Semester 1 | Master of Applied Mathematics - Grenoble

Applied probability and Statistics

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

Credits

6 ECTS, CM 22.5h, TD 18h, TP 9h

Instructor

Frédérique Leblanc and Clémentine Prieur

Description

The aim of this course is to provide basic knowledge of applied probability and an introduction to mathematical statistics.

Applied probability

Estimation (parameter)

Sample comparison

Statistical tests

This course includes practical sessions.

Assessment

1/2 for the applied proba part 1/2 for the statistics part

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.

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