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Licence en sciences mathématiques (Diploma of the Second Cycle (Licence) in Mathematical Sciences) [MATH2]
>> Programme management
>> Admission procedure
>> General structure of the programme
>> Programme content
>> >>> > MATH21 - First year
>> >>> > MATH22 - Second year
>> Positioning of the degree within the University cursus

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Programme management

MATH Département de mathématique

Responsable académique : Yves Félix

Contact : Martine Everard

Tél. 010478696
everard@math.ucl.ac.be

Admission procedure

The regular conditions and admission procedures are detailed on the web page "Access to studies" : http://www.ucl.ac.be/etudes/libres/acces.html

General structure of the programme

The second cycle of university studies, ("licence") programme in Mathematical Sciences offers three orientations : the classical orientation, the statistics orientation and the mathematical economics orientation. The only students entitled access to the mathematical economics orientation are those who have followed a course on mathematical economics on their MATH 12 programme.

The statistics and mathematical economics orientations are characterised by the presence of a certain number of advanced courses in the corresponding speciality ; they also foster the orientation of the thesis towards the selected speciality. All orientations lead to the same "licencié" degree in Mathematical Sciences.

Programme content

MATH21 First year

Core courses

MATH2171

A préciser (in French)

MATH2480

Differential geometry[30h+15h] (5 credits)1q (in French)

Yves Félix, Luc Haine, Pierre Van Moerbeke

MATH2430

A préciser (in French)

MATH2111

A préciser (in French)

SC2140

Questions of religious sciences[15h] (1 credits)1q (in French)

José Reding

This course will be followed in the 1st or2nd year.

The students who do not take or pass the oral expression test in English will take the following course :

ANGL2461

Anglais - expression orale pour les mathématiciens[30h] (2 credits)2q

Françoise Stas

1. Specific programme for the classical orientation

A. Compulsory courses

Besides the common courses, the students will follow the below-listed compulsory courses :

MATH2112

A préciser (in French)

MATH2120

A préciser (in French)

INMA2325

A préciser (in French)

PHYS2111

Introduction to non-linear dynamics[30h+22.5h] (4.5 credits)2q (in French)

Jean Bricmont, Luc Haine

B.Options

In addition, the students will take courses from the following list, for a total of at least 16 ECTS.

1. Algebra - Geometry - Logic

MATH2121

Galois Theory[30h] (3 credits)ENCours cyclique dispensé cette année académique2q (in French)

Francis Borceux

MATH2391

Theory of categories (First part)[22.5h] (2.5 credits)2q (in French)

Francis Borceux, Enrico Vitale (coord.)

MATH2392

Theory of categories (Second part)[22.5h] (2.5 credits)2q (in French)

Francis Borceux, Enrico Vitale (coord.)

MATH2450

Mathematical logic[45h] (4.5 credits)1+2q (in French)

Jean-Roger Roisin

MATH2130

Riemannian geometry[22.5h] (2.5 credits)EN Cours non dispensé cette année académique1q (in French)

N.

2 Analysis - Mechanics

MATH2401

Lie groups[22.5h+7.5h] (2.5 credits)EN Cours non dispensé cette année académique2q (in French)

N.

MATH2460

A préciser (in French)

3. Physics

PHYS2121

A préciser (in French)

PHYS2122

Theoretical and mathematical physics II[22.5h+15h] (3 credits)EN Cours non dispensé cette année académique2q (in French)

N.

PHYS2131

Sperical astronomy and mathematical astronomy[22.5h+15h] (3 credits)1q (in French)

Pascale Defraigne, Jean-Pascal van Ypersele de Strihou

PHYS2140

Internal geophysics[22.5h+15h] (3 credits)1q (in French)

Thierry Camelbeeck, Véronique Dehant

PHYS2143

A préciser (in French)

The Mathematics Department can authorise the registration of another course or seminar of the Physics "licence" on the student's programme.

