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# M1 Course offer

### Object-oriented & software design (S7)

3 ECTS, CTD 12h, TP 24h

##### 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.

• 1/2 practical
• 1/2 final written exam
##### Prerequisite

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

### 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.

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

See the contents from the associated course at UPMF.

### 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
• 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)
• 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

### 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.

• 1/2 practical
• 1/2 final written exam

### 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.

• 1/2 practical
• 1/2 final written exam
##### Prerequisite

Elementary notions of linear algebra and analysis.

### Français langue étrangère

3 ECTS

French as a second language.

Organised by CUEF: cuef.xtek.fr

Important dates:

• Compulsory test: Sept 27th 6:00pm

### English

3 ECTS

English for french-speaking students.

### 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
• 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

### Modeling activity 1: Project (S8)

3 ECTS

January science and/or industrial project.

### 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

##### 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.

### 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
1. 3ECTS = CM 16.5h + TD 16.5h - Joined with Ensimag 2A 4MMMVAM (head: Emmanuel Maitre)
2. 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
1. 3ECTS = Lecture 16.5h + Lab 16.5h - Course joined with M1 MoSIG
2. 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
• Binary encoding of information
• Zn* group, field theory
• Symmetric cryptography
• Asymmetric cryptography, RSA
• Hash, DSA
• Lossless compression
• Error correcting codes
• Linear codes
• Cyclic codes

This course include practical sessions.

##### Organization
1. 3ECTS = TD 19h + TP 15h - Course joined with Pure Mathematics M1 (head: François Dahmani)
2. 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
1. Multiple linear regression. Least squares, Gaussian linear model, test of linear hypotheses, one-way analysis of variance.
2. Principal Components Analysis (PCA).
3. Classification, linear discriminant analysis, perceptron, Naive Bayes
4. 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
1. 3ECTS = Lecture 16.5h + Practical 7.5h + Lab 9h - Course Joined with Ensimag 2A (head: Jean-Baptiste Durand and Olivier Gaudoin)
2. 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
• What is OR?
• Linear Programming
• Duality
• Mixed Integer Programming
• Dynamic programming
• Constraint Programming
• Complexity theory and Scheduling
##### Organization
1. 3ECTS = CM 18h + TD 18h - Course joined with M1 MoSIG (Head: Nadia Brauner)
2. 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)
• Basics of statistics and probability
• Linear programming

## 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 