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Master [120] of science in Mathematics

AnnéesTravail de fin d'étude


Retour en début de pageStudy objectives

Mathematics contains a profusion of different kinds of ideas leading to the discovery of new geometric universes, new areas of functions, new algebraic structures, all of which are linked to one another by very strong links which, overall, create great simplicity, richness and  beauty.

In the research focus, the programme combines general training in the key areas of basic mathematics with more advanced training in one of the Department’s research areas: functional analysis, differential equations, variation calculus, the geometric theory of measurement, algebraic groups, category theory, the theory of integrable systems and its links with complex algebraic geometry, noncommutative geometry, algebraic topology and knot theory.
This training leads to the acquisition of skills such as abstraction, analysis and modelling of complex situations, the sense of precision and rigour in reasoning, self-assessment and ability to communicate, including in English. These skills can be put to good use in many different professions. 

In the teaching focus, the programme combined general training for secondary school teachers with specific training in mathematics, highlighting the connection between theory and  practice ; there is also the possibility of additional training in mathematics or teaching another scientific subject. These additional training courses expand the range of skills for future teachers.

The Master in Mathematics at UCL is jointly organized with a similar programme at the Facultés Universitaires Notre-dame de la Paix (FUNDP) in Namur. Both the overall structure of the programme as well as students’ progression are basically the same at both universities. However, the training activities are grouped in specific special subjects at each university.

 


Retour en début de pageGeneral presentation of the programme

The programme comprises core subjects of 60 credits, a focus of 30 credits (research or teaching) and 30 credits for optional subjects or 30 credits for the option course in statistics.

 

Wathever the focus or the options chosen, the programme of this master shall totalise 120 credits, spread over two years of studies each of 60 credits

Core courses

Focus

Optional courses


Retour en début de pagePositioning of the programme

Whatever focus is chosen, the Master in Mathematics gives direct access to the doctorate in science.

 


Admission

University Bachelors
Diploma Special Requirements Access Remarks
UCL Bachelors
Intitulé du programme appelé par le code   Direct access  
Bachelor in Physics [180.0] Si l'étudiant a suivi la Minor in Mathematics [30.0]   Direct access  
Bachelor in Engineering [180.0] Si l'étudiant a suivi la Minor in Mathematics [30.0] ou si l'étudiant a suivi le programme de majeure en mathématiques appliquées  Direct access  
Belgian Bachelors of the French speaking Community
Intitulé du programme appelé par le code   Direct access  
Belgian Bachelors of the Dutch speaking Community
Intitulé du programme appelé par le code   Direct access  
Foreign Bachelors
Intitulé du programme appelé par le code   Direct access  

Non university Bachelors
Diploma Access Remarks
> Find out more about links to the university
 

Holders of a 2nd cycle University degree
Diploma Special Requirements Access Remarks
"Licenciés"
 
Intitulé du programme appelé par le code   Direct access  
Masters
 
Intitulé du programme appelé par le code   Direct access  

Holders of a non-University 2nd cycle degree
Diploma Access Remarks
> Find out more about links to the university
 

Adults taking up their university training
> See the website www.uclouvain.be/vae

Personalized access
Reminder : all Masters (apart from Advanced Masters) are also accessible on file.

Admission and Enrolment Procedures for general registration

See the general admission requirements



Contact

Retour en début de pageCurriculum management

Département de mathématique

Retour en début de pageUseful contacts

Secrétariat du département



Teaching method

Retour en début de pageStrong points of the pedagogical approach

The courses in the research focus enable students to acquire mathematical tools. They will mostly be accompanied by work which forms the main part of the assessment. Individual work, group work and work in the library will be encouraged. The ‘research courses’ are directly linked to the most advanced research areas in the Department. There is a wide network of inter-university links as well as international ones. 
Students will be encouraged to take courses (research focus) at other universities. Students who are not doing an Erasmus exchange are recommended to take advantage of these agreements to make their training for research more effective. It is not possible in every institution to develop a group of courses designed to provide advanced training for the different areas of research. The second year programme includes a course in each of the research areas and, through inter-university agreements, offers the possibility of more advanced training by borrowing specific courses from other institutions.
The interdisciplinary nature of the programme is reflected in the compulsory part of the two focuses with courses borrowed from the programmes of the Masters in Physics and Mathematical Engineering. Advanced teacher training in other subjects than mathematics is possible for students taking the teaching focus.