4. Probability- Statistics - Operational Research

INMA2471

Optimization models and methods[30h+22.5h] (5 credits)EN Cours non dispensé cette année académique2q (in French)

François Glineur

MATH2440

Statistical analysis[30h+22.5h] (5 credits)2q (in French)

Ingrid Van Keilegom, Rainer von Sachs

STAT2416

Multivariate probabilities ans statistics[10h+5h] (2.5 credits) (in French)

Ingrid Van Keilegom

5. Numerical Analysis

INMA2380

Matrix theory[30h+22.5h] (5 credits)2q (in French)

Paul Van Dooren

INMA1170

Numerical analysis[22.5h+30h] (5 credits)1q (in French)

Pierre-Antoine Absil, Paul Van Dooren, Paul Van Dooren

6. Computer Studies

INGI2101

A préciser (in French)

LINF2121

A préciser (in French)

LINF2125

Projet de programmation : application de gestion[0h+60h] (6 credits)EN Cours non dispensé cette année académique (in French)

Marco Saerens

2. Specific programme for the Statistics orientation

A. Compulsory courses

Besides the courses common to the three orientations, the students will follow the compulsory courses listed below :

MATH2440

Statistical analysis[30h+22.5h] (5 credits)2q (in French)

Ingrid Van Keilegom, Rainer von Sachs

INMA2380

Matrix theory[30h+22.5h] (5 credits)2q (in French)

Paul Van Dooren

INMA2471

Optimization models and methods[30h+22.5h] (5 credits)EN Cours non dispensé cette année académique2q (in French)

François Glineur

PHYS2111

Introduction to non-linear dynamics[30h+22.5h] (4.5 credits)2q (in French)

Jean Bricmont, Luc Haine

STAT2411

Data Analysis[22.5h+7.5h] (5 credits)1q (in French)

Isabelle De Macq (supplée Léopold Simar), Léopold Simar

STAT2412

Linear models[22.5h+7.5h] (5 credits)2q (in French)

Christian Hafner

STAT2416

Multivariate probabilities ans statistics[10h+5h] (2.5 credits) (in French)

Ingrid Van Keilegom

STAT2430

Statistical computing[20h+20h] (7 credits)1q (in French)

Bernadette Govaerts

3. Specific programme for the Mathematical Economics orientation

Besides the courses common to the three orientations, the students will follow the compulsory courses listed below :

PHYS2111

Introduction to non-linear dynamics[30h+22.5h] (4.5 credits)2q (in French)

Jean Bricmont, Luc Haine

MATH2440

Statistical analysis[30h+22.5h] (5 credits)2q (in French)

Ingrid Van Keilegom, Rainer von Sachs

ECON2115

Micro-economics[60h+30h] (12 credits) (in French)

Jacques-François Thisse

INMA2325

A préciser (in French)

ECON2125

Macro-economics[60h+30h] (12 credits)1+2q (in French)

David De la Croix, Frédéric Docquier

MATH22 Second year

The students must present a thesis (MATH 2999). The choice of a thesis director must be approved by the Mathematics Departement by the third week of the first quadrimester of the second year, at the latest. The preparation of the thesis is equivalent to about 25 credits. The thesis readers are appointed by the Mathematics Departement by the beginning of the 2nd quadrimester of the 2nd year, at the latest. The list of thesis readers will be communicated to the jury secretary.

A. Core courses

Philosophical teachings :

SC2001

Introduction to contemporary philosophy[30h] (2 credits)2q (in French)

Mark Hunyadi

or

SC2220

Philosophy of science[30h] (2 credits)2q (in French)

Michel Ghins

MATH2190

Mathematical methodology[30h] (3 credits)1q (in French)

Michel Willem

MATH2900

Mathematics Seminar[30h] (3 credits)1+2q (in English)

Camille Debiève, Yves Félix, Alphonse Magnus

This seminar is organised in the context of the "Language plan".

SC2140

Questions of religious sciences[15h] (1 credits)1q (in French)

José Reding

This course will be followed in the 1st or 2nd year, according to choice..

B. Options

SC2002

Elements of mathematics and physics history[30h] (4.5 credits)1q (in French)

Patricia De Grave

1. Algebra - Geometry - Logic

MATH2230

Algebraical topology[45h] (5 credits)1q (in French)

Yves Félix, Pascal Lambrechts

MATH2380

Number theory[30h] (3 credits)1q (in French)

Jean-Jacques Quisquater, Jean-Pierre Tignol

MATH2350

Cryptography[22.5h] (2.5 credits)2q (in French)

Jean-Jacques Quisquater

MATH2220

Greater geometry[30h] (3 credits)1q (in French)

N.

MATH2450

Mathematical logic[45h] (4.5 credits)1+2q (in French)

Jean-Roger Roisin

MATH2121

Galois Theory[30h] (3 credits)ENCours cyclique dispensé cette année académique2q (in French)

Francis Borceux

MATH2130

Riemannian geometry[22.5h] (2.5 credits)EN Cours non dispensé cette année académique1q (in French)

N.

