# Teaching

## Spring 2018

### Differential Geometry (1st year graduate students)

This term I am teaching assistant for the Differential Geometry course of Marco Mazzucchelli. The lectures are held in English. The course webpage is here.

The exercise sheets:

Here is an extra exercise giving the geometric interpretation of a connection on a vector bundle (.pdf,.tex) and its solution (.pdf,.tex).

And here is a summary of the formulas relating the different notions of curvatures (.pdf,.tex).

## Fall 2017

With Valentin Seigneur, we were teaching assistants for the Advanced geometry course of Jean-Claude Sikorav.

The lectures were held in English. Here are the exercise sheets:

• sheet 1: reminder on topology and calculus (.pdf,.tex).
• sheet 2: manifolds, differentiable maps (.pdf,.tex).
• sheet 3: tangent spaces, tangent maps (.pdf,.tex).
• sheet 4: submanifolds, partitions of unity (.pdf,.tex).
• sheet 5: vector fields (.pdf,.tex).
• sheet 6: Frobenius Theorem (.pdf,.tex).
• sheet 7: multilinear algebra (.pdf,.tex).
• sheet 8: differential forms, orientability (.pdf,.tex).
• sheet 9: exterior differential, Stokes Theorem (.pdf,.tex).

### "Classical" geometry course for the Agrégation

For the third year, I was instructor for the classical geometry course (affine, euclidean,...) for graduate students preparing the Agrégation, an advanced teaching qualification exam.

Here are some lecture notes. And the exercise sheets (in french):

• sheet 1: group actions (.pdf,.tex),
• sheet 2: semi-direct products (.pdf,.tex),
• sheet 3: affine spaces, barycenters (.pdf,.tex),
• sheet 4: affine subspaces (.pdf,.tex),
• sheet 5: affine independence, spanning families, frames (.pdf,.tex),
• sheet 6: affine maps (.pdf,.tex),
• sheet 7: affine group (.pdf,.tex),
• sheet 8: barycentric coordinates (.pdf,.tex),
• sheet 9: classical affine theorems (.pdf,.tex),
• sheet 10: isometries and similitudes in a EUclidean affine space (.pdf,.tex),
• sheet 11: complex numbers in geometry (.pdf,.tex),
• sheet 12: angles (.pdf,.tex),
• sheet 13: isometries and similitudes in a Euclidean affine space (.pdf,.tex),
• sheet 14: Euclidean geometry (.pdf,.tex),
• sheet 15: convexity (.pdf,.tex),
• sheet 16: separation, extremal points (.pdf,.tex),
• bonus: submanifolds (.pdf,.tex).

## Spring 2017

### Preparation for the Agrégation (graduate students)

Preparation of graduate students for the Agrégation (french advanced teaching qualification exam) written and oral exams.

## Fall 2016

### Smooth manifolds (1st year graduate students)

Teaching assistant for the Smooth manifolds course of Marco Mazzucchelli. Here is the course webpage.

Some exercise sheets (in french) :

• sheet 1: topology, calculus (.pdf,.tex),
• sheet 2: manifolds, smooth maps (.pdf,.tex),
• sheet 3: tangent spaces, differential (.pdf,.tex),
• sheet 4: submanifolds, embeddings (.pdf,.tex),
• sheet 5: Sard's theorem, transversality (.pdf,.tex).
• sheet 6: multilinear algebra (.pdf,.tex).
• sheet 7: vector bundles (.pdf,.tex).
• sheet 8: vector fields and Lie derivative (.pdf,.tex).
• sheet 9: differential forms and orientability (.pdf,.tex).
• sheet 10: exterior differential, Stokes and Frobenius theorems (.pdf,.tex).

### "Classical" geometry for the Agrégation

I taught classical geometry (affine, projective, euclidean) to graduate students preparing the Agrégation, an advanced teaching qualification exam.

Here are some lecture notes and the exercise sheets:

• sheet 1: group actions (.pdf,.tex),
• sheet 2: semi-direct products (.pdf,.tex),
• sheet 3: affine spaces, barycenter (.pdf,.tex),
• sheet 4: affine subspaces (.pdf,.tex),
• sheet 5: affine independence, spanning families, frames (.pdf,.tex),
• sheet 6: affine maps (.pdf,.tex),
• sheet 7: the affine group (.pdf,.tex),
• sheet 8: barycentric coordinates (.pdf,.tex),
• sheet 9: classical theorems (.pdf,.tex),
• sheet 10: complex numbers and geometry (.pdf,.tex),
• sheet 11: isometries and similarities in a Euclidean vector space, orthogonal group (.pdf,.tex),
• sheet 12: angles (.pdf,.tex),
• sheet 13: isometries and similitudes in a Euclidean affine space (.pdf,.tex),
• sheet 14: Euclidean geometry (.pdf,.tex),
• sheet 15: convexity (.pdf,.tex),
• sheet 16: separation, extremal points, projection on a convex set (.pdf,.tex),
• sheet 17: projective spaces, subspaces, spanning families (.pdf,.tex),
• sheet 18: homographies (.pdf,.tex),
• sheet 19: cross-ratio and homogeneous coordinates (.pdf,.tex),
• sheet 20: affine-projective relations (.pdf,.tex),
• bonus: submanifolds (.pdf,.tex).

