Coursebooks

Probabilistic methods

MATH-467

Lecturer(s) :

Pach János

Language:

English

Remarque

Cours donné en alternance tous les 2 ans (donné en 2018-19)

Summary

We systematically explore the exciting fact that randomness (i.e., coin flipping) can be used profitably to construct various mathematical structures with unexpected and often paradoxical properties, and to efficiently solve otherwise hopelessly difficult computational tasks.

Content

Keywords

random variable, expected value, probabilistic method, random graph, coloring

Learning Prerequisites

Required courses

Probability theory

Recommended courses

Discrete Mathematics or Graph Theory

Important concepts to start the course

Graph, random variable, expectation, variance, binomial coefficients, asymptotics

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Lectures and exercises

Expected student activities

Attending the lectures, solving the exercises, reading sections from the textbook

Assessment methods

Exam written

Supervision

Office hours Yes
Assistants Yes

Resources

Bibliography

Noga Alon-Joel Spencer: The Probabilistic Method (Wiley)

Stasys Jukna: Extremal Combinatorics (Springer)

 

In the programs

Reference week

 MoTuWeThFr
8-9  MAA330  
9-10    
10-11  MAA330  
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

legend

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