 

Retour en début de pageEvaluation

Students will mainly be assessed on the basis of individual work (e.g. reading, consultation of databases and bibliographic references, writing monographs and reports, presentation of seminars, dissertation and work placement). Where necessary, students will also be assessed on how much they have learned from lectures. As far as possible, there will be continuous assessment, including regular ‘open book examinations’. Certain activities will not be given a precise mark but will be officially certified. Assessment of the dissertation is in two stages : a ‘progress report’ at the end of the first year of the Master and the final presentation.



Internationalisation
Courses on special topics are given by many visiting lecturers from different foreign institutions and some Belgian ones. The titles are generic to be as flexible as possible and suitable for the development of research. These courses are usually in English.

 

The Department would like to encourage future researchers to establish contact with other research teams in neighbouring universities. Exchanges are also designed to provide additional training for certain areas of research.
Students doing either focus will have the opportunity to do an Erasmus, Mercator or other kind of exchange, lasting one semester. For the teaching focus, the exchange must take place in the second semester of the first year. For the research focus, it musts take place in the second semester of the first year or during the second year.

 



Core courses
Legend
Mandatory Optional
Courses not taught this academic year Periodic courses not taught this academic year
Periodic courses taught this academic year Two year courses

Click on the course code to see detailed informations (objectives, methods, evaluation...)
Year
1 2
Mandatory LMAT2110

Differential geometry I  (in French) Luc Haine 30h + 30h  5credits  1q  x  
Mandatory LPHY2111

Introduction à la dynamique non linéaire  (in French) Jean Bricmont 30h + 15h  5credits  1q  x  
Mandatory LMAT2120

Galois theory and groups representtions  (in French) Pierre-Emmanuel Caprace, Jean-Pierre Tignol 45h + 15h  5credits  2q  x  
Mandatory LMAT2130

Partial differential equations : Poisson and Laplace equations  (in French) Michel Willem 30h + 30h  5credits  1q  x  
Mandatory LMAT2140

Algebraic topology  (in French) Yves Félix, Pascal Lambrechts 45h  5credits  2q  x  
Mandatory LMAT2150

Category theory I and foundations of mathematics  (in French) Marino Gran, Enrico Vitale 45h  5credits  2q  x  

MandatoryPhilosophy (2credits)
2 credits to choose between
Optional LSC2001

Introduction to contemporary philosophy  (in French) Gilbert Gérard 30h  2credits  2q  x x
Optional LSC2220

Philosophy of science  (in French) Michel Ghins 30h  2credits  2q  x x
Optional LFILO2003E

Questions d'éthique dans les sciences et les tecniques (partie séminaire)  (in French) N.   2credits    x x
Mandatory LMAT2999

Mémoire   (in French) N.   26credits      x
Mandatory LMAT2997

Thesis tutorial  Yves Félix 15h  2credits      x
 


Focuses

Teaching focus
Legend
Mandatory Optional
Courses not taught this academic year Periodic courses not taught this academic year
Periodic courses taught this academic year Two year courses

Click on the course code to see detailed informations (objectives, methods, evaluation...)
Year
1 2
Mandatory LMAT2310

Stages d'enseignement en mathématique (en ce compris le séminaire d'intégration des stages)  (in French) Christiane Hauchart 15h + 40h  7credits    x x

MandatoryModule
Mandatory LAGRE2220

General didactics and education to interdisciplinarity  (in French) Ghislain Carlier, Marie-Laurence De Keersmaecker, Myriam De Kesel (coord.), Jean-Louis Dufays, Philippe Parmentier, Marc Romainville, Bernadette Wiame 22.5h + 15h  3credits    x x
Mandatory LMAT2320

Didactique et épistémologie de la mathématique  (in French) Christiane Hauchart 60h  6credits    x x

MandatoryDidactique et épistémologie d'une autre discipline (en ce compris le stage d'écoute) (4credits)
un cours au choix parmi les cours suivants
Optional LPHY2320A

Didactique et épistémologie de la physique (en ce compris le stage d'écoute)  (in French) Jim Plumat, Yvonne Scieur 37.5h + 10h  4credits    x x
Optional LGEO2320A

Didactique et épistémologie de la géographie (en ce compris le stage d'écoute)  (in French) Marie-Laurence De Keersmaecker 37.5h + 10h  4credits    x x
Optional LSNAT2320A

Didactique et épistémologie des sciences naturelles (mineure) en ce compris le stage d'observation   (in French) Myriam De Kesel, Martine Delvigne, Bernard Feltz, Michel Ghins, Bernard Tinant 37.5h + 10h  4credits    x x

MandatoryModule
Mandatory LAGRE2120

The school institution and its context  (in French) Etienne Bocquet (coord.), Dominique Grootaers, Christian Lannoye, Jacquy Masset 22.5h + 25h  4credits    x x
Mandatory LAGRE2400

