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Fiches de cours 2017-2018
Packing and covering
MATH-465
Enseignant(s) :
Langue:
English
Remarque
Pas donné en 2017-18 - Cours donnés en alternance tous les deux ansSummary
How many objects of a given shape and size can be packed into a large box of fixed volume? We give a systematic introduction into the rich theory that has grown out of the above questions. Connections to number theory, coding theory, potential theory, and robotics will also be presented.Content
- Geometry of numbers
- Approximation of convex sets by polygons
- Packing and covering with congruent convex discs
- Lattice packing and lattice covering
- The method of cell decomposition
- Methos of Blichfeldt and Rogers
- Efficient ramdom arrangements
Keywords
- Packing
- Covering
- Tiling
- Convexity
- Random
Learning Prerequisites
Required courses
- Linear Algebra
- Probability
Recommended courses
Discrete Mathematics of Graph Theory
Learning Outcomes
By the end of the course, the student must be able to:- Analyze the structure economic arrangements of congruent balls and other bodies in the plane and in the space.
- Prove the main theorems in the field.
- Explore how symetric configurations inevitably occur as best solutions of certain problems in geometric optimization.
- Use basic knowledge of constructions and estimates concerning good approximation of plane convex sets by polygons.
Transversal skills
- Use a work methodology appropriate to the task.
Teaching methods
Lectures and exercise sessions
Expected student activities
Solution of homework problems and other assignment
Assessment methods
Oral exam
Supervision
Office hours | Yes |
Others | Office hours Tuesday morning |
Resources
Bibliography
Pach-Agarwal: Combinatorial Geometry (Wiley)
Websites
Dans les plans d'études
- SemestreAutomne
- Forme de l'examenEcrit
- Crédits
5 - Matière examinée
Packing and covering - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- Crédits
5 - Matière examinée
Packing and covering - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- Crédits
5 - Matière examinée
Packing and covering - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- Crédits
5 - Matière examinée
Packing and covering - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- Crédits
5 - Matière examinée
Packing and covering - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- Crédits
5 - Matière examinée
Packing and covering - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
Semaine de référence
Lu | Ma | Me | Je | Ve | |
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8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
En construction
Cours
Exercice, TP
Projet, autre
légende
- Semestre d'automne
- Session d'hiver
- Semestre de printemps
- Session d'été
- Cours en français
- Cours en anglais
- Cours en allemand