Study program – MAPPA: Mathematical Analysis and Probability

All students from both institutions spend the first year in Padova and the second year in PSL.
Three standard programs are available:
A – Program in Analysis
B – Program in Probability and Finance
C – Program in Probability and Statistical Mechanics

Individual study programs are also possible, see details below.

The following study programs are for actual MAPPA students, enrolled for the academic years 2024/2026. Minor changes are possible for the 2025/2027 edition.

A – Program in Analysis 2024/2026

First year in Padova

Year	Semester	Course	Italian SSD	ECTS
1	I	Differential Geometry	MAT/03	8
1	I	Introduction to Partial Differential Equations	MAT/05	6
1	I	Functions Theory	MAT/05	8
1	I	Stochastic Analysis	MAT/06	7
1	I / II	Non-linear Analysis OR Calculus of Variation	MAT/05	8
1	II	Partial Differential Equations 1	MAT/05	8
1	II/I	Partial Differential Equations 2 OR Harmonic Analysis	MAT/05	6
1	I/II	Dynamical Systems OR Symplectic Mechanics OR Numerical Methods for Differential Equations	MAT/07 - MAT/08	6-7
1		Student Seminar		4

Second year in PSL

Year	Semester	Course	ECTS
2	I	Recommended: A review of differential calculus for ODEs and PDEs	0
2	I	Recommended: A review of functional analysis tools for PDEs	0
2	I	Introduction to non-linear elliptic PDEs	6
2	I	Introduction to evolution PDEs	6
2	II	Variational problems and optimal transport	6
2	I/II	4 courses among the following (*): Introduction to dynamical systems; Continuous optimization; Dynamics of semi-linear wave equation; Variational and geodesic methods for image analysis; Numerical methods for deterministic and stochastic problems; Introduction to control theory; Spectral theory and variational methods; Introduction to control theory.	24
2	II	Research internship + final dissertation	18

* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.

B – Program in Probability and Finance 2024/2026

First year in Padova

Year	Semester	Course	Italian SSD	ECTS
1	I	Differential Geometry	MAT/03	8
1	I	Introduction to Partial Differential Equations	MAT/05	6
1	I	Stochastic Analysis	MAT/06	7
1	I	Introduction to Stochastic Processes	MAT/06	8
1	II	Advanced Stochastic Processes	MAT/06	7
1	II	Numerical methods for differential equations	MAT/08	7
1	II	Partial Differential Equations 2	MAT/05	6
1	II	Stochastic methods for finance	MAT/06 - SECS-S/06	7
1		Student Seminar		4

Second year in PSL

Year	Semester	Course	ECTS
2	I	Recommended: A review of differential calculus for ODEs and PDEs	0
2	I	Recommended: A review of probability theory foundations	0
2	I	Stochastic calculus	6
2	I	Numerical methods for deterministic and stochastic problems	6
2	I	Continuous-time Markov processes	6
2	I/II	4 courses among the following (*): Stochastic control; Rough paths and SDEs; Monte Carlo and finite difference methods with applications in finance; Valuation of financial assets by absence of arbitrage; Machine learning in finance; Mean-field game theory; Variational problems and optimal transport	24
2	II	Research internship + final dissertation	18

* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.

C – Program in Probability and Statistical Mechanics 2024/2026

First year in Padova

Year	Semester	Course	Italian SSD	ECTS
1	I	Differential Geometry	MAT/03	8
1	I	Introduction to Partial Differential Equations OR Function Theory	MAT/05	6-8
1	I	Stochastic Analysis	MAT/06	7
1	I	Introduction to Stochastic Processes	MAT/06	8
1	II	Advanced stochastic processes	MAT/06	7
1	II	Numerical Methods for Differential Equations	MAT/08	7
1	II	Partial Differential Equations 1	MAT/05	8
1	II	Symplectic Mechanics OR Advanced Mathematical Physics	MAT/07	6
1		Student seminar		4

Second year in PSL

Year	Semester	Course	ECTS
2	I	Recommended: A review of probability theory foundations	0
2	I	Limit theorems and large deviations	6
2	I	Continuous-time Markov processes	6
2	II	Introduction to statistical mechanics	6
2	I/II	4 courses among the following (*): Integrable probability and the KPZ universality class; Random walks and random media; High-dimensional probability; Determinantal processes, random matrices and hyperuniformity; Stochastic calculus	24
2	II	Research internship + final dissertation	18

* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.

D – Individual study programs

Individual study programs can be presented during the first semester of the program. In the first year, students have the possibility of including selected courses from the MSc in Data Science and from the MSc in Computational Finance at the University of Padova.
Please contact Prof. M. Cirant and C. Fontana in Padova or Prof. C. Toninelli in PSL to prepare your plan. Please note that all individual programs need to be approved and comply with Annex 1 of the MAPPA agreement.