice A Polynôme d'Alexander et forme quadratique d'un entrelacs orienté: Formule de Conway et invariant de Robertello
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267
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Appendix
Appendice B L'INVARIANT DE CASSON D'UN NŒUD DE GENRE 1 À SURFACE DE SEIFERT DÉNOUÉE
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270
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Chapter
I. Représentations irréductibles d'un groupe libre À DEUX GÉNÉRATEURS
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270
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Chapter
II. Un ouvert de représentations irréductibles DU GROUPE FONDAMENTAL D'UNE SURFACE DE GENRE 2
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272
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Chapter
III. DÉMONSTRATION DU THÉORÈME B.l
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274
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Appendix
Appendice C Un calcul élémentaire de l'invariant de Casson des sphères d'homologie entière fibrées de Seifert à trois fibres exceptionnelles
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276
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Chapter
§0. Introduction
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276
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Chapter
§1. Présentation des espaces et énoncé du théorème
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277
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Chapter
§2. Scindement de Heegaard de $\Sigma(a_1,a_2,a_3)$
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279
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Bibliography
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288
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Article
AUTOMATIC GROUPS: A GUIDED TOUR
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291
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Chapter
1. Background in geometric group theory
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291
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Chapter
2. The beginnings of automatic groups
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293
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Chapter
3. Finite state automata
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294
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Chapter
4. Automatic groups : definitions and examples
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296
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Chapter
5. Hyperbolic groups are automatic
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303
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Chapter
6. INTERESTING PROPERTIES
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307
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Chapter
7. Related topics, open problems, and a vision of the future
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309
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Bibliography
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312
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Article
TOEPLITZ SEQUENCES, PAPERFOLDING, TOWERS OF HANOI AND PROGRESSION-FREE SEQUENCES OF INTEGERS
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315
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Abstract
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315
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Chapter
1. Toeplitz sequences
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315
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Chapter
2. Paperfolding sequences and Toeplitz transforms
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317
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Chapter
3. Iteration of continuous functions and Toeplitz transforms
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319
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Chapter
4. Towers of Hanoi and Toeplitz sequences
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320
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Chapter
5. Progression-free sequences and Toeplitz sequences
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320
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Chapter
6. MISCELLANEOUS QUESTIONS
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321
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Bibliography
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326
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Article
RATIONALITY OF PIECEWISE LINEAR FOLIATIONS AND HOMOLOGY OF THE GROUP OF PIECEWISE LINEAR HOMEOMORPHISMS
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329
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Chapter
Introduction
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329
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Chapter
§1. Lemmas
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330
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Chapter
§2. Discontinuous invariants
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332
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Chapter
§3. Homology of the group of piecewise linear homeomorphisms
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334
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Chapter
§4. Construction of cocycles of the group $PL_c(R)$
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336
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Chapter
§5. SURJECTIVITY OF $(j_+)_\star$
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339
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Bibliography
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344
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Article
BARKER SEQUENCES AND DIFFERENCE SETS
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345
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Chapter
Introduction
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345
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Chapter
0. Preliminaries
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347
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Chapter
1. DIFFERENCE SETS
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348
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Chapter
2. Periodic Barker sequences
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353
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Chapter
3. Barker sequences
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361
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Chapter
4. The use of the Multiplier Theorem
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364
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Chapter
5. COMMENTS ON THE EXAMPLES IN TABLES II
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373
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Bibliography
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381
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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41
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Front matter
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Index
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Back matter
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Back matter
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Back matter
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