Master in Mathematics and Economic Decision

Brochure

Language of instruction English
Duration 2 years
ECTS 120
Program type Full-time education
Diploma National diploma

The two-years Master's program in Mathematics and Economic Decision is the Toulouse School of Economics Master in Applied Mathematics and Statistics. It benefits from the strength of both the TSE’s Mathematics and Economics departments. Interdisciplinarity is very important in recent developments in research, for example at the interface between optimization and statistics. These developments have wide and natural applications in economics and in the industry: artificial intelligence, big data, game theory, high-dimensional analysis, machine learning, network analysis, stochastic analysis, etc.

The first year is dedicated to acquiring a broad and rigorous knowledge in mathematics and statistics and its applications to economics.

The second year is targeted to students interested in research-based training in Applied Mathematics and Statistics. It is offered in partnership with the Master’s in Research and Innovation at Université Toulouse III - Paul Sabatier. For students aiming at a PhD in Applied Mathematics and Statistics at TSE, this is the first year of a PhD program in the north American system and the first year of the doctoral program in Applied Mathematics and Statistics at TSE. The program faculty provides assistance to these students to obtain funding and be paid for the remaining years of the PhD. The availability of courses from the departments of Economics, in particular from the doctoral track in Economics, and Computer Science allows to engage in PhD.s with a strong interdisciplinary aspect.

The second year of the Master is also a good fit for a student who prefers a professional integration directly after the Master and positions requiring a strong methodological research-based training, for example as a mathematical engineer with a strong background in Economics.

Alternatively, after the first year, the students may apply to other second year Master’s programs at TSE. The second year of the Master in Data Science for Social Science is particularly suited for a professional integration after the Master. Students who are interested in the PhD. in Economics may apply to the Economic Theory and Econometrics second year master.

The program is certified by ANITI, the Artificial Intelligence hub in Toulouse. Various professors hold ANITI research chairs.

Program 2026-2027

M1 "Applied Mathematics, Statistics" - Mathematics and Economic Decision - International track

(Syllabi are updated regularly; these documents are not binding)

SEMESTER 1	SEMESTER 2
Compulsory courses: Advanced Analysis Probability and Statistics for Data Science Introduction to Convex Optimization for Machine Learning* Intermediate Econometrics * Computational Data Science (Python)* FLE Professional Development	Compulsory courses: Foundations of Machine Learning Mathematical Game Theory FLE Compulsory only if you choose the track Towards the second year of master MED below: Games and Convergence to Equilibria (taught during Semester 1) Advanced Mathematics and Statistics
Electives: Choose 1 out of 5: Markov Chains and applications**** Macroeconomics Theory of Incentives Market Power & Regulation	Optional: Towards the second year of master MED track:* (3 electives from 7) Martingales Theory and Applications** Stochastic Methods for Optimization and Sampling Topics in AI Time series Dynamic Optimization Market Finance Corporate finance Econometrics and Economics Track:* (5 electives from 13) Games and Convergence to Equilibria (Taught during Semester 1) Advanced Mathematics and Statistics Stochastic Methods for Optimization and Sampling Topics in AI Martingales Theory and Applications** Dynamic Optimization Program Evaluation Time series Market Finance Advanced Macroeconomics Advanced Microeconomics Corporate Finance Industrial Organization
Optional : Math Camp: Algebra Refresher* Probability refresher* Static Optimization refresher* Econometrics refresher*	UE15 - Internship or Master Thesis++

SEMESTER 1

SEMESTER 2

Compulsory courses:

Advanced Analysis
Probability and Statistics for Data Science
Introduction to Convex Optimization for Machine Learning*
Intermediate Econometrics *
Computational Data Science (Python)*
FLE
Professional Development

Compulsory courses:

Foundations of Machine Learning
Mathematical Game Theory
FLE

Compulsory only if you choose the track Towards the second year of master MED below:

Games and Convergence to Equilibria (taught during Semester 1)
Advanced Mathematics and Statistics

