Master in mathematics (académique)
The number next to every module is the sum of the ECTS of the compulsory courses. It is about the minimum of ECTS required for each module. The student will have to add the ECTS of the optional courses which he/she will join.
For more information, please contact the department secretary of the formation.
Semestre 1
| CM (UE) | TD (UE) | ECTS | |
| Module 1 | 12 | ||
| Commutative Algebra | 45 | 5 | |
| Differential Geometry | 45 | 5 | |
| Student Project as part of a compulsary or optional course | 60 | 2 | |
| Module 2 | 10 | ||
| Partial Differential Equations I | 45 | 5 | |
| Probability (Martingale Theory) | 45 | 5 | |
| Module 3 | 8 | ||
| Algorithmic Number Theory (optionnel) | 30 | 4 | |
| Applied Didactics of Mathematics I (optionnel) | 30 | 4 | |
| Basics of Discrete Mathematics (optionnel) | 30 | 4 | |
| Probabilistic Models in Finance (optionnel) | 30 | 4 | |
| TOTAL (cours obligatoire / cours optionnel) | 180 / 120 | 60 | 30 |
Semestre 2
| CM (UE) | TD (UE) | ECTS | |
| Module 1 | 12 | ||
| Complex Manifolds | 45 | 5 | |
| Homological Algebra | 45 | 5 | |
| Mathematics Seminar | 60 | 2 | |
| Module 2 | 10 | ||
| Partial Differential Equations II | 45 | 5 | |
| Probability (Stochastic Analysis) | 45 | 5 | |
| Module 3 | 8 | ||
| Algebraic Number Theory (optionnel) | 30 | 4 | |
| Applied Didactics of Mathematics II (optionnel) | 30 | 4 | |
| Introduction to Continuous Time Models in Mathematical Finance (optionnel) | 30 | 4 | |
| Introduction to Graph Theory (optionnel) | 30 | 4 | |
| TOTAL (cours obligatoire / cours optionnel) | 180 / 120 | 60 | 30 |
Semestre 3
option Financial Mathematics
| CM (UE) | TD (UE) | ECTS | |
| Module 1 | 15 | ||
| Advanced Stochastic Modeling and Financial Applications | 30 | 5 | |
| Continuous-time stochastic calculus and interest rate models | 30 | 5 | |
| SDE and PDE (Solving PDE by running a Brownian motion) | 30 | 5 | |
| Module 2 | 15 | ||
| Advanced econometrics (optionnel) | 40 | 15 | 6 |
| Numerical Methods in Finance (optionnel) | 30 | 5 | |
| Numerical Methods in Finance (optionnel) | 30 | 5 | |
| TOTAL (cours obligatoire / cours optionnel) | 90 / 100 | / 15 | 30 |
option General Mathematics
| CM (UE) | TD (UE) | ECTS | |
| Module 1 | 15 | ||
| Harmonic Analysis and Representation Theory | 30 | 5 | |
| Supergeometry | 30 | 5 | |
| Riemann Surfaces | 30 | 5 | |
| Module 2 | 15 | ||
| Groebner bases and applications (optionnel) | 30 | 5 | |
| Lie algebras and Lie groups (optionnel) | 30 | 5 | |
| Applied Didactics of Mathematics II (+ student project) * (optionnel) | 30 | 5 | |
| Internship in a Secondary School (1 month) * (optionnel) | 60 | 10 | |
| TOTAL (cours obligatoire / cours optionnel) | 90 / 150 | 30 | |
Semestre 4
option Financial Mathematics
| CM (UE) | TD (UE) | ECTS | |
| Module 1 | 10 | ||
| Fiber bundles and connections (optionnel) | 30 | 5 | |
| Algebra and Topology (optionnel) | 30 | 5 | |
| Stochastic Analysis, Fractional Processes and Applications to Finance | 30 | 5 | |
| Module 2 | 20 | ||
| Master Thesis | 0 | 20 | |
| TOTAL (cours obligatoire / cours optionnel) | 30 / 60 | 30 | |
option General Mathematics
| CM (UE) | TD (UE) | ECTS | |
| Module 1 | 10 | ||
| Fiber bundles and connections | 30 | 5 | |
| Algebra and Topology | 30 | 5 | |
| Module 2 | 20 | ||
| Master Thesis | 0 | 20 | |
| TOTAL (cours obligatoire) | 60 | 30 | |
| URL: http://wwwen.uni.lu/studies/fstc/master_in_mathematics_academique/programme2 | Date: Thursday May 24 2012 10:07:48 am |