Transcript Master - Universidad de La Rioja

Programmes in Mathematics & LMD system
Paris Dauphine University
Logroño, 25-27 October 2007
Universidad de la Rioja
Conferencia de decanos y directores de matemáticas
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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)
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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by the one year DEA or DESS have been replaced by a research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.
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doctorat
doctorat
DESS
DEA
M2
Maîtrise
M1
Licence
L3
L2
DEUG
DU MI2E
L1
Until 2004-2005
Since 2005-2006
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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.
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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.
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Licence MI2E
Mention Mathématiques appliquées
Mathématiques et Modélisation des Problèmes Economiques
ECTS
L3
28 to 40
L2
32
L1
0 to 15 0 to 18 4
28
Maths
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12 to 16 4 to 8
16
12
C.S.
Eco
7
4
4
En
DUMI2E L1
Mathematics 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.
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DUMI2E L2
Mathematics 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+ 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.
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DUMI2E L3
Mathematics 28 to 40 ECTS
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
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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).
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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
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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.
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Master MIDO
Mention Mathématiques de la Modélisation et de la Décision (MMD)
First year M1
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++, …
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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
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Master MIDO Mention MMD
First year M1
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
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Master MIDO Mention MMD
First year M1
elective courses
Applied probabilities &
analysis
Statistics
(12ECTS)
(12 ECTS)
•
Data analysis
•
Functional analysis and
non linear analysis
•
Non parametric statistics
•
Markov chains control
•
Distributions, PDE,
Black & Sholes model
•
Dynamical variables
econometrics
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Master MIDO Mention MMD
Second 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 )
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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 processing
with participation in the European master in Bayesian statistics and
Decision Analysis
• PDE stochastic and deterministic modelling
(EDP-MAD Modélisation aléatoire et déterministe )
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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
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Research center : CEREMADE
Centre de Recherche de Mathématiques de la Décision
Website
www.ceremade.dauphine.fr
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Carreer opportunities for students.
(MIDO department Mathematics Master and computer science Master)
Companies
Public
administration,
research and
education
15%
Industry
5%
Insurance
20%
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HI and
consulting
21%
Consulting
and auditing
9%
Banking
30%
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Carreer opportunities for students.
(MIDO department Mathematics Master and computer science Master)
Sectors
Information
systems
25%
Insurance
16%
Statistics
11%
R&D
10%
Software
7%
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Finance
31%
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Double diploma
Autonoma- Madrid Paris-Dauphine
In 2000, an agreement has been signed
leading to a joint degree.
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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
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University website
www.dauphine.fr
• coming soon in English and in Spanish.
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Martine Bellec
Vice Présidente
Université Paris Dauphine
Paris France
[email protected]
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