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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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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: LA CONJECTURE abc
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3
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Chapter: 1. Introduction
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3
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Chapter: 2. La conjecture abc
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4
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Chapter: 3. Applications de la conjecture abc
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6
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Chapter: 4. A LA RECHERCHE DE FORMES EFFECTIVES
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15
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Chapter: 5. GÉNÉRALISATIONS
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20
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Bibliography
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22
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Article: DOUBLE VALUED REFLECTION IN THE COMPLEX PLANE
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25
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Chapter: Introduction
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25
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Chapter: 1. Double valued reflection
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26
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Chapter: 2. Conic sections
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29
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Chapter: 3. The intrinsic theory: genus zero
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33
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Chapter: 4. Riemann maps
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36
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Chapter: 5. INVOLUTIONS ON A TORUS
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40
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Chapter: 6. Embedding of tori
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43
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Chapter: 7. A RECTANGULAR LATTICE
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46
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Bibliography
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48
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Article: KLYACHKO'S METHODS AND THE SOLUTION OF EQUATIONS OVER TORSION-FREE GROUPS
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49
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Abstract
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49
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Chapter: 1. Introduction
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50
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Chapter: 2. The crash theorems
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52
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Chapter: 3. TWO TRANSVERSALITY LEMMAS
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57
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Chapter: 4. Application to the Kervaire problem
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61
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Chapter: 5. The general case
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67
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Chapter: 6. Further Applications
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71
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Bibliography
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73
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Article: CENTRALISERS IN THE BRAID GROUP AND SINGULAR BRAID MONOID
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75
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Abstract
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75
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Chapter: 1. Introduction and Basic Definitions
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75
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Chapter: 2. Commutation and stabilisers
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80
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Chapter: 3. Proof of Theorem 2.2
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82
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Chapter: 4. Centralisers of braid subgroups
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84
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Chapter: 5. The singular braid monoid and the map η
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87
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Chapter: 6. Results regarding injectivity of η
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89
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Chapter: 7. Centralisers in $SB_n$
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94
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Bibliography
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95
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Article: MOYENNES SUR CERTAINS ENSEMBLES DE DIVISEURS D'UN ENTIER
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97
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Abstract
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97
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Chapter: 1. Introduction
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97
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Chapter: 2. Propriétés arithmétiques de $\bar{f}$, $\hat{f}$ et $\tilde{f}$
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100
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Chapter: 3. Valeurs moyennes de $\bar{f}$, $\hat{f}$ et $\tilde{f}$
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106
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Chapter: 4. Mesure de l'écart entre f et les moyennes $\bar{f}$, $\hat{f}$ et $\tilde{f}$
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113
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Chapter: 5. GÉNÉRALISATIONS ET EXEMPLES
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115
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Bibliography
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122
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Article: EMPILEMENTS DE CERCLES ET REPRÉSENTATIONS CONFORMES: une nouvelle preuve du théorème de Rodin-Sullivan
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125
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Chapter: I. Introduction
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125
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Chapter: II. Le Théorème de Rodin-Sullivan : ÉNONCÉ ET SCHÉMA DE LA PREUVE
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126
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Chapter: IV. Estimations à priori des rayons
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135
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Chapter: V. Changement de variable
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139
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Chapter: VI. Inégalité de Harnack
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142
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Chapter: VII. Commentaires
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149
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Chapter: 1. Sur l'inégalité de Harnack
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149
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Chapter: 2. Sur le théorème de Rodin-Sullivan
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150
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Bibliography
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151
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Article: UNIFORM DISTRIBUTION ON DIVISORS AND BEHREND SEQUENCES
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153
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Chapter: 1. DEFINITIONS AND BASIC RESULTS
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153
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Chapter: 2. Functions of moderate growth
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164
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Chapter: 3. Functions of excessive growth: the case $f(d) = d^\alpha$
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174
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Chapter: 4. FUNCTIONS OF EXCESSIVE GROWTH : THE CASE f(d) =θd
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180
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Chapter: §5. Additive functions
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190
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Chapter: 6. Metric results
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193
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Bibliography
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196
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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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Issue 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Article: ON THE GAUSS-BONNET FORMULA FOR LOCALLY SYMMETRIC SPACES OF NONCOMPACT TYPE
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201
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Abstract
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201
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Chapter: Introduction
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201
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Chapter: 1. The formula of Allendoerfer and Weil
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203
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Chapter: 2. An exhaustion of locally symmetric spaces
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204
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Chapter: 2.1. Reduction theory and geometry at infinity
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204
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Chapter: 2.2. An exhaustion by polyhedra
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207
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Chapter: 3. ESTIMATES FOR THE BOUNDARY SUBPOLYHEDRA
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209
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Chapter: 4. A NEW PROOF OF THE GAUSS-BONNET FORMULA
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212
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Bibliography
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213
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Article: INTRODUCTORY NOTES ON RICHARD THOMPSON'S GROUPS
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215
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Chapter: §1. Introduction to F
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216
