Numerical Analysis

Numerical Analysis courses at SMA

Contact person: Professor Marco Picasso

Bachelor (3rd semester) :

• Analyse numérique (Buffa/Kressner)

Bachelor (5th and 6th semesters) :

• Advanced numerical analysis (Picasso)
• Continuous optimisation (Boumal)
• Introduction to PDEs (Colombo)
• Numerical approximation of pdes (Buffa)

Master (not always given):

• Stochastic simulation (Nobile)
• Computational linear algebra (Kressner)
• Randomized matrix computations (Kressner)
• Numerical integration of stochastic differential equations (Nobile)
• Numerical methods for conservation laws (Licht)
• Numerics for fluids, structures and electromagnetics (Buffa)
• Optimization on manifolds (Boumal)
• Mathematics of Machine learning (Chizat)
• Numerical analysis and computational mathematics (Grigori)
• Error control in scientific modeling (Herbst)
• HPC for numerical methods and data analysis (Grigori)
• Numerical integration of dynamical systems (Bluementhal)

Description :Computational Science is a multidisciplinary field that uses computers to solve complex problems. Computational science includes mathematical modeling, numerical analysis, scientific computing, algorithms, computer science. Applications of computational science are numerical simulations (reconstructions/prediction of past/future events), model fitting, data analysis, optimization of known scenarios. Computational Science has strong mathematical links with analysis, probability and statistics.

Bachelor students interested in the Numerical Analysis/Scientific Computing/Computational Science track may choose:

- the Master of Mathematics with the Applied Mathematics orientation (90 credits),
- the Master of Applied Mathematics (ingéniérie mathématique in French, industrial internship, 120 credits),
- the Master of Computational Science and Engineering (120 credits).

Useful/related courses :

Bachelor

• Analyse fonctionnelle I (Buffoni)
• Equations differentielles ordinaires (Krieger)
• Equations aux dérivées partielles d'évolution (Buffoni)
• Mesure et intégration (Stubbe)

Master

• Optimal transport (Colombo)
• Dispersive PDEs (Widmayer)
• Computational finance (Pulido/Glau/Pasricha/Goel)
• Parallel and high performance computing
• Inequalities and trace theory for Sobolev space (Nguyen)

Related Minors :

• Computational Science and Engineering
• Financial Engineering