MATH2391

Theory of categories (First part)[22.5h] (2.5 credits)2q (in French)

Francis Borceux, Enrico Vitale (coord.)

MATH2392

Theory of categories (Second part)[22.5h] (2.5 credits)2q (in French)

Francis Borceux, Enrico Vitale (coord.)

MATH2395

Discrete mathematics - combinatorial strucutres[30h] (3 credits)2q (in French)

Philippe Delsarte, Jean-Pierre Tignol

2. Analysis - Mechanics

MATH2200

Infinitesimal analysis (complements)[45h] (5 credits)2q (in French)

Thierry De Pauw, Thierry De Pauw

MATH2401

Lie groups[22.5h+7.5h] (2.5 credits)EN Cours non dispensé cette année académique2q (in French)

N.

MATH2410

Differential topology[30h] (3 credits)1q (in French)

Pierre Van Moerbeke

MATH2420

Complex analytic functions[30h] (3 credits)1q (in French)

Pierre Van Moerbeke

MATH2421

Convex analysis and calculation of variations[30h] (3 credits)1q (in French)

Michel Willem

MATH2490

??? ordinary or partial differential equations[45h] (4.5 credits)1q (in French)

Jean Mawhin

INMA2335

A préciser (in French)

INMA2345

Differential Equations : boundary value problems[30h] (3 credits)2q (in French)

Denis Bonheure

3. Physics

PHYS2140

Internal geophysics[22.5h+15h] (3 credits)1q (in French)

Thierry Camelbeeck, Véronique Dehant

PHYS2143

A préciser (in French)

PHYS2144

Universe models[15h] (1.5 credits)2q (in French)

Jean-Marc Gérard

PHYS2290

A préciser (in French)

4. Probability- Statistics - Operational research

MATH2370

Theory of games[22.5h] (2 credits)1q (in French)

Jean-François Mertens

MATH2360

Stochastic processes (statistics)[30h] (3.5 credits)1q (in French)

Jean-Marie Rolin

MATH2372

Stochastic processes[30h] (3 credits)1q (in French)

Jean-François Mertens

MATH2440

Statistical analysis[30h+22.5h] (5 credits)2q (in French)

Ingrid Van Keilegom, Rainer von Sachs

INMA2450

Combinatorial optimization[30h+15h] (4 credits)1q (in French)

Laurence Wolsey

INMA2460

Optimization : Nonlinear programming[30h+15h] (4 credits)2q (in French)

Yurii Nesterov

INMA2470

Discrete stochastic models[30h+22.5h] (5 credits)1q (in French)

Philippe Chevalier

STAT2411

Data Analysis[22.5h+7.5h] (5 credits)1q (in French)

Isabelle De Macq (supplée Léopold Simar), Léopold Simar

STAT2412

Linear models[22.5h+7.5h] (5 credits)2q (in French)

Christian Hafner

STAT2416

Multivariate probabilities ans statistics[10h+5h] (2.5 credits) (in French)

Ingrid Van Keilegom

5. Numerical Analysis - Computer Studies

MATH2830

Numerical analysis seminar[30h] (2 credits)1q (in French)

Alphonse Magnus, Paul Van Dooren

INMA2710

Numerical algorithms[30h+15h] (4 credits)1q (in French)

Paul Van Dooren

INGI2123

A préciser (in French)

INGI2131

A préciser (in French)

INGI2132

Languages and translators[30h+30h] (5 credits)EN Cours non dispensé cette année académique2q (in French)

Baudouin Le Charlier (coord.), Peter Van Roy

SINF1252

Introduction to computer systems[30h+30h] (5 credits)2q (in French)

Marc Lobelle

MATH2180

Numerical analysis II[45h] (4.5 credits)1+2q (in French)

Alphonse Magnus

Specific programme for the classical orientation

Besides the core courses, the students will take a minimum of 27 credits from the list below, spread over two or three of the five course titles. The activities chosen under any course heading may not surpass 20 credits. A seminar will be subject to examination or a graded piece of work.

The Mathematics Department may authorise the registration of a course or seminar not featuring on the list below on the minimal programme of the student, equivalent to 30 hours ; this course will be of a mathematical level analogous to that of those courses. The Mathematics Department may also authorise the registering of a course or seminar chosen from the UCL programmes on the minimal programme of the student.

The content of the MATH2392 and MATH2450 courses changes each year. These courses feature on the programme of the first and second year. They may be taken as options both in the first and the second year of the programme.