Electives: Choose 1 out of 5:

Markov Chains and applications****
Macroeconomics
Theory of Incentives
Market Power & Regulation

Optional:

Towards the second year of master MED track:* (3 electives from 7)

Martingales Theory and Applications****
Stochastic Methods for Optimization and Sampling
Topics in AI**
Time series
Dynamic Optimization
Market Finance
Corporate finance

Econometrics and Economics Track:* (5 electives from 13)

Games and Convergence to Equilibria (Taught during Semester 1)
Advanced Mathematics and Statistics
Stochastic Methods for Optimization and Sampling **
Topics in AI **
Martingales Theory and Applications****
Dynamic Optimization
Program Evaluation **
Time series **
Market Finance**
Advanced Macroeconomics **
Advanced Microeconomics **
Corporate Finance**
Industrial Organization **

Optional : Math Camp:

Algebra Refresher***
Probability refresher***
Static Optimization refresher***
Econometrics refresher***

UE15 - Internship or Master Thesis++

* The student chooses to follow either the MED 2 track or the Econometrics and Economics track (leading to Year 2 of Economic Theory and Econometrics)

++ A minimum grade of 10 out of 20 is required.

** Masters 2 Directors recommend to attend some options:

Topics in AI or Stochastic Methods for Optimization and Sampling or Time Series: M2 D3S
Industrial Organization: M2 EMO
Corporate Finance et Market Finance: M2 Finance
Time Series et Program Evaluation: M2 EEE
Program Evaluation: M2 EEE, M2 ETE
Advanced Macroeconomics: M2 ETE
Advanced Microeconomics: M2 ETE

*** Mathematics refresher course, open to M1 and M2 students (see the announcement on the website for exact dates; courses are generally held in late August)
Courses Topics in AI and Stochastic Methods for Optimization and Sampling are only open to the first 45 applicants.

**** To select the “Martingales Theory and Applications” course in UE4, students must have previously taken the “Markov Chains and Applications” course in UE3

Bonus points

Participation in sports or cultural activities, civic engagement or work-related activities may be eligible for bonus points. For further details, please refer to the French assessment guidelines (MCC) for the course shown opposite.

Program 2026-2027

M2 Applied Mathematics, Statistics - Mathematics and Economic Decision International track
(Syllabi are updated regularly; these documents are not binding)

SEMESTER 3 - 4

Core courses:

Reading course (6 credits)

Each student is supervised by one of our faculty on working on a research level book and preparing a seminar and report on a particular aspect.

Here is a list of example of themes covered in previous years:

Optimal Transport and its Applications (J. Bolte) · American Options (S. Villeneuve)
Functional Data Analysis and Detection of Changes in the Mean Function (D. Paindaveine)
Reproducing Kernel Hilbert Spaces and Applications (C. Thomas)
Solutions of Stochastic Differential Equations (S. Villeneuve)
Ising Model and Mean Field Theory Solution in Economics and Social Sciences (A. Blanchet)
The Delegation Problem (D. Martimor)
A Theoretical Primer on the Neural Tangent Kernel (J. Chhor)
Langevin Diffusion as a Wasserstein Gradient Flow (S. Villeneuve)
Linearization of Dynamical Systems (J. Bolte)
Feynman-Kac Framework for Parabolic PDEs: Foundations and Application to Option Pricing (E. Votchkova)
Repeated Games (J. Renault and J. Hörner)

Advanced courses in 2026/2027

Games and Convergence to Equilibria (B. Ziliotto)
Advanced Mathematics and Statistics (Topic and professor TBA)
Diffusion Models in Generative AI (J. Chhor)
Prophet Inequalities (B. Ziliotto)
Advanced Topics in AI – Theory: Reinforcement Learning Theory/Sequential Learning (A. Azize))