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Chapter: §2. Tree diagrams
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218
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Chapter: §3. Presentations for F
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225
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Chapter: §4. Further properties of F
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227
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Chapter: §5. Thompson's group T
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233
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Chapter: §6. Thompson's group V
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240
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Chapter: §7. Piecewise integral projective structures
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248
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Bibliography
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254
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Article: SQUARE-FREE TOWER OF HANOI SEQUENCES
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257
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Abstract
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257
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Chapter: 0. Square-free strings and the Olive sequence
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257
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Chapter: 1. A FINITE ALPHABET
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260
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Chapter: 2. Smaller alphabets
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262
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Bibliography
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263
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Article: CHARACTERISTIC CLASSES, ELLIPTIC OPERATORS AND COMPACT GROUP ACTIONS
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265
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Chapter: 0. Introduction
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265
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Chapter: 1. CHARACTERISTIC CLASSES AND MULTIPLICATIVE SEQUENCES
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266
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Chapter: 2. The index of an elliptic complex
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271
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Chapter: 3. The Lefschetz fixed point formula
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277
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Chapter: 4. The Lefschetz Theorem for foliated manifolds
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282
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Chapter: 5. Group Actions and the Lefschetz Theorem
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287
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Chapter: 6. The Rigidity Theorem of Witten
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290
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Bibliography
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292
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Article: BARBIER'S THEOREM FOR THE SPHERE AND THE HYPERBOLIC PLANE
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295
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Chapter: 1. Introduction
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295
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Chapter: 2. Curves of constant width in the euclidean plane
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297
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Chapter: 3. Geodesic parallel coordinates
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302
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Chapter: 4. Proof of the main results
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307
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Bibliography
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308
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Article: SYSTEMS OF CURVES ON A CLOSED ORIENTABLE SURFACE
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311
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Chapter: 1. Introduction
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311
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Chapter: 2. Necessary conditions
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315
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Chapter: 3. SUFFICIENCY FOR A SINGLE HOMOLOGY CLASS
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317
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Chapter: 4. SUFFICIENCY FOR INDEPENDENT HOMOLOGY CLASSES
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319
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Chapter: 5. Disjoint simple closed curves on a planar surface
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320
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Chapter: 6. SUFFICIENCY IN THEOREM 3
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324
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Chapter: 7. Various instructive examples
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332
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Chapter: 8. Some Final Observations
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335
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Bibliography
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339
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Article: THE ZERO-IN-THE-SPECTRUM QUESTION
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341
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Abstract
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341
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Chapter: 1. Introduction
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341
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Chapter: 2. DEFINITION OF $L^2$ -COHOMOLOGY
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343
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Chapter: 3. General Properties of $L^2$-Cohomology
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351
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Chapter: 4. Very Low Dimensions
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358
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Chapter: 4.1 One Dimension
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358
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Chapter: 4.2 Two Dimensions
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361
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Chapter: 5. Universal Covers
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362
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Chapter: 5.1 Big and Small Groups
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363
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Chapter: 5.2 Two and Three Dimensions
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365
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Chapter: 5.3 Four Dimensions
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367
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Chapter: 5.4 More Dimensions
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369
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Chapter: 6. Topologically Tame Manifolds
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372
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Bibliography
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375
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Article: IN DEFENSE OF EULER
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377
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Bibliography
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382
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Article: FACTOR EQUIVALENCE RESULTS FOR INTEGERS AND UNITS
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383
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Abstract
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383
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Chapter: 1. Introduction
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383
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Chapter: 2. Factorizability and factor equivalence
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384
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Chapter: 3. Rings of integers
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386
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Chapter: 4. S-UNITS
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387
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Chapter: 5. Applications
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391
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Bibliography
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393
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Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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395
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Article: UNDERSTANDING THE PROCESSES OF ADVANCED MATHEMATICAL THINKING
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395
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Chapter: Introduction
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395
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Chapter: THE DEVELOPMENT OF MATHEMATICAL THINKING
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395
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Chapter: compression of knowledge in mathematics
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398
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Chapter: VISUALISING MATHEMATICAL CONCEPTS
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400
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Chapter: USING SYMBOLISM TO COMPRESS PROCESS INTO CONCEPT
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404
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Chapter: SEQUENTIAL AND PROCEDURAL COMPRESSION
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406
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Chapter: transition to formal mathematics
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407
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Chapter: Can we teach students to "think mathematically" ?
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410
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Chapter: Reflections on mathematical thinking
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412
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Bibliography
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413
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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27
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Back 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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