Semester 1. Skills Courses Hours ECTS. Inferential Statistics 30. Data Analysis 24. Partial Differential Equations and Finite Differences 30

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1 1.1.1 M1 Curriculum The M1 provides the fundamental tools in Computer Science and Mathematics necessary for the M2. It is based on the three pillars characteristic to this master. As well as the fundamentals, students will be taught the essential elements of project management. This first year will culminate in a large transversal team project. The M1 is divided into two semesters. Each semester is worth 30 ECTS. Semester 1 Skills Courses Hours ECTS Data exploration Mathematics for Computer science Software and Architecture Inferential Statistics 30 Data Analysis 24 Partial Differential Equations and Finite Differences 30 Operational Research: Linear Optimization 20 Combinatory Optimization 18 Complexity theory 9 Object-Oriented Modelling (OOM) with UML 30 Object-Oriented Design and Programming with Java 30 Relational Database: Modelling and Design Engineering Science Research Initiation Initiative Modern languages Signal and System 21 3 Review a scientific paper 9 1 PPP 15 5 FFL: French and Foreign languages 40 Total M1: Semester Semester 2 Skills Courses Hours ECTS Mathematics Simulation and Stochastic Process 30 10

2 for Computer Science Introduction to Predictive Modelling 21 Deterministic and Stochastic Optimization 30 Introduction to Data Mining 21 Engineering science Signal processing 30 3 Software and Architecture PLSQL 21 Architecture and Network Programming 30 Parallel Programming 30 8 Project Management AGIL Methods & Transverse Project 21 2 Final research Final research project on BIG DATA 50 5 Languages French and Foreign languages 21 2 Total M1 : Semester Data exploration Inferential Statistics Lecturer: Marietta Manolessou Objective of the module The aim of this course is to present the principles and technical tools of Inferential Statistics. More precisely, by the end of the course the student will be able to analyze numerical data in large quantities, for the purpose of reaching conclusions in probabilities, based on the data in a representative sample. We study with the usual methods of estimations and tests. The techniques introduced are illustrated via a series of EXCEL tutorials Topic in detail Reminder on Probabilities (Random Variables, Random Vectors, Probability Distribution, Functions, Independence and Dependence of random Variables - Conditional Probabilities and Expectation values) Convergence, Limit theorems 1. Estimation - Proprieties of an estimator (Unbiased Estimator-Consistent and Efficient estimator) (Examples Exercises) - Usual estimators (Examples Exercises) - Maximum Likelihood estimation (Examples Exercises)

3 - Estimation by interval of confidence (Examples Exercises) 2. Hypothesis Testing - General principles (Examples Exercises) - Test of a usual level of significance (Examples Exercises) - Test of Variance (Examples Exercises) - Usual tests of comparison (one and two samples) (Examples Exercises) - Chi-square tests (Examples Exercises) Bibliography Probability Statistics and Queuing theory with Computer Science Applications, Arnold O. Allen, Academic Press, 1990 Maîtriser l aléatoire, Eva Cantoni, Philippe Huber, Elvezio Ronchetti, Springer, 2006 Mathematical Statistics with Applications, Kandethody, M. Ramachandran, Chris P. Tsokos, Elsevier, 2009 A Course in Mathematical Statistics, George G. Roussas, Academic Press, 1977 Probabilités Analyse des données et statistique, G. Saporta, Editions Technip Tutorial by M. Manolessou Websites > Statistique : course webpage : website featuring the Scilab programs : website featuring files containing statistics studies data : website featuring online classes : website of the free press review Modulad (Le Monde des Utilisateurs de L Analyse de Données) : website of the free online newspaper Electronic Journal of Statistics : website of the free online newspaper Electronic Journal of Applied Statistical Analysis : website of the free online newspaper InterStat : website of the free online newspaper Journal of Data Science : website of the free online newspaper Journal of Modern Applied Statistical Methods : website of the free online newspaper Journal of Statistical Software : website of the free online newspaper Statistics Surveys Data Analysis Lecturers: Hervé de Milleville and Marietta Manolessou Objective of the module In Descriptive Statistics, a population is studied on one or two variables. Data analysis or multidimensional data analysis is an extension to several Variable-descriptive Statistics. This course is a first approach to the different multidimensional analyses of methods used to examine large masses of information. We shall discuss three types of problems: descriptive analysis, explanatory models and classification. SAS software will be used on different data corpora.

