Programmes in Mathematics LMD system Paris Dauphine University

Programmes in Mathematics & LMD system Paris Dauphine University Logroño, 25 -27 October 2007 Universidad de la Rioja Conferencia de decanos y directores de matemáticas Logroño 26 octobre 2007 1

A brief background : MASS degrees • In the early seventies, the mathematics department at Paris Dauphine launched a new programme combining mathematics and economics, on the same model as mathematics and physics which is more usual. • This combination created a surprise and some scepticism among the academics but then the idea had been admitted and adopted by other French universities. • These programmes were referred as MASS degrees Mathématiques Appliquées aux Sciences Sociales (Applied Mathematics and Social Sciences) Logroño 26 octobre 2007 2

The LMD reform • The old system of the first two years of undergraduate study (recognized by a DEUG diploma), plus one year for the Bachelor’s degree “licence” is being replaced by the new “licence”, described as L 1, L 2, L 3 • The one year course after the old licence called ‘maîtrise”, followed by the one year DEA or DESS have been replaced by a research master or a professional master, referred to as M 1, M 2. • Many degrees names have changed. Logroño 26 octobre 2007 3

doctorat do cto rat DESS DEA M 2 Maîtrise M 1 Licence L 3 L 2 DEUG DU MI 2 E L 1 Until 2004 -2005 Since 2005 -2006 Logroño 26 octobre 2007 4

The LMD reform at Dauphine Since October 2005, at Dauphine all programmes have been designed following the LMD scheme. Basicaly this means: semester based programmes, each semester being validated for 30 ECTS. Logroño 26 octobre 2007 5

The LMD reform at Dauphine • Furthermore in October 2005, the mathematics and computer science departments merged in a new department MIDO Mathématiques, Informatique, Decision et Organisation • The programmes in mathematics and computer science remain quite distinct. Logroño 26 octobre 2007 6

Licence MI 2 E Mention Mathématiques appliquées Mathématiques et Modélisation des Problèmes Economiques ECTS L 3 28 to 40 L 2 32 L 1 0 to 15 0 to 18 4 8 12 to 16 4 to 8 28 16 12 Maths C. S. Eco Logroño 26 octobre 2007 7 4 4 En

DUMI 2 E L 1 Mathematics 28 ECTS hours Short description (key words) Algebra 1 6 20+40 Elementary logic. Vectoriel spaces. Linear applications. Matrices and polynomes. Analyse 1 6 20+40 Numerical sequences. Function of one variable. Continuity. Differentiation. Taylor’s formula Algebra 2 6 20+40 Norms, scalar product. Determinant. Diagonalisation. Analyse 2 6 20+40 Riemann integral. Differential equations. Linear differential equations. Function of several variables Proba 1 4 20+40 Discrete probabilities. Random variables. Some usual laws. Logroño 26 octobre 2007 8

DUMI 2 E L 2 Mathematics 32 ECTS hours Short description Linear Algebra 3 4 20+20 Quadratic forms. Scalar products. Euclidian spaces Analyse 3 6 20+40 Numerical series. Convergences. Probability 6 20+40 Axiomatic. Usual random variables (discrete and continuous). Large numbers law. Simulation. Numerical analysis 4 20+40+ Classical numerical algorithms. Resolution using Matlab. 20 Differential calculus and optimisation 6 20+40 Optimisation. Minimisation without constraints. Minimisation with constraints and Lagrange multipliers. Quadratic optimisation. Statistics 6 20+40 Parametrical statistics. Estimation. Asymptotic properties. Logroño 26 octobre 2007 9

DUMI 2 E L 3 Mathematics 28 to 40 ECTS hours Lebesgue Integral and probabilities 8 40+40 Measure theory. Integration. Probability laws. Convergences. Borel Cantelli lemma. Large numbers laws. Differential calculus and optimisation 8 40+40 Topology. Local inversion. Implicit functions theorems. Optimisation (Euler, KTT, convexity and duality) Numerical statistics or Complex analysis 6* 20+20 Simulation and data processing using R software. Introduction to holomorphic functions Mathematical statistics 4 20+20 Exponential families. Sufficiency. Fisher information. Point estimation. Hypothesis testing. Bayesian statistics. Consistency Introduction to functional analysis and Fourier analysis 4 20+20 Lp spaces. Introduction to Hilbertian spaces. Fourier series and Fourier transform. Measures weak convergence. Dynamical systems 4 20+20 Cauchy-Lipschitz theorem. Gronwall lemma. Linear differential systems. Liapounov and Hamiltonian systems. Short description Logroño 26 octobre 2007 10

The students • At the end of the second year students have a choice to opt for Economics or Business, or leave Dauphine to enter Business schools mostly. These students represent about 20 to 25% of the second year population • But new students apply to enter at level L 3, coming from other universities or preparatory classes (intensive classes for competitive entrance) to engineering schools, so the number of students stays stable (around 180 -200). Logroño 26 octobre 2007 11

