S2 MAndatory | Master of Applied Mathematics - Grenoble

Computing science for big data and High Performance Computing

Mon, 01 Jan 0001 00:00:00 +0000

Credits

6 ECTS, CTD 33h, TP 16.5h

Instructors

Silviu Maniu and Martin Schreiber

Description

This course is composed of two parts “Introduction to database” and “High Performance Computing”. Its aim is to give an introduction to numerical and computing challenges of large dimension problems.

Content

Introduction to database
Introduction to big data
Introduction to high performance computing (HPC)
Numerical solvers for HPC

This course relies on practical sessions.

Prerequisites

C++, Python, Algorithm, Data-structure

Internship

Mon, 01 Jan 0001 00:00:00 +0000

Credits

3 ECTS

Instructor

Sylvain Meignen, Boris Thibert

Description

Industrial and/or research internship.

The students have to do an internship (of at least 8 weeks from mid May to end of August, see the planning) in a company or in a laboratory. No report is required (except for Ensimag students that follow the double diploma, who have to give a report to ensimag).

Modeling Project

Mon, 01 Jan 0001 00:00:00 +0000

Credits

3 ECTS,

Instructor

Marek Bucki

Numerical optimisation

Mon, 01 Jan 0001 00:00:00 +0000

Credits

6 ECTS, CTD 33h, TP 16.5h

Instructors

Hadrien Hendrikx and Ieva Petrulyonite

Description

This program provides the mathematical and numerical backgrounds for solving standard optimisation problems using (mostly) first-order methods, with a thorough understanding of which algorithm to choose when, how to tune the parameters, and what is the theory behind. Concrete examples will be investigating, and in particular the training of machine learning models.

Content

Introduction, classification, examples.
Theoretical results: convexity and compacity, optimality conditions, duality
Algorithmic for unconstrained optimisation (gradient descent, line search, stochastic methods)
Algorithms for non differentiable problems (prox, subgradient).

This course includes practical sessions in Python.

Prerequisites

Basic algebra (linear spaces, matrix computation) Basic calculus (Norm, Banach spaces, Hilbert spaces, basic differential calculus) The students should be able to compute the gradient and the Hessian of real functions on IR^n and also differentials of simple functions such as quadratic forms. Knowing how to code in Python is required to pass the course, as there will be graded practical sessions.