## Spring 2016

### Preparation for the Agrégation (graduate students)

Preparation of graduate students for the Agrégation (french advanced teaching qualification exam) written and oral exams.

## Fall 2015

### Smooth manifolds (1st year graduate students)

Teaching Assistant for the Smooth manifolds course of Marco Mazzucchelli. Here is the course webpage.

Exercise sheets (in french) :

• sheet 1: manifolds, diffeomorphisms (.pdf,.tex),
• sheet 2: tangent spaces, differential (.pdf,.tex),
• sheet 3: submanifolds (.pdf,.tex).
• sheet 4: submanifolds continued (.pdf,.tex).
• sheet 5: multilinear algebra (.pdf,.tex).
• sheet 6: vector bundles (.pdf,.tex).
• sheet 7: vector fields and Lie derivative (.pdf,.tex).
• sheet 8: differential forms and orientability (.pdf,.tex).
• sheet 9: exterior derivative, Stokes and Frobenius theorems (.pdf,.tex).

And also the smooth structure on the Grassmannian (.pdf,.tex), still in french.

### "Classical" geometry for the Agrégation

I taught classical geometry (affine, projective, euclidean) to graduate students preparing the agregation, an advanced teaching qualification exam. The lecture notes by Florian Lavigne.

Exercise sheets (in french) :

• sheet 1: group actions (.pdf,.tex),
• sheet 2: affine spaces (.pdf,.tex),
• sheet 3: barycentric coordinates (.pdf,.tex).
• sheet 4: affine maps, semidirect product (.pdf,.tex).
• sheet 5: projective spaces, homographies, projective duality (.pdf,.tex).
• sheet 6: homographies and cross-ratio (.pdf,.tex).
• sheet 7: euclidean geometry, angles (.pdf,.tex).
• bonus: submanifolds (.pdf,.tex).

## Fall 2014

### Analyse 3 (Calculus, 2nd year undergrad)

Both exercice sessions and weekly oral examination in Calculus for 2nd year undergraduate students. Here are some related documents (in french).

Exercise sheets:

• sheet 1: integration (.pdf,.tex),
• sheet 2: series (.pdf,.tex),
• sheet 3: normed vector spaces (.pdf,.tex),
• sheet 4: topology of normed vector spaces (.pdf,.tex),
• sheet 5: limits and continuity in several variables (.pdf,.tex),
• sheet 6: calculus (.pdf,.tex),
• sheet 7: inverse function theorem, implicit function theorem, extrema (.pdf,.tex).

### Algèbre 5 (Group Theory, 3rd year undergrad)

Weekly oral examination in Group Theory for 3rd year undergraduate students.

## Spring 2014

### Techniques Mathématiques de Base (Basic Mathematics, 1st year undergrad)

Exercise sessions in Basic Mathematics for 1st year undergraduate students (majoring in Physics). Here are some documents (in french) related to these sessions.

Exercise sheets:

• sheet 1: complex numbers(.pdf,.tex),
• sheet 2: complex numbers 2 (.pdf,.tex),
• sheet 3: geometry (.pdf,.tex),
• sheet 4: linear algebra (.pdf,.tex),
• sheet 5: linear algebra 2 (.pdf,.tex),
• sheet 6: real analysis (.pdf,.tex),
• sheet 7: special functions (.pdf,.tex),
• sheet 8: mean value theorem, Taylor's formula (.pdf,.tex),
• sheet 9: integration (.pdf,.tex),
• sheet 10: linear differential equations (.pdf,.tex).

Homework assignments:

## Fall 2013

### Topologie Générale (Topology, 3rd year undergrad)

Weekly oral examination in Topology for 3rd year undergraduate students.

## Spring 2013

### Mathématiques 2 (Calculus, 1st year undergrad)

Exercises sessions in Calculus for 1st year undergraduate students (majoring in Physics).

Exercise sheets (in french):

• sheet 1: functions of several variables (.pdf,.tex),
• sheet 2: calculus 1 (.pdf,.tex),
• sheet 3: calculus 2 (.pdf,.tex),
• sheet 4: calculus 3 (.pdf,.tex),
• sheet 5: vector fields (.pdf,.tex),
• sheet 6: integration (.pdf,.tex),
• sheet 7: line integrals (.pdf,.tex),
• sheet 8: Green's theorem and surfaces integrals (.pdf,.tex),
• sheet 9: Gauss' and Stokes' theorems (.pdf,.tex).

Some lecture notes I wrote, and the source files .tar.gz (.tex and figures).

## Fall 2012

### Analyse 1 (Real Analysis, 1st year undergrad)

Weekly oral examination in Real Analysis for 1st year undergraduate students.