4 At the end of the course, based on a corpus of multidimensional data, students will know how to: Identify which technique to use to solve a problem Prepare data sets to launch the associated technical program selected Interpret the results provided by the software However, this remains an introduction course; to go further, students will need to: Look more closely at the technical data preparation (very little discussed in this module) Explore some of the methods discussed Discover new methods of analysis The techniques introduced are illustrated during a series of tutorials via EXCEL Topic in detail General principles of factor analysis Analysis of Variance (Examples -Exercises) Simple Linear Regression (Examples -Exercises) Multiple Linear Regression (Examples Exercises) Correlation Analysis (Montgomery and Peck Theorem) (Examples Exercises) Non-Linear regression with transformed variables (Examples -Exercises) Principal Components Analysis Factorial correspondence analysis Bibliography Probability Statistics and Queuing theory with Computer Science Applications, Arnold O. Allen, Academic Press, 1990 Analyse des données, Michel Volle, Economica Probabilités Analyse des données et statistique, G.Saporta, Editions Technip Factor Analysis as a Statistical Method, Lawley, D.N., Maxwell, A.E., Butterworths Mathematical Texts, England, 1963 Multivariate Analysis, Mardia K.V., Kent J.T., Bibby J.M., Academic Press, London 1979 Printed tutorial by M. Manolessou Introduction to Data Mining Lecturer: Maria Malek Objective of the module This introductory course in data mining allows students to have a first approach of the problems and applications of data mining. It also lets students learn several models and their application on different types of data Topic in detail 1. Data Mining fields, Data Mining Process, Data Mining Tasks, Data and attribute natures. 2. Machine Learning: Supervised and unsupervised algorithms. Classification models, classifier validation methodology. Precision and recall measures, confusion matrix, and cross validation method.

5 3. Comparison of supervised and unsupervised models: K-nearest neighbours and K-means algorithms 4. Supervised machine learning methods: Candidate elimination and version space Decision Trees: ID3 and C4.5 algorithms Neural Networks 5. Association Rules: Apriori and AprioriTid algorithms Association rules generation Properties of simple and strict redundancy 7. Meta Learning: Bagging and Adaboost 8. Comparative study and discussion Bibliography Advances in Knowledge Discovery and Data Mining, Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy, AAAI/MIT Press, 1996 Data Mining: Practical machine learning tools and techniques, 2nd Edition, Ian H. Witten, Eibe Frank, Morgan Kaufmann, Introduction to Prediction Models Lecturer: Hervé de Milleville Objective of the module The purpose of this subject is the study of a sequence of numeric values representing the evolution of a quantity over time (temporal or time series). Such value sequences can be expressed mathematically in order to analyze behaviour, usually to understand the past and to predict future behaviour (short-term forecasting) Topic in detail The methods discussed are: Single and double moving averages Single and double Exponential Smoothing Holt-Winter Model The ARMA methods The detection of seasonality by autocorrelation The software used is EXCEL and SAS Bibliography Statistical Methods for Forecasting Bovas Abraham, Johannes Ledolter, Publisher: Wiley Introduction aux séries temporelles, Master statistique et économétrie, Aragon Y. Cours séries temporelles, DESS Mathématiques de la décision & DESS Actuariat, A. Charpentier Méthode de prévision à court terme, Edition Ellipses, Mélard G. Cours de séries temporelles, Maîtrise d économétrie, Viano M.C. Initiation à l analyse des séries temporelles et à la prevision, Mélard G., Revue Modulad 2006, n 35 (free online press review)

