# Conférences et Activités ### Mathematical Induction: Pascal and Fermat

(Shahab Shahabi, Dawson College)

Résumé:  We will start with mathematical induction, exploring its different guises: simple induction, double induction, strong induction, (and “attach and retreat” in induction, given the time).

As one of the main statements dealt with using induction is Binomial Theorem, in the second part of the talk we will supply its proof, and if time permits, give a few applications.

In the last part of the talk, we would discuss some elementary number theory. Here “Fermat’s Little Theorem” is a good fit. Using induction we will give a relatively short proof, which has the added advantage that it is independent from the theory of congruence relations.

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### La méthode de l’induction en mathématiques.

(Richard Fournier, Dawson College)

Résumé:   Après quelques explications sur le principe d’induction, je donnerai des preuves par induction de certaines identités et inégalités élémentaires.

### Graph theory

(Ben Seamone, Dawson College)

Résumé: What is the fewest number of colours required to colour the regions in a geo-political map so that no regions sharing a border receive the same colour?  How can you solve a complicated scheduling problem?  How does information spread in a network?  How can mobile networks be efficiently constructed so that information can be communicated quickly?  All of these questions can be formulated in the language of a branch of mathematics known as graph theory.  After learning some basic definitions and terminology, we will explore some classic problems in graph theory, including some problems that are still unsolved.

### Combinatoire Énumérative et Probabilité

(Alexander Hariton, Dawson College)

Résumé: Nous discuterons des fondements élémentaires de la combinatoire énumérative, y compris les permutations, les combinaisons et certains principes de base d’énumération. Nous introduirons également le concepte de probabilité et nous appliquerons les méthodes d’énumération à des problèmes de probabilité discrète.

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