Advanced courses in 2025/2026

Introduction to Nonsmooth Optimization (E.Pauwels)
Markov Decision Processes (S. Villeneuve)
Diffusion Models in Generative AI (J. Chhor)
Prophet Inequalities (B. Ziliotto)

Electives (total 30 credits):

Courses by invited professors
In 2026-2027:

Policy Gradient Methods and Large Language Models (G. Mahajan) (3 credits)

2 additional courses of 3 credits will be announced soon

In 2025-2026:

An Introduction to viscosity solutions with applications in Economics (A. Davini) (3 credits)
Strategic aspects of bandit models (E. Shmaya) (3 credits)
Functional Data Analysis (D. Paindaveine) (3 credits)

In 2024-2025:

Statistical theory of deep learning (J. Schmidt-Hieber)
Selected topics in nonsmooth optimization (G. Li)
Bi level optimization (D. Salas)

One course (6 credits) from Master Research and Innovation at University of Toulouse (among A4-A9): https://departement-math.univ-tlse3.fr/m2ri-syllabus-2026-2027

Courses in M1 MED, also available in M2

Advanced Analysis (S. Villeneuve) (3 credits), highly recommended for those admitted directly in M2 MED
Mathematical Game Theory (J. Renault) (3 credits)
Martingale Theory and Applications (J. Chhor and L. Miclo) (3 credits)

AI, Machine Learning, Econometrics and Statistics (")

Advanced Topics in AI – Applied: Graphs in Machine Learning (A. Azize) (3 credits)
Behavioral Science for Ethics in AI (JF Bonnefon) (3 credits)
Big Data Management with AI and Cloud Computing (3 credits)
Mathematics of Machine and Deep Learning Algorithms (E. Pauwels) (6 credits)
Optimization for Deep Learning (J. Bolte) (3 credits)
High-Dimensional Statistics and Econometrics (E. Gautier) (3 credits)
Econometrics 1 (P. Lavergne and E. Gautier) (6 credits)
Econometrics 2 (N. Meddahi and K. Jochmans) (6 credits)
Extreme Risk Analysis (A. Daouia) (3 credits)
Nonparametric Models (A. Daouia) (3 credits)
Survey Sampling (A. Ruiz-Gazen) (3 credits)
Graph Analysis (M. Hoffman) (3 credits)

(")
- Nonparametric Estimation is taught in Econometrics 1 and Nonparametric Models.
- Causal Inference is taught in High-Dimensional Statistics and Econometrics, Econometrics 1 and 2.
- Mathematical Game Theory in M1 is also useful for AI (multi-agent AI, reinforcement learning, online learning, calibration, and algorithmic game theory)

Economics and Mathematics

Game Theory (A. Sanktjohanser and S. Shahanaghi) (6 credits)
Topics in Econometrics and Empirical Economics (6 credits)
Optimization for Economics (D. Martimort and A. Smolin) (6 credits)
Stochastic Optimal Control in Economics (S. Villeneuve and JP. Decamps) (6 credits)

Economics

Economic Theory (T. Mariotti and A. Smolin) (6 credits)
Microeconomics 1 (F. Salanié and T. Mariotti) (6 credits)
Macroeconomics 1 (F. Collard and C. Hellwig) (6 credits)
Microeconomics 2 (P. Rey) (6 credits)
Advanced IO ( D. Jeon and A. De Cornière) (6 credits)
Structural Models and Policy Evaluation (O. De Groote) (6 credits)
Institutions and Political Economy (J. Miquel-Florensa) (6 credits)
Contract Theory (6 credits)
Empirical IO (3 credits)
Topics in Econometrics (3 credits)
Empirical and Structural Econometrics (P. Diegert) (3 credits)
Topics in Incentive Theory: Markets and Contracts (A. Attar) (3 credits)
Learning in Games (B. Ziliotto) (3 credits)
Learning and experimentation (J.Hörner) (3 credits)

Finance

Capital Markets (A. Guembel and F. Declerck) (6 credits)
Corporate Finance: Theory and Empirics (U. Hege and S. Rossetto) (6 credits)