6 1.3 Mathematics for computer science Signals and Systems Lecturer: Guy Almouzni Objective of the module The acquisition of basic knowledge in signal processing and systems theory Topic in detail Time Representations of Signals Time Representations of Systems Frequency Representations of Signals Frequency Representations of Systems Sampling - Interpolation - Quantization Linear filtering, Analysis & Synthesis of digital filters, Multirate filtering Bibliography Théorie et traitement des signaux, F. de Coulon, Dunod Traitement du signal, P. Duvaut, Hermès Traitement numérique des signaux, M. Kunt, Dunod Méthodes et techniques de traitement du signal, J. Max, Masson Applications of digital signal processing, A.V. Oppenheim, Prentice-Hall Digital signal processing, A.V. Oppenheim, R.W. Schafer, Prentice-Hall Signals and systems, A.V. Oppenheim, A.S. Willsky, Y.T. Young, Prentice-Hall Signal analysis, Papoulis, McGraw-Hill Automatique, M. Rivoire, J.L. Ferrier, Eyrolles Signaux & systèmes linéaires, Y. Thomas, Masson Signal Processing Lecturer: Guy Almouzni Objective of the module The aim of this course is to allow the control and design of tools for signal processing applications in the field of information processing Topic in detail 1. Mathcad simulation tool Tutorial 2. Random signals, Autocovariance, Ergodicity Transmitting a random signal in a linear system, Process for generating a random signal: 1st order formers filters, Generating process: MA, AR, ARMA 3. Signal synthesis, AR, MA, ARMA models, White noise 4. Characterization (Analysis - Frequency transforms) Cepstral analysis, Spectral Analysis, Wavelets, Correlation estimators DSP estimator: periodogram, correlogram, from the AR model of the signal 5. Signal conditioning, Denoising Preaccentuation, Desaccentuation, Denoising 6. Transmission Coding, Equalization, Adaptive filtering 7. Linear Prediction Coding Linear Prediction Coding, Lossy compression

7 8. Optimal filtering Least squares, RLS 9. & 10. Project Adaptive filtering Prediction (economical cycles) Optimal filtering Signal compression Conditioning Filtering, Signal detection Signal characterization, Spectrogram, Wavelets Bibliography Introduction à la théorie du signal et de l information, F. Auger, Technip Traitement numérique du signal : simulation sous Matlab, G. Blanchet, M. Charbit, Hermès Traitement des signaux pour les systèmes sonar, M. Bouvet, Masson Signal et communication numérique, J.M. Brossier, Hermès Eléments de théorie du signal : aspects aléatoires, M. Charbit, Ellipses Processus stochastisques : estimation et prédiction, M. Gevers, L. Vandendorpe, UCL Traitement Numérique des Signaux, Atelier de TNS, M. Kunt, Dunod/PPR Signaux & systèmes linéaires : cours/exercices, Y. Thomas, Masson Traitement linéaire du signal numérique, F. Truchetet, Hermès Simulation and Stochastic Process Lecturer: Marietta Manolessou Objective of the module This course aims to study the properties of stochastic processes using simulation of random variables. It is therefore strongly practice-oriented even if the main concepts and properties are discussed in class Topic in detail Simulation of probability laws Random number generator Simulation experiments Simulation of laws Scheme polls to discrete distributions Inversion method for discrete distributions Inversion method for continuous distributions Simulation of the normal law by TCL Simulation of the normal law via Box-Muller Stochastic Processes Definitions and properties Trajectories and states of a stochastic process Properties of a process Markov Chain Definitions Transient, recurrent and absorbing states Convergence White Noise Definition Simulation and validation Brownian motion Definition

8 Simulation: normalization method of random walk Simulation: Euler random method Validation (normality test) Poisson process Bibliography Markov models and algorithms, Bernard Ycart, Ed Springer-SMAI Operational Research: Linear Optimization Lecturer: Marietta Manolessou Objective of the module In this course, you will learn methods of linear optimization, and implement them Topic in detail 1. Linear Optimization (a) Simplexe -classical, 2. Penalties-Duality 3. Integer Numbers programming (Method of Decreasing Congruencies) 4-5. Dynamic Programming following Bellmann, Determinist cases, discrete and continuous cases Non-deterministic discrete case 6-7. Transport and Affectation problems Bibliography Linear programming and Extensions, G. Dantzig, N.J.Princeton, Princeton, University Press, 1963 Précis de Recherche Opérationnelle, R.Faure, Dunod, Paris, 1979 Linear Programming: Methods and Applications, 5 th edition, S.Gass, New York, Mc Graw-Hill, 1985 Lectures of the Ecole Nationale Supérieure des Télécommunications, Paris Combinatorial Optimization: Algorithms and Complexity, C. Papadimitriou and K. Steinglitz, Englewood Cliffs, N.J. Prentice-Hall, Deterministic and Stochastic Optimization Lecturer: Forest Jean Paul Objective of the module In this course, you learn nonlinear optimization methods and how to implement them on a computer. Deterministic and stochastic methods and heuristic methods are addressed Topic in detail Deterministic methods: - Gradient - Gradient with optimal steps - Conjugate Gradient

