ECTS credits
4 credits
Semester
Fall
Prerequisites
 Programs of the course units Mathematics 1A, Computer Science 1A and EconomicsBusiness 1A from Ecole Centrale Méditerranée Engineering programme (see syllabus 1A)
 Basics of the Python language
Learning objectives
 Apply a field of applied mathematics (ProbabilityStatistics, Finite Elements, Optimal Transport) to applications
 Design a computer program by implementing the necessary steps with the adequate tools: modeling, algorithms, programming environment in Python
 Understand advanced concepts in economics about markets or strategic behavior or process data related to an economics problem.
Description of the programme
The major course unit MathematicsComputer ScienceEconomics (MIE) is divided into 3 periods, each period is equal to 4 weeks (18h et 6h d’autonomie). For each period, the student must choose one subcourse offered in one of the following fields: Mathematics, Computer Science or Economics. There is one constraint for the student's choices (except for international credit mobility students such as Erasmus+ students): at the end of the semester the student must have studied subcourses in at least two different fields among Mathematics, Computer Science and Economics.
Choice of a course among Mathematics, Computer Science or Economics at each period

Period 1 (Temps 1) 
Period 2 (Temps 2) 
Period 3 (Temps 3) 
Mathematics 
Probability & statistics 
Variational methods and finite elements 
Introduction to the theory of optimal transport 
Computer Science 
Algorithm design 
Data driven programming 
Scientific Python 
Economics 
Innovation and market power: monopoly and 
Strategic behaviours: game theory 
Inequalities: data and public policies 
Mathématiques
 M1 : Probability and statistics
 Conditional probability and conditional expectation: definition, conditional probability distribution, properties, Bayes formula, martingales
 Inferential statistics: parametric estimation (maximum likelihood, moment method, regular model and Fisher information, confidence interval, parametric tests (likelihood ratio test) and nonparametric tests (chisquare)
 M2 : Variational methods and finite elements
 Distributions : definition, convergence, derivative
 Hilbert space, Sobolev spaces, inequalities (CauchySchwarz, Minkowski), Green formula, seminorm
 Variational methods: LaxMilgram theorem, Galerkin methode (definition, convergence and order).
 Finite elements: definition, approximation space, convergences for the local approximation and for the global approximation, convergence theorem for the Lagrange finiteelement method
 M3 : Introduction to the theory of optimal transport
 Monge and Kantorovitc formulations,
 Kantorovitch duality, cconcave functions, applications in economics: matching equilibrium
 Wasserstein distance, generalized Wassertsein distance (unbalanced optimal transport)
 Computational methods: Sinkhorn algorithm, entropic regularization, BenamouBrenier formulation
Computer Science
 I1 : Algorithm design
 Algorithm divide & conquer
 Sequence alignment problem: sequence alignement problem, sequence alignement algorithm
 Dynamic programming and NPcompleteness
 Greedy algorithms: principles and implementation
 Enumeration problem: branchandbound strategy and backtracking strategy
 I2 : Data driven programming
 Eventdriven programming and persistent objects. Python object. CRUD principle. MVC design template.
 Persistence managers: ORM, DAO. web servers. HTML/CSS. Django, pony ORM, Django ORM.
 I3 : Scientific Python
 Data manipulation and data analysis with Python: libraries Numpy and Scipy
 Graphs in Python: library Matplotlib
 Dataframe manipulation and representation: libraries Pandas and Seaborn
 Image processing: library Scikitimage
Economics
 E1 : Innovation and market power: monopoly and rents
 Market, market structures, competitive case
 Monopoly: simple monopoly, production of a sustainable good, price discrimination, product selection
 Strategic interactions: oligopoly, Cournot model, Bertrand model, industrial economic strategies
 E2 : Strategic behaviours: game theory
 Dominated strategy and Iterated elimination of strictly dominated strategies (IESDS)
 Nash equilibrium: definition, best answers, connection between IESDSNash
 Mixed strategy: definition, investigation of mixed equilibrium, Nash theorem, interpretation of mixed Nash equilibrium
 Games with continuous action space
 Sequential games
 Matching
 E3 : Economics : data and public policies
 inequalities in economics: definition, measure, inequality factors
 Public policies addressing inequalities
 Public policy evaluation: experimental and quasiexperimental evaluation methods
Generic central skills and knowledge targeted in the discipline
 M1: Model a statistical experiment for an i.i.d. sample and implement standard pointwise and interval estimation methods and testing procedures
 M2: Write and analyze a week formulation for a PDE. Implementation in Finite Element software.
 M3: Formulate the optimal transport problem and calculate Wasserstein distances
 I1: Understand the main categories of algorithms and how to implement them
 I2: Implement eventdriven programming in Python and understand the notion of persistence
 I3: Program in Python with the Numpy, Scipy, Matplotlib, Pandas, Seaborn and Scikitimage libraries
 E1: Identify the different types of markets, understand the notions of monopoly and oligopoly
 E2: Classify strategies and understand Nash equilibrium
 E3: Understand inequalities in economics and implement tools to evaluate public policies addressing them
How knowledge is tested
Continuous assessment
Bibliography
A bibliography will be proposed at the beginning of each subcourse offered in the major course unit MathematicsComputer ScienceEconomics.
Teaching team
 Mathematics
 M1 : Christophe Pouet, Mitra Fouladirad, Frédéric Schwander
 M2 : Guillaume Chiavassa
 M3 : Magali Tournus
 Computer Science
 I1 : François Brucker, Pascal Préa
 I2 : Emmanuel Daucé, Manon Philibert
 I3 : Muriel Roche, Manon Philibert
 Economics
 E1 : Nicolas Clootens, Santiago LopezCantor
 E2 : Nicolas Fournier (AixMarseille Université), Hajare El Hadri, Santiago LopezCantor, Ayoub Salih
 E3 : Hajare El Hadri
Sustainable Development Goal
Climate action
Peace, justice and strong institutions
Reduced inequalities
Responsible consumption and production
 Total hours of teaching72h
 Master class54h
 18h