M1 Course offer
Object-oriented & software design (S7)
Objective
The objective of this course is to present the computer sciences basics useful for applied mathematics.
Content
Compilation (const, inline, loops, Gnu Make …)
C++: genericity (template), code reuse (STL), efficient programming
Objects and hierarchical memory, notions of cache and locality (e.g., BLAS)
Basics of algorithmics
Complexity
Error propagation, floating point computing
This course relies on practical sessions.
Grading
1/2 practical
1/2 final written exam
Prerequisite
Good knowledge of C programming (including low-level concepts such as pointers and memory allocation)
Course content
(head: Laurence Pierre)
Applied probability and Statistics (S7)
6 ECTS, CM 24h, TP 24h
Mutualized with M1 SSD Applied probability and Statistics
The aim of this course is to provide basic knowledge of applied probability and an introduction to mathematical statistics.
Contents:
Applied probability
Estimation (parameter)
Sample comparison
Statistical tests
This course includes practical sessions.
Grading:
See the contents from the associated course at UPMF.
Course content for probability
Course content for statistics
Partial differential equations and numerical methods (S7)
6 ECTS, CM 16.5h, TD 16.5h, TP 16.5h
Objectives
Give an overview of modelling using partial differential equations.
Content
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
Grading
1/2 practical
1/2 final written exam
Prerequisite
Basic notions of real analysis, including Taylor formula, functions of several real variables and 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
Course content (part 1)
Course content (part 2)
Signal and image processing (S7)
6 ECTS, CTD 36h, TP 18h
The aim of this course is to provide the basics mathematical tools and methods of image processing and applications.
Contents:
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.
Grading:
1/2 practical
1/2 final written exam
(head: Cécile Amblard)
Geometric modelling (S7)
6 ECTS, CTD 36h, TP 18h
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.
Content
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.
Grading
1/2 practical
1/2 final written exam
Prerequisite
Elementary notions of linear algebra and analysis.
(head: Boris Thibert)
Français langue étrangère
English
3 ECTS
English for french-speaking students.
(head: Virginia Gardner)
Computing science for big data an HPC (S8)
6 ECTS, CTD 18h, TP 36h
The aim of this course is to give an introduction to numerical and computing problematics of large dimension problems.
Content
This course relies on practical sessions.
(head: Christophe Picard)
Prerequisites
Modeling activity 1: Project (S8)
Modeling activity 2: Internship (S8)
3 ECTS
Industrial and/or research internship.
Numerical Optimization: mathematical background and case studies (S8)
6 ECTS, CTD 36h, TP 18h
This program combines case studies coming from real life problems or models and lectures providing the mathematical and numerical backgrounds.
Content
Introduction, classification, examples.
Theoretical results: convexity and compacity, optimality conditions, KT theorem
Algorithmic for unconstrained optimisation (descent, line search, (quasi) Newton)
Algorithms for non differentiable problems
Algorithms for constrained optimisation: penalisation, SQP methods
Applications and case studies
This course includes practical sessions.
Lab
Main results
(head: Laurent Desbat)
Prerequisite
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.
Présentation
Variational methods applied to modelling (S8)
Objectives
The aim of this course is to get deep knowledge of PDE modelling and their numerical resolution, in particular using variational methods such as the Finite Elements method.
Content
Introduction to modelling with examples.
Boundary problem in 1D, variational formulation, Sobolev spaces.
Stationary problem, elliptic equations.
Finite element method: algorithm, errors…
Evolution models, parabolic equations, splitting methods
Extensions and applications, FreeFEM++
This course include practical sessions.
A description of the course is available here
Organization
3ECTS = CM 16.5h + TD 16.5h - Joined with Ensimag 2A
4MMMVAM (head: Emmanuel Maitre)
3ECTS = CTD 3h + TP 18h - MSIAM specific course (in-depth and practical session) (head: Clément Jourdana)
Prerequisites
notions of distribution theory, linear algebra, integral calculus, some notions of programming in some high level language, basic numerical analysis, as numerical integration of differential equations, basic notions on Hilbert spaces, usual partial differential operators (gradient, divergence, laplacian…)
3D Graphics (S8)
Objectives
The aim of this course is to give mathematical grounds and algorithms for the modelling, animation, and synthesis of images.
Content
Projective rendering methods
Animation, cinematic methods
Geometrical modelling, 3D, deformation
Case study
This course include practical sessions. Implementation using OpenGL.
Organization
3ECTS = Lecture 16.5h + Lab 16.5h - Course joined with M1 MoSIG
3ECTS = Lecture 19.5h + Lab 1.5h - MSIAM specific course (in-depth and practical session)
A description of the course is available here
Prerequisites
Programming skills using a high level language
Computer Algebra and Cryptology (S8)
Objectives
The aim of this course is to give mathematical grounds of security, integrity, authentication and cryptology.
Course
This course include practical sessions.
Organization
3ECTS = TD 19h + TP 15h - Course joined with Pure Mathematics M1 (head: François Dahmani)
3ECTS = TD + TP - MSIAM specific course (in-depth and practical session) (head: Pierre Karpman)
A description of the course is available here
Statistical analysis and document mining (S8)
Objectives
The aim of this course is to present the statistical approaches for analysing multivariate data. The information age has resulted in masses of multivariate data in many different field: finance, marketing, economy, biology, environmental sciences,…The theoretical and practical aspects of multivariate data analysis are given equal importance. This balance is achieved through practicals involving actual data analysis using the R software.
Content
Multiple linear regression. Least squares, Gaussian linear model, test of linear hypotheses, one-way analysis of variance.
Principal Components Analysis (PCA).
Classification, linear discriminant analysis, perceptron, Naive Bayes
Text mining, numeric representation of texts, connexion with graph clustering.
Prerequisites
Elementary notions in probability theory (probability distribution, joint probability density function for random vectors, conditional distribution, expectation, variance, covariance, Gaussian distribution)
Elementary notions in mathematical statistics (estimator, confidence interval, statistical tests).
As a bonus: simple linear regression, linear algebra (matrix reductions), elementary notions in Rstudio and the R software.
Organization
3ECTS = Lecture 16.5h + Practical 7.5h + Lab 9h - Course Joined with Ensimag 2A (head: Jean-Baptiste Durand and Olivier Gaudoin)
3ECTS = Lecture 14h + Lab 6h - MSIAM specific course (in-depth and practical session) (head: Modibo Diabaté)
Introduction to Operations Research (S8)
Course objectives
The main objective of this course is to provide basics tools in operations research
Content
Organization
3ECTS = CM 18h + TD 18h - Course joined with M1 MoSIG (Head: Nadia Brauner)
3ECTS = CTD 14h + TP 6h - MSIAM specific course (in-depth and practical session) (Head: Franck Iutzeler)
Prerequisites
Classical algorithms (sort, divide and conquer)
Algorithms complexity calculation
Programming: basic notions (variables, fonctions, if, for, while, tables)
Language Python or Java
Basic notions on graphs (basic definitions, graph search, trees, shortest paths)
Basic notions on linear algebra and matrix analysis (matrix multiplication, invertible matrix definition)
ECTS total
30 ECTS per semester:
1st semester compulsory courses 27 ECTS
1st semester language course 3 ECTS
2nd semester compulsory courses 18 ECTS
2nd semester with choice 12 ECTS