Mathematical Engineering

Plans d’études

Applied Mathematics 2024-25

Block 1

Courses

Language

Master 1

l

e

p

Master 2

l

e

p

Specialisations/Orientations

Exam

Credits / Coefficient

HSS : Introduction to project

/ Section SHS

Divers enseignants

FR/EN

-

-

-

-

-

-

Winter session

3

/ Section SHS

Divers enseignants

FR/EN

-

-

-

-

-

-

Summer session

3

Group 1

Courses

Language

Master 1

l

e

p

Master 2

l

e

p

Specialisations/Orientations

Exam

Credits / Coefficient

Mathematics projects (master)

MATH-498 / Section MA

Profs divers

FR

-

-

10h

-

-

10h

Winter/Summer session
During the semester

10

Group 2

Courses

Language

Master 1

l

e

p

Master 2

l

e

p

Specialisations/Orientations

Exam

Credits / Coefficient

Abstract analysis on groups

MATH-416 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Advanced analytic number theory (pas donné en 2024-25. Cours donné en alternance tous les deux ans)

MATH-521 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Algebraic geometry III - selected topics

MATH-535 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Algebraic geometry II - schemes and sheaves

MATH-510 / Section MA

Filipazzi, Mukhopadhyay

EN

4h

4h

-

-

-

-

Winter session
Written

10

Applied biostatistics

MATH-493 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
During the semester

5

Applied statistics

MATH-516 / Section MA

EN

-

-

-

1h

3h

-

a

Summer session
During the semester

5

MATH-449 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Calculus of variations (Cours donné en alternance tous les deux ans)

MATH-437 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Complex manifolds (Pas donné en 2024-25. Cours donné en alternance tous les deux ans)

MATH-473 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Written

5

Computational linear algebra (pas donné en 2024-25)

MATH-496 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Computational linear algebra

MATH-453 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Differential geometry IV - general relativity

MATH-530 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Oral

5

Diophantine approximation (pas donné en 2024-25)

MATH-540 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Oral

5

Dispersive PDEs (Cours donné en alternance tous les deux ans)

MATH-478 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Distribution and interpolation spaces (Cours donné en alternance tous les deux ans)

MATH-502 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Empirical processes

MATH-522 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

MATH-518 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Oral

5

Error control in scientific modelling

MATH-500 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Oral

5

Foundations of probabilistic proofs

CS-459 / Section IN

EN

4h

1h

-

-

-

-

a

Winter session
During the semester

6

Gaussian processes (pas donné en 2024-25)

MATH-426 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Oral

5

Gödel and recursivity (Cours donné en alternance tous les deux ans )

MATH-483 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Written

5

Harmonic analysis (pas donné en 2024-25. Cours donné en alternance tous les deux ans)

MATH-405 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Homotopical algebra (Pas donné en 2024-25)

MATH-436 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

HPC for numerical methods and data analysis

MATH-505 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Oral

5

Integer optimisation (pas donné en 2024-25)

MATH-504 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Introduction to dynamical systems

MATH-523 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Oral

5

Introduction to riemannian geometry (pas donné en 2024-25)

MATH-422 / Section MA

FR

-

-

-

2h

2h

-

Summer session
Oral

5

Introduction to stochastic PDEs

MATH-485 / Section MA

EN

-

-

-

3h

2h

-

a

Summer session
Oral

5

MATH-434 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Linear algebraic groups (Pas donné en 2024-25)

MATH-479 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Martingales in financial mathematics

MATH-470 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Oral

5

Mathematical modelling of behavior

MATH-463 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Metric embeddings (Pas donné en 2024-25)

MATH-513 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Written

5

Multivariate statistics

MATH-444 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Nonlinear Schrödinger equations (Pas donné en 2024-25)

MATH-514 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Nonparametric estimation and inference

MATH-524 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Number theory II.a - Modular forms

MATH-511 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Number theory II.b - selected topics (Cours donné en alternance tous les deux ans)

MATH-417 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Number theory II.c - Cryptography

MATH-489 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Numerical integration of dynamical systems

MATH-452 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Numerical integration of stochastic differential equations

MATH-450 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Numerical methods for conservation laws

MATH-459 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Oral

5

Numerics for fluids, structures & electromagnetics (Pas donné en 2024-25. Cours donné en alternance tous les deux ans.)