9 - Newton's method - Projection method - Method with penalty Methods with memory/ stochastic methods : - Tau search - Simulated annealing - Genetic algorithms Bibliography Combinatorial Optimization : Algorithms and Complexity, C. Papadimitriou, K. Steiglitz, Englewood Cliffs, N.J. Prentice-Hall, 1982 Recent advances in Mathematical Programming, A. W. Tucker, Mc GRAW-HILL, New York Operations Research : Applications and Algorithms, W.L. Winston, PWS-KENT, 1991 Optimisation Numérique, J.F. Bonnans, J.C. Gilbert, C. Lamarechal, C. Sagastizabal, Springer, 1998 Cours sur les méthodes d'optimisation, Littérature de physique et maths, A. Soukharev, A. Timokhov, Moscow, 2008 Bases des méthodes d'optimisation, V. Lesine, U. Lisovetz, Mai, Moscow, 1998 Méthodes d'optimisation, V. Bonnaillie-Noel, ENS lectures of Algorithmes de minimization, S. Chaznoz, A. Daare, Paris7 University lectures, CEA Saclay, 2005 Optimisation Quadratique, H. Zidani, P. Ciarlet, ENSTA lectures of 2005 Introduction dans les méthodes d'optimisation, A. Attenkov, V. Saroubine, Science, Moscow, 2008 Optimisation, I. Galeev, Science, Moscow, 2006 Numerical methods for least square problems, A. Bjorck, SIAM, 1996 Introduction à l'analyse numérique matricielle et à l'optimisation, P.G. Ciarlet, Masson, 1994 Convex Analysis and Minimization Algorithms, J-B. Hiriart-Urruty, C. Lemarechal, Springer, 1993 Linear and Nonlinear Programming, D.G. Luenberger, Addison-Wesley, 1984 Numerical Optimisation, J. Nocedal, S.J. Wright, Springer Combinatorial Optimization and Complexity Theory Lecturer: Jean-Paul Forest and Houcine Senoussi Objective of the module Introduce the theory of decidability through its themes (Can a problem be solved via a computer? - classes of problems). Give students the means to assess the difficulty of a problem, what is feasible (on computer) and what is not Topic in detail Algorithms and complexity Graph theory Turing machine Formal languages Decidability Undecidable problems Halting problem

10 Complexity classes P and NP NP-complete problems Bibliography Computational complexity, C. H. Papadimitriou Addison-Wesley, 1994 Introduction à la calculabilité, 3rd edition, P. Wolper, Dunod, 2006 Introduction to the Theory of Computation, 2 nd edition, Michael Sipser, Course Technology, 2005 Calculabilité et décidabilité, J.-M. Autebert, Masson Calculateurs, calculs, calculabilité, O. Ridoux, G. Lesventes, Eyrolles Partial Differential Equations and Finite Differences Lecturer: Irina Kortchemski Objective of the module In this course we will study: Numerical and analytical methods to solve models commonly encountered in fluid mechanics, telecommunications, biology, medicine, industry, finance, etc. All of these models are represented by EDP. The different approaches to the discretization of PDEs, the stability and the convergence of discrete equations. We will compare the analytical and numerical solutions in simple cases Topic in detail Lecture 1. Mathematical modelling and differential equations in partial derivatives Lecture 2. Ordinary differential equations Lecture 3. Principles of finite difference method for the PEDs Mesh Taylor formula Discretization of derivatives Lecture 4. Basic strategy in approaches to discretization Explicit Euler methods Implicit methods Crank -Nicolson Lecture 5. Boundary conditions Dirichlet Boundary conditions Neumann Boundary conditions Periodic Boundary conditions Lecture 6. Schemes on several different temporal levels Lecture 7. Parabolic equations Thomas Algorithm Numerical solution of the heat equation by Crank-Nicolson, Implementation Lecture 8. Consistency, Stability. Convergence, Lax theorem Lecture 9. Elliptic Equations Discretization of boundary conditions Jacobi and Gauss-Seidel iterative methods, Sparse matrix Discretization and implementation in polar coordinates