See specifications in french  (in French) Michel Dupuis, Anne Ghysselinckx (coord.) 20h  2credits    x x

MandatoryModule
Mandatory LAGRE2020

To understand the adolescent in school situation, to manage the interpersonal relationship and to animate the class group  (in French) Anne Chevalier, Ann d'Alcantara, Bernard Demuysere, Christian Lannoye, Marie-Christine Liesse, Pierre Meurens, Pascale Steyns, Philippe van Meerbeeck, Marie-Cécile Wagner (coord.) 22.5h + 22.5h  4credits    x x
 


Research focus
Legend
Mandatory Optional
Courses not taught this academic year Periodic courses not taught this academic year
Periodic courses taught this academic year Two year courses

Click on the course code to see detailed informations (objectives, methods, evaluation...)
Year
1 2
Mandatory LMAT2160

Mathematics seminar  (in French) Alphonse Magnus, Enrico Vitale 0h + 45h  6credits      x

MandatoryCours approfondis (24credits)
L'étudiant choisit 24 crédits parmi les cours approfondis de recherche, les cours de recherche donnés par des professeurs visiteurs et des cours de recherche donnés dans d'autres universités.

MandatoryCours approfondis de recherche
au moins 1 cours parmi
Optional LMAT2210

Algebra  (in French) Jean-Pierre Tignol 45h  6credits  1q    x
Optional LMAT2220

Category theory II  (in French) Enrico Vitale 45h  6credits  2q    x
Optional LMAT2230

Geometric measure theory  (in French) Thierry De Pauw 45h  6credits  2q    x
Optional LMAT2240

Algebraic topology II  (in French) Yves Félix, Pascal Lambrechts 45h  6credits  1q    x
Optional LMAT2250

Calculus of variations and non linear elliptic equations  (in French) Michel Willem 45h  6credits  1q    x
Optional LMAT2260

Complex geometry  (in French) Luc Haine 45h  6credits  2q    x
Optional LMAT2270

Geometry and mathematical physics  (in French) Pierre Bieliavsky 45h  6credits  2q    x

OptionalCours de recherche donnés par des professeurs visiteurs
Optional LMAT2910

Advanced topics in mathematics 1  N. 30h  6credits      x
Optional LMAT2920

Advanced topics in mathematics II   Enrico Vitale (coord.) 30h  6credits      x
Optional LMAT2930

Advanced topics in mathematics 3  N. 30h  6credits  Courses not taught this academic year    x

OptionalCours de recherche donnés dans d'autres universités
 



Cours au choix ou option

Cours au choix [30.0]
Legend
Mandatory Optional
Courses not taught this academic year Periodic courses not taught this academic year
Periodic courses taught this academic year Two year courses

Click on the course code to see detailed informations (objectives, methods, evaluation...)
Year
1 2

OptionalCours au choix complémentaires à la finalité didactique
Optional LMAT2330

Seminar on the teaching of mathematics  (in French) Yves Félix, Christiane Hauchart, Enrico Vitale 0h + 30h  5credits    x  
Optional LPHY2330

Séminaire de didactique de la physique  (in French) Jim Plumat 0h + 30h  5credits    x  
Optional LCHM2330

Séminaire de didactique de la chimie  (in French) Agnès Gnagnarella, Bernard Tinant 0h + 30h  5credits    x  
Optional LBIO2330

Séminaire de didactique de la biologie  (in French) Myriam De Kesel 0h + 30h  5credits    x  
Optional LGEO2330

Séminaire de didactique de la géographie  (in French) Marie-Laurence De Keersmaecker 0h + 30h  5credits    x  

OptionalCompléments de mathématique
Optional LMAT2410

Partial differential equation : heat equation, brownian moves and numerical aspects  (in French) Alphonse Magnus 30h + 15h  5credits  2q  x  
Optional LMAT2420

Differential geometry II  (in French) Tom Claeys 30h + 15h  5credits  1q  x  
Optional LMAT2430

Differential topology  (in French) Gery Debongnie 30h + 15h  5credits    x  
Optional LMAT2440

Number theory  (in French) Pierre-Emmanuel Caprace 30h + 15h  5credits  1q  x  
Optional LMAT2450

Cryptography  Olivier Pereira 30h  5credits  1q  x  
Optional LMAT2460

Finite mathematics and combinatorial structures  (in French) Mélanie Raczek 30h  5credits  1q  x  
Optional LMAT2470

Processus stochastiques (statistique)  