The aim of this course is to provide the necessary foundations for each student to be able to use the appropriate mathematical tools to develop well-founded reasoning and prove properties. It provides an overview of demonstration techniques, recurrence, bijections and algorithms, the basics of enumeration and combinatorics, divisibility, discrete structures and graphs, probabilities, modelling of classical laws, and random walks.

Ressources

• TD1 Correction TD1
  • Sum of the cubes - visual proof 1
  • Sum of the cubes - visual proof 2
  • Sum of the cubes - visual proof 3
• TD2 Correction TD2
  • Explaination about The Josephus Problem

• TD3 Correction TD3

• TD4 Correction TD4
  • Video about Catalan Numbers (in french)
  • Another one: Catalan Numbers (in english)
• TD5 Correction TD5