What about computer science courses content ? First year • S 1 Info 1 (6 ECTS, 30+15+15) architecture and Java (first level) • S 2 Info 2 (5 ECTS, 20+20) algorithmic • S 2* Practical tools (internet and web, excel and OR, access and data bases) Second year • S 3 Info 3 (4 ECTS, 20+20+20) Java second level : introduction to object oriented programming • S 4 Info 4 (4 ECTS, 20+20+20) advanced algorithmic and Java Logroño 26 octobre 2007 12

What about economics? • S 1 An introduction to macroeconomics(4 ECTS, 20+20): basic notions in macroeconomics. • S 2 Microeconomics 1 (4 ECTS, 20+20) : The consumer choice, the producer choice, introduction to general equilibrium and Pareto optimum • S 3 Macroeconomics 1 (4 ECTS, 20+20) : Short run macroeconomics. Equilibrium. Analysis in a closed economy. • S 3* Ecomomic policies (4 ECTS, 20+20) Issues in contemporary economies. • S 4 Microeconomics 2 (4 ECTS, 20+20) imperfect competition. Market failures. The welfare theorems. • S 4* Macroeconomics 2 (4 ECTS, 20+20) Open economy. Logroño 26 octobre 2007 13

Master MIDO Mention Mathématiques de la Modélisation et de la Décision (MMD) First year M 1 4 choices Economics & Finance Actuarial sciences Statistics Applied probabilities and analysis A common core (28 ECTS) Electives modules (12 ECTS) Optional modules (24 ECTS) the above modules or game theory, wavelets, marketing, microeconomics, C++, … Logroño 26 octobre 2007 14

Master MIDO Mention MMD First year M 1 Common core (28 ECTS) • • • Discrete stochastic processes Functional analysis and dynamical programming Generalised linear models Continuous stochastic processes Numerical analysis or signal processing English Logroño 26 octobre 2007 15

Master MIDO Mention MMD First year M 1 elective courses • • • Economy & Finance Actuarial sciences (12 ECTS) (20 ECTS) Portfolio management Asset pricing (mathematical modelling) Risk economy • Portfolio management • Asset pricing (mathematical modelling) • Dynamical variables econometrics • Mathematics for insurance 1 • Mathematics for insurance 2 Logroño 26 octobre 2007 16

Master MIDO Mention MMD First year M 1 elective courses Applied probabilities & analysis Statistics (12 ECTS) (12 ECTS) • Data analysis • Functional analysis and non linear analysis • Non parametric statistics • Markov chains control • Distributions, PDE, Black & Sholes model • Dynamical variables econometrics Logroño 26 octobre 2007 17

Master MIDO Mention MMD Second year M 2 • Insurance, Economy & Finance (Mathématiques de l’Assurance, de l’Economie et de la Finance • Statistical & financial engineering (Ingénierie Statistique et Financière ) • Actuarial sciences (Actuariat) • Statistical information processing (Traitement Statistique de l’Information) • PDE stochastic and deterministic modelling (EDP-MAD Modélisation aléatoire et déterministe ) Logroño 26 octobre 2007 18

Master MIDO Mention MMD Second year M 2 • Insurance, Economy & Finance Co-diploma with ENSAE • Statistical & financial engineering Both classical training and vocational training • Actuarial sciences Validated by the chamber of actuaries • Statistical information processing with participation in the European master in Bayesian statistics and Decision Analysis • PDE stochastic and deterministic modelling (EDP-MAD Modélisation aléatoire et déterministe ) Logroño 26 octobre 2007 19

Third cycle : Doctoral studies • About 15 Ph. D thesis are defended each year. 3 major fields • Mathematical microeconomics and finance • Probabilities and statistics (Bayesian statistics, data analysis) • PDE Logroño 26 octobre 2007 20

Research center : CEREMADE Centre de Recherche de Mathématiques de la Décision Website www. ceremade. dauphine. fr Logroño 26 octobre 2007 21

Carreer opportunities for students. (MIDO department Mathematics Master and computer science Master) Logroño 26 octobre 2007 22

Carreer opportunities for students. (MIDO department Mathematics Master and computer science Master) Logroño 26 octobre 2007 23

Double diploma Autonoma- Madrid Paris-Dauphine In 2000, an agreement has been signed leading to a joint degree. Logroño 26 octobre 2007 24

The LMD reform Main advantages • Adoption and generalisation of the credits system • Presentation of courses in term of objectives Drawbacks • Funny diploma names • Too many courses units • Too much time spent in student assessment Logroño 26 octobre 2007 25

University website www. dauphine. fr • coming soon in English and in Spanish. Logroño 26 octobre 2007 26

Martine Bellec Vice Présidente Université Paris Dauphine Paris France Martine. Bellec@dauphine. fr Logroño 26 octobre 2007 27