MATH-468 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Oral

5

Optimal transport (Cours donné en alternance tous les deux ans)

MATH-476 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Oral

5

Optimization on manifolds (Cours donné en alternance tous les deux ans.)

MATH-512 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
During the semester

5

Probabilistic methods in combinatorics

/ Section MA

EN

-

-

-

2h

2h

-

Summer session
Written

5

Randomized matrix computations (Cours donné en alternance tous les deux ans)

MATH-403 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Oral

5

Regression methods

MATH-408 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Representation Theory II - Lie groups and algebras

MATH-429 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Written

5

Representation theory of semisimple lie algebras (pas donné en 2024-25 - Cours donné en alternance tous les deux ans )

MATH-492 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Written

5

Riemann surfaces

MATH-410 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Written

5

MATH-318 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Written

5

Spectral theory (Cours donné en alternance tous les deux ans.)

MATH-561 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Oral

5

Statistical analysis of network data

MATH-448 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Statistical computation and visualisation

MATH-517 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
During the semester

5

Statistical inference

MATH-562 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Written

5

Statistical machine learning

MATH-412 / Section MA

Obozinski, Zemel

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Statistical mechanics and Gibbs measures (Pas donné en 2024-25. Cours donné en alternance une année sur deux.)

MATH-486 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Oral

5

Statistical theory

MATH-442 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Statistics for genomic data analysis (Cours donné en alternance tous les deux ans )

MATH-474 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
During the semester

5

Stochastic epidemic models (Pas donné en 2024-25)

MATH-560 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Stochastic simulation

MATH-414 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Written

5

Student seminar in pure mathematics

MATH-563 / Section MA

EN

2h

2h

-

-

-

-

Winter session
During the semester

5

Theory of stochastic calculus

MATH-431 / Section MA

EN

-

-

-

2h

2h

-

a

Summer session
Written

5

Topics in arithmetic geometry (Pas donné en 2024-25)

MATH-494 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Oral

5

Topics in high-dimensional probability

MATH-519 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
Oral

5

Topics in machine learning (Pas donné en 2024-25)

MATH-520 / Section MA

EN

2h

2h

-

-

-

-

a

Winter session
During the semester

5

Topics in stochastic analysis

MATH-487 / Section MA

EN

3h

2h

-

-

-

-

a

Winter session
Oral

6

Topology IV.a -Algebraic K-theory (Pas donné en 2024-25)

MATH-488 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Written

5

Topology IV.b - cohomology rings (Pas donné en 2024-25)

MATH-506 / Section MA

EN

2h

2h

-

-

-

-

Winter session
Written

5

Topology IV.b - homotopy theory

MATH-497 / Section MA

EN

-

-

-

2h

2h

-

Summer session
Written

5

Internship

Courses

Language

Master 1

l

e

p

Master 2

l

e

p

Specialisations/Orientations

Exam

Credits / Coefficient

Engineering internship (master in Applied Mathematics) (Stage d'au minimum 17 semaines après le 2ème semestre de Master. Inscription par la bourse aux stages)

MATH-596 / Section MA

Profs divers

FR

-

-

680h

-

-

680h

Winter/Summer session
During the semester

30

Master project

Courses

Language

Master 1

l

e

p

Master 2

l

e

p

MP Spring

l

e

p

MP Autumn

l

e

p

Exam

Credits / Coefficient

Engineering internship credited with master project (master in Mathematical Sciences) (Stage d'au minimum 8 semaines à partir du 3ème semestre de Master. Inscription par la bourse aux stages)

MATH-597 / Section MA

Profs divers

FR

-

-

320h

-

-

320h

-

-

320h

-

-

320h

Winter/Summer session
During the semester

0

Master project in Mathematics

MATH-599 / Section MA

Profs divers

FR/EN

-

-

-

-

-

-

-

-

900h

-

-

900h

Winter/Summer session
Oral

30