11 Lecture 10. Hyperbolic equations Advection equation Upwind scheme Lax-Friedrichs scheme Lax-Wendroff scheme Leap-Frog scheme Crank-Nicolson scheme Lecture 11. Numerical solution of two dimensional heat equations Lecture 12. Nonlinear PEDs Numerical solution of the one-dimensional Burgers equation Mac-Cormack method Crank-Nicolson method Numerical solution of the Korteweg de Vries equation Numerical solution of the Sine-Gordon equation Fourier analysis of PEDs, Dispersion relation Bibliography Numerical Methods for Scientists and Engineers, H. M. Antia, Birkhauser Numerical Modelling in Material Science and Engineering, M. Rappaz, M. Bellet, M. Deville, Springer Numerical Partial Differential Equations, J.W. Thomas Numerical Methods for Partial Differential Equations, W.F. Ames, Nelson and Sons LTD. London, 1969 Numerical solution of PDE : Finite difference methods, G.D. Smith, Clarendon Press, Oxford, 1978 Computational Methods for Fluid Dynamics, J.H. Ferziger and M. Peric, Springer, 1996 Numerical Recipes. The art of Scientific Computing, W. Press, S. Teokolsky, W. Vetterling, Brian P. Flannery, Cambridge University Press, 2011 Computational Physics, N. Giorgano, H. Nakanishi, Pearson, Pearson Hall, Architecture and software Object Oriented Modelling with UML Lecturer: Bernard Glonneau Objective of the module This course aims to teach student modelling and design programs using the object approach. The language used is UML. The purpose of this course is to: Provide a software development methodology to start off with in the real world until the completion of the program Learn how to design objects that can later be re-used Topic in detail Modelling: Why s and How s What does UML contain, and what is left out? Complex and Knows relations, class diagram Improving models with O.C.L Who and which part of the software is involved, when and how? Use-case diagram Who does what in what order? Scenarios

12 What does state mean for objects? State diagram Object oriented design Interface Introduction to Design Patterns Bibliography Conception et programmation orientée objet, Bertrand Meyer, Eyrolles Modélisation objet avec UML, Pierre-Alain Muller, Nathalie Gaertner, Eyrolles Object-Oriented Analysis and Design with Applications, 3 rd edition, Grady Booch, Robert A. Maksimchuk, Michael W. Engel, Bobbi J. Young, Ph.D. Jim Conallen, Kelli A. Houston, Addison-Wesley, 2007 UML specifications by the OMG (use the UML 2.0 version) OCL specifications by the OMG Designs Patterns - Elements of Reusable Object-Oriented Software, Erich Gamma, Richard Helm, Ralph Johnson, John Vlissides, Addison Wesley Object Management Group (OMG) : Object-oriented Design and Programming with Java Lecturer: Rachid Chelouah Objective of the module This course involves learning object-oriented programming with the Java language and introducing some design patterns Topic in detail Programming paradigms Classes and object members UML Mapping of the association Class members and inheritance Packages Interfaces - Eclipse Collections The exceptions Input/output Files and Flow Generic programming Enumerations - Annotations Bibliography Java in a Nutshell, David Flanagan, O'Reilly La programmation objet en Java, Michel Divay, Dunod JavaDoc JRE 1.6 and 1.7

13 1.4.3 Relational Databases Modelling, Design and administration Lecturer: Nga Nguyen, Barth George Objective of the module Databases are now a central element of a vast majority of information systems, solving the issue of long-term storage of complex and extensive data in a powerful and effective way. Databases can also be regarded as an overlay file system, to provide an optimal and efficient way of storing and especially accessing this data. First, this course introduces the concept of databases and provides students with basic skills in modelling, designing, handling and using data models. Then we move on to the more advanced concepts: Optimal implementation of treatments on the DBMS Design of distributed databases Safety management through roles Optimization of queries on large data volumes Topic in detail Basic concepts Entity-Relationship Model (conceptual data models, logical data models and normalization) : 2 lectures SQL Data Definition Language : 1 lecture SQL Data Manipulation Language : 4 lectures Index and View : 1 lecture Transaction : 1 lecture Advanced concepts Processing in a database PL/SQL language Triggers Procedures, functions and packages Distributed databases Concept : single MCD and multiple MLD Different kinds of fragmentation: horizontal, vertical and mixed Reconstituting views Materialized views Database links Roles in a database Application roles Other roles System privileges Object privileges Introduction to the administration of a database SPARC architecture Tablespace Repository Accelerators Indexes : b-trees, bitmaps, inversed Clusters

