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

Geometric modeling

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

Credits

6 ECTS, CTD 33h, TP 16.5h

Instructor

Boris Thibert

Description

This course is an introduction to the differential geometry of curves and surfaces with a particular focus on spline curves and surfaces that are routinely used in geometrical design softwares.

Differential geometry of curves

Approximation of curves with splines, Bézier and spline curves, algorithms,…

Differential geometry of surfaces, metric and curvature properties,…

This course includes practical sessions.

Assessment

1/2 practical

1/2 final written exam

Prerequisite

Elementary notions of linear algebra and analysis.

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.

Object-oriented & software design

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

Credits

3 ECTS, CTD 15h, TP 18h

Instructor

Laurence Pierre and Martin Schreiber

Description

This course is an introduction to the main concepts of object-oriented programming, elaborated on C++. It mainly considers: Basics on classes, instances, constructors and destructors, aggregation. Memory management, pointers, references. Operator overloading. Genericity, template classes. STL (Standard Template Library) objects. Inheritance, polymorphism. The objective of this course is to present the computer sciences basics useful for applied mathematics.

Assessment

1/2 practical 1/2 final written exam

Prerequisite

Good knowledge of C programming (including low-level concepts such as pointers and memory allocation)

Partial differential equations and numerical methods

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

Credits

6 ECTS, CM 16.5h, TD 16.5h, TP 16.5h

Instructors

Emmanuelle Crépeau

Eric Blayo, Ibrahim Cheddadi, Martin Schreiber

Description

Give an overview of modelling using partial differential equations.

Types of equations, conservation laws

Finite differences methods

Laplace equation

Parabolic equations (diffusion)

Hyperbolic equations (propagation)

Non linear hyperbolic equations

This course include practical sessions.

Course Organization

3ECTS = Lecture 16.5h + Lab 16.5h - Course Joined with Ensimag 2A 4MMMEDPS

3ECTS = Lecture 16.5h + Lab 1.5h - MSIAM specific course (in-depth and practical session)

Assessment

1/2 practical 1/2 final written exam

Prerequisite

Basic notions of real analysis, including Taylor formula
functions of several real variables
partial derivatives methods for solving first order ordinary differential equations (linear case, variation of constants method, separable ODEs…)
Basic notions on Fourier series and Fourier transform.

https://moodle.caseine.org/enrol/index.php?id=137

Signal and image processing

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

Credits

6 ECTS, CTD 33h, TP 16.5h

Instructor

Sylvain Meignen

Description

The aim of this course is to provide the basics mathematical tools and methods of image processing and applications.

Image definition Fourier transform, FFT, applications Image digitalisation, sampling Image processing: convolution, filtering. Applications Image decomposition, multiresolution. Application to compression This course includes practical sessions.

Assessment

1/2 practical 1/2 final written exam