Coursebooks 2017-2018

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Combinatorial geometry

MATH-402

Lecturer(s) :

Pach János

Language:

English

Summary

Can we plant n trees in an orchard, not all along the same line, so that every line determined by two trees will pass through a third? This was raised by Sylvester and has generated interest among mathematicians. It led to the birth of combinatorial geometry with ties to convexity and graph theory.

Content

The course offers an introduction to this rapidly developing field, where combinatorial and probabilistic (counting) methods play a crucial role.

Topics: Extremal graph theory, Repeated distances in space, Arrangements of lines and curves, Geometric graphs, Epsilon nets, Discrepancy theory, Applications in computational geometry.

Keywords

forbidden graph, hypergraph, incidence, arrangement, Vapnik-Chervonenkis dimension, random sampling

Learning Prerequisites

Required courses

Discrete Mathematics

Recommended courses

Probability Theory

Important concepts to start the course

graph, planar graph, random variable, expected value, variance

Teaching methods

Lectures, exercises

Expected student activities

Solving homework problems, answering questions during lecture and exercise sessions

Assessment methods

Written

Supervision

Office hours Yes
Assistants Yes

Resources

Bibliography

J. Pach and P. Agarwal: Combinatorial Geometry,
J. Matousek: Lectures on Discrete Geometry

Ressources en bibliothèque

In the programs

  • Applied Mathematics, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Combinatorial geometry
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Combinatorial geometry
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Combinatorial geometry
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Combinatorial geometry
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Combinatorial geometry
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Combinatorial geometry
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9 BS260
9-10
10-11 BS260
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German