# Teaching

###### Introduction to model category structures, ETH Zurich

###### 2018 - 2020

Abstract: The goal of this seminar is to get an introduction to model structures through different examples

such as topological spaces, simplicial sets or chain complexes. To get further into this theory, we develop

the notion of derived functors with applications to homotopy limits and colimits. This seminar is destined

to master students and takes the form of a working group. The participants have to give didactic

presentations.

###### Mathematics for engineers, Exercise sessions (12 hours), Paris 13

###### 2015 - 2016

Abstract: This course is destined for students in telecommunication with alternating practical periods in

a company. The goal is to introduce basic notions of arithmetic progressions, series, function series, power

series as well as the theory of integration. At the end of this course, students are expected to be familiar

with Fourier series and their applications to signal processing.

###### Analysis, Lectures/Exercise sessions (72 hours), Paris 13

###### 2015 - 2016

Abstract: This course is split into three parts. First, we remind the students of the notions of complex

numbers and roots of unity. Then we introduce abstract notions of functions as graphs and the study of

usual functions (exponential, logarithm, trigonometric functions...). Finally, the last part is devoted to the

theory of integration and differential linear equations of rank 1.

###### Formal language, Lectures/Exercise sessions (42 hours), IUT of Villetaneuse

###### 2012 - 2015

Abstract: This course is split into three parts. The first one consists in introducing some basic notions

of logic (such as propositions, quantifiers, predicates...). The purpose is to get the students accustomed

to the mathematical language. Thereafter, we introduce different ways to proof statements (by induction,

reduction to absurdity, case-based reasoning...). The last part is devoted to the notions of partial/total

orders, equivalence relations and a short introduction to graph theory.

###### Graphs and languages, Lectures/Exercise sessions (42 hours), IUT of Villetaneuse

###### 2013 - 2015

Abstract: This course follows up the previous one about the formal language. The purpose is to get

the students in computer science accustomed to algorithms used in graph theory such as the four color

algorithm. The students are expected to be able to program basic algorithms in C++ and to program

automata that recognizes strings containing some patterns.

###### Linear algebra, Exercise sessions (36 hours), IUT of Villetaneuse

###### 2012 - 2013

Abstract: This course is destined for students in computer science. The purpose is to get the students to

accustomed to algorithms such as Gaussian elimination, linear regression... First, we give the definitions of

vector spaces and linear maps. Then, we introduce the notions of systems of linear equations and matrices

using the geometrical point of view (intersections of hyperplanes). We also introduce the determinant,

rank-nullity theorem and basis completion theorem.