Programmes in Mathematics & LMD system Paris Dauphine University Logroño, 25-27 October 2007

Logroño 26 octobre 2007 1

Programmes in Mathematics & LMD system Paris Dauphine University

Logroño, 25-27 October 2007Universidad de la Rioja

Conferencia de decanos y directores de matemáticas


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)


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 L1, L2, L3

• The one year course after the old licence called ‘maîtrise”, followed by the one year DEA or DESS have been replaced by a research master or a professional master, referred to as M1, M2.

• Many degrees names have changed.


DEUG

Maîtrise

Licence

DESS DEA

L2DU MI2E

L1

L3

M2

M1

doct

orat

doct

orat

Since 2005-2006Until 2004-2005


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.


The LMD reform at Dauphine

• Furthermore in October 2005, the mathematics and computer science departments merged in a new department MIDOMathématiques, Informatique, Decision et Organisation

• The programmes in mathematics and computer science remain quite distinct.


16 12 428

Maths C.S. Eco En

L1

32 12 to 16 4 to 8L2 8

4L3 28 to 40 0 to 15 0 to 18

Licence MI2E

Mention Mathématiques appliquées

Mathématiques et Modélisation des Problèmes Economiques

ECTS

4


DUMI2E L1Mathematics 28 ECTS

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.


DUMI2E L2Mathematics 32 ECTS

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+20

Classical numerical algorithms. Resolution using Matlab.

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.


DUMI2E L3Mathematics 28 to 40 ECTS

ECTS hours Short description

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.


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 L3, 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).


What about computer science courses content ?

First year • S1 Info1 (6ECTS, 30+15+15) architecture and Java (first level) • S2 Info2 (5ECTS, 20+20) algorithmic• S2* Practical tools (internet and web, excel and OR, access and data bases)

Second year• S3 Info 3 (4ECTS, 20+20+20) Java second level : introduction to object oriented programming• S4 Info 4 (4ECTS, 20+20+20) advanced algorithmic and Java


What about economics?

• S1 An introduction to macroeconomics(4ECTS, 20+20): basic notions in macroeconomics. • S2 Microeconomics 1 (4ECTS, 20+20) : The consumer choice, the producer choice, introduction to general equilibrium and Pareto optimum

• S3 Macroeconomics 1 (4ECTS, 20+20) : Short run macroeconomics. Equilibrium. Analysis in a closed economy.• S3* Ecomomic policies (4ECTS, 20+20) Issues in contemporary economies.• S4 Microeconomics 2 (4ECTS, 20+20) imperfect competition. Market failures. The welfare theorems.• S4* Macroeconomics 2 (4ECTS, 20+20) Open economy.


Master MIDO

Mention Mathématiques de la Modélisation et de la Décision (MMD)

First year M1

4 choices

Economics&

Finance

Actuarial sciences

Applied probabilities and analysis

Statistics

A common core (28 ECTS)

Electives modules (12 ECTS)

Optional modules (24 ECTS) the above modules or game theory, wavelets,

marketing, microeconomics, C++, …


Master MIDO Mention MMD

First year M1

Common core (28 ECTS)

• Discrete stochastic processes • Functional analysis and dynamical programming• Generalised linear models• Continuous stochastic processes• Numerical analysis or signal processing• English


Master MIDO Mention MMDFirst year M1

elective courses

Economy & Finance(12 ECTS)

• Portfolio management

• Asset pricing (mathematical modelling)

• Risk economy

Actuarial sciences

(20 ECTS)

• Portfolio management

• Asset pricing (mathematical modelling)

• Dynamical variables econometrics

• Mathematics for insurance 1

• Mathematics for insurance 2


Master MIDO Mention MMDFirst year M1

elective courses

Statistics(12ECTS)

• Data analysis

• Non parametric statistics

• Dynamical variables econometrics

Applied probabilities & analysis

(12 ECTS)

• Functional analysis and non linear analysis

• Markov chains control

• Distributions, PDE, Black & Sholes model


Master MIDO Mention MMDSecond year M2

• 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 )


Master MIDO Mention MMD

Second year M2

• 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 processingwith participation in the European master in Bayesian statistics and Decision Analysis

• PDE stochastic and deterministic modelling

(EDP-MAD Modélisation aléatoire et déterministe )


Third cycle : Doctoral studies

• About 15 PhD thesis are defended each year.

3 major fields• Mathematical microeconomics and finance• Probabilities and statistics (Bayesian statistics, data analysis)• PDE


Research center : CEREMADE

Centre de Recherche de Mathématiques de la Décision

Website

www.ceremade.dauphine.fr


Companies

HI and consulting

21%

Consulting and auditing

9%Banking

30%

Insurance20%

Industry5%

Public administration, research and

education15%

Carreer opportunities for students. (MIDO department Mathematics Master and computer science Master)


Sectors

Insurance16%

Statistics11%

Finance31%

Software7%

R&D10%

Information systems

25%

Carreer opportunities for students. (MIDO department Mathematics Master and computer science Master)


Double diploma

Autonoma- Madrid Paris-Dauphine

In 2000, an agreement has been signed

leading to a joint degree.


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


University website

www.dauphine.fr

• coming soon in English and in Spanish.


Martine BellecVice Présidente

Université Paris DauphineParis France

[email protected]

Programmes in Mathematics & LMD system Paris Dauphine University Logroño, 25-27 October 2007

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