Computer Science

Advanced Topics in Artificial Intelligence (F. Amblard, S. Cussat-Blanc, and U. Grandi) (6 credits)
Innovative Data Management (J. Aligon and J.-M. Thevenin) (6 credits)
Techniques du Décisionnel et Big Data (One course of your choice from UE3 Technologies du décisionnel of the Master 2 ISIADE) (3 credits)

Mandatory:

Master thesis or Internship, examples:

Signals on a Graph: Event-Centric GNN Forecasts of Pre-Earning Straddle P&L Prediction (Internship at BNP)
A Deep Learning Module for Brain Decoding and Encoding (Internship at Centre de Recherche Cerveau et Cognition)
Computable General Equilibrium Modelling in Environmental Economics (Internship at OECD)
Quasi-Gradient Systems and Metrics (thesis)
Accelerating Simulated Annealing via Optimal Transport (thesis)
Nonparametrics and Neural Networks: Minimax Rates & Implicit (thesis)
The Welfare Implications of Expanding the Action Space with Outside Option in Social Learning (thesis)
Beyond Large Support in Nonparametric Models of Causal Inference (thesis)

Optional:

Statistical Software: R
Statistical Software: Python

Math Camp:*

Algebra Refresher*
Probability Refresher*
Optimization Refresher*
Econometrics Refresher*
Economics refresher*

* Refresher course, open to M1 and M2 students (see the announcement on the website for exact dates; courses are generally held in late August)

Bonus points

At TSE, learning is enhanced by guest speakers, most of whom are professionals from various industries. These experts bring practical experience and real-world insights, complementing the teachings of our academic professors. This synergy provides students with a well-rounded education rooted in both theory and professional practice.

Semester 1 Master 2

Sylvia Gil Casals (Data Scientist at microsoft and INSA Toulouse), Mathematics of Machine and Deep Learning Algorithms + Data mining
Adil Zouitine (Teacher at ISAE Supaéro) Mathematics of Machine and Deep Learning Algorithms

Semester 2 Master 2

Rémi Périchon (Consultant Data AVISIA), Big Data

95% of graduates with a 5-year degree in mathematics find a job within six months, compared with only 80% of those who studied another discipline at university.

High-tech industries (energy, petroleum research, chemistry, etc.) have needs, also have major needs in the field of mathematics.
Consulting sector (survey institutes, consultancy firms, digital services companies, etc.) offers major employment opportunities for applied mathematics engineers, who are responsible for designing and operating databases.
Banking, insurance and finance sector is always on the lookout good mathematicians to calculate risks and minimise losses.

* Employment:
- Teacher-researcher in a university
- Preparation for 2nd level teaching exams: CAPES, agrégation.
- research engineers
- research engineers in mathematical modelling
- Applied mathematics engineer
- Statistical research manager in a banking or insurance company.
- Administrative entrance exam for the public sector and local authorities.
- Financial analysis and engineering
- Management and engineering studies, research and industrial development

Ressource in French to see job opportunities:

Ressource in English:

https://www.siam.org/Portals/0/Student%20Programs/Thinking%20of%20a%20Ca...

Admission is based on academic excellence.

Courses are entirely taught in English: a C1 English language certificate may be required depending on the applicant’s profile (IELTS Academic, TOEFL iBT or CAE).

Applicants who do not hold a degree obtained in the French higher education system are required to submit GRE test results.

Applications are submitted through TSE's eCandidatures platform.

First year admission:

TSE students may apply if they validated their undergraduate degree and have excellent results in Mathematics.

External students may apply if they successfully completed a BA or BSc in Economics and Mathematics.

Second year admission:

TSE students who passed their M1 MED will be automatically admitted. Students from other M1 programs may apply if they have excellent results in key subjects of the MED program.

External students may apply if they successfully completed a 4-year undergraduate degree or a Master’s degree in the fields of Economics and Mathematics.

Apply to the MED program