14 The request plan Bibliography Bases de données, G. Gardarin, Eyrolles, 2003 Base de données et Langage SQL, L. Audibert Merise et UML pour la modélisation des systèmes d'information, J. Gabay, Dunod, 2001 Oracle PL/SQL Programming, Steven Feuerstein and Bill Pribyl, O'Reilly The website with the best Oracle books: Architecture and Network Programming Lecturer: Bernard Glonneau Objective of the module Students will discover and become familiar with the concepts and techniques of networks. The first part leads to developments in Java, the second part to developments in C. they will also be introduced to R.M.I. (Java) programming that is widely used in parallel computing Topic in detail Network models TCP Implementation in JAVA language UDP Implementation in JAVA language http Implementation in JAVA language Proxy and firewalls R.M.I. techniques in JAVA language Network administration protocols Bibliography Réseaux: architecture, protocoles, applications, Andrew Tanenbaum, InterEditions, 1990 TCP/IP: architecture, protocoles, applications, Douglas Comer, InterEditions, 1992 Les Réseaux, Pujolle, Eyrolles Parallel programming Lecturer: Rachid Chelouah Objective of the module - Introduce general techniques and specific algorithms of parallel and distributed computing - Discover new concepts related to cloud computing Topic in detail General concepts Multithreading programming with Java Multiprocessing programming with java Review the independence of loops Limiting threads Different modes of parallelization Taxonomy Flynn

15 Complexity and Amdhal law OpenMp MPI Bibliography OpenMP official website:

16 Project management V-Model and Agile Methods Lecturers: Bernard Glonneau and Rachid Chelouah Objective of the module The objective of the course is to explain the two main methods of project management used today in software development projects: the V-model and Agile methodologies Topic in detail From V-model to Agile methods The manifesto and the panorama of Agile methods SCRUM XP Kanban Bibliography Extreme programming pocket guide, author: Chromatic, editor: O'Reilly Les services agiles et les processus, authors: Thierry Chamfrault and Claude Durand, editor: Dunod Balancing Agility and Discipline: a Guide for the Perplexed, authors: Barry Boehm et Richard Turner, editor: Addison Wesley Scrum : le guide pratique de la méthode agile la plus populaire, author: Claude Aubry, editor: Dunod Initiation to the research Lecturer: Rachid Chelouah Objective of the module The objective of this module is to introduce students to methodologies for scientific analysis of documents related to one of the three pillars of the master. This allows the student to prepare for the final research project Topic in detail Students will be provided with scientific papers relating to their courses of the current semester (Parallel Architecture, Data mining, Networking, etc.), and they will need to: Choose one paper and make a scientific comment of it as if they were a reviewer Present the author s problems How the authors have modelled theirs problems The methods chosen by the authors to solve their problems How the authors interpreted their results Comment on whether they have presented different perspectives to their work Analyze whether the bibliography is recent enough, well adapted to their studies, etc.

17 1.4.8 Transverse Project and finalized research Objective of the module The objective of this module is to confront the students with a large project in the working conditions of a professional environment: the development of a decision-support software around the issues of Big Data. At the end of this project, students will have a real experience of an IT project in: Project management Unit testing and integration testing Topic in detail Students will be required to follow these steps: Conduct interviews Detailed Functional Specifications Definition of the different teams and resource management projects (svn, etc.) Detailed Specifications Modelling and design of the database Design and development of unit modules Integration of modules in a development environment or pre-production Recipe and beginning of production 1.5 FLE Beginners FLE Lecturer: Lamouri Ines Objective of the module Students will reach a sufficient level for good communication in everyday academic and professional life Topic in detail Everyday French Discovering the key aspects of French culture to facilitate integration Working from texts and audio-visual materials Using the language from personal experiences in the field Mastering the general vocabulary that is useful to life in school Systematic vocabulary acquisition using methods that reflect the four skills The year will be punctuated with level tests to monitor the smooth progress of students.