Specific programme for the Statistics orientation

A. Compulsory courses

Besides the common courses, the students will take the following compulsory courses :

MATH2360

Stochastic processes (statistics)[30h] (3.5 credits)1q (in French)

Jean-Marie Rolin

STAT2410

Discrete data analysis.[22.5h+7.5h] (5 credits)2q (in French)

Patrick Bogaert

STAT2413

Non parametric statistics[22.5h+7.5h] (5 credits)1q (in French)

Ingrid Van Keilegom

STAT2414

Times series[22.5h+7.5h] (5 credits)1q (in French)

Rainer von Sachs

B. Free-choice courses

7 credits, from among :

ACTU2111

Non life Insurance I[30h+15h] (4.5 credits)1q (in French)

Antoine Delwarde (supplée Michel Denuit), Antoine Delwarde (supplée Michel Denuit), Michel Denuit

INMA2470

Discrete stochastic models[30h+22.5h] (5 credits)1q (in French)

Philippe Chevalier

MATH2372

Stochastic processes[30h] (3 credits)1q (in French)

Jean-François Mertens

STAT2415

Introduction to Bayesian statistics.[15h] (2.5 credits)2q (in French)

N.

STAT2510

Statistical quality control.[15h] (2.5 credits)2q (in French)

Bernadette Govaerts

STAT2520

Design of experiment.[22.5h+7.5h] (5 credits)2q (in French)

Bernadette Govaerts, Éric Le Boulengé

STAT2530

Statistics in clinical trials.[22.5h+7.5h] (5 credits)2q (in French)

Annie Robert

STAT2540

Survey and Sampling[15h] (2.5 credits)2q (in French)

Yves Berger

STAT2550

Data Mining[15h+15h] (5 credits)2q (in French)

Libei Chen

C. Options

The minimum option is for 6 credits, to be chosen from one or two of the four following titles :

1. Algebra, Geometry - Logic

2.Analysis - Mechanics

3.Physics

5. Numerical Analysis - Computer Studies

Specifc programme for the Mathematical Economics orientation

A. Compulsory courses

Besides the common courses, the students will take the following compulsory courses :

MATH2421

Convex analysis and calculation of variations[30h] (3 credits)1q (in French)

Michel Willem

ECON2135

Econometrics: methods and applications[45h+45h] (12 credits) (in French)

Luc Bauwens

ECON2238

Financial economics[30h] (4 credits)1q (in French)

Pierre Giot

ECON2243

Game and Information Theory[30h] (4 credits)1q (in French)

Hylke Vandenbussche

B. Free-choice courses

One course to be chosen from among :

ECON2244

General Equilibrium Theory[30h] (4 credits)1q (in French)

François Maniquet

ECON2245

Econometrics[30h+15h] (4 credits)2q (in French)

Luc Bauwens

ECON2247

Growth and Development[30h] (4 credits)2q (in French)

Raouf Boucekkine

MATH2360

Stochastic processes (statistics)[30h] (3.5 credits)1q (in French)

Jean-Marie Rolin

MATH2372

Stochastic processes[30h] (3 credits)1q (in French)

Jean-François Mertens

C. Options

The minimum option is for 6 credits, to be chosen from one or two of the four following courses :

1.Algebra - Geometry - Logic

2. Analysis - Mechanics

3. Physics

5. Numerical Analysis - Computer Studies

Positioning of the degree within the University cursus

The three orientations may be prolonged by third study cycle (masters) programmes, extended study diplomas and PhDs, either in the same speciality or in a complemetary speciality. For example :

  • the DEA in Pure and Applied Mathematics (for research in mathematics)
  • the master's programme in statistics, the DES and DEA programmes in Statistics (for an initiation or perfection in the domain of statistics)
  • the master's programme in Actuarial Sciences
  • the DES in Applied Sciences, orientation : Computer Studies
  • the DEA in Economic Sciences, the DES in Econometrics, and the DES in Financial Economics, for "licence" diploma holders in Mathematics coming from the Mathematical Economics orientation.

The "licence" diploma holders in Mathematical Sciences from the Statistics orientation may, in addition, obtain the DES in Statistics in one year instead of two.

The "licence" diploma holders in Mathematical Sciences who have added a certain number of Computer Studies courses to their programme, are entitled access to the second year of the "licence" programme in Computer Studies (orientation : General Computer Studies) in line with certain procedures still to be specified (please address the secretary's office of the MATH Department or the programme manager for the "licence" in Computer Studies).



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Person in charge : Jean-Louis Marchand - Information : info@sc.ucl.ac.be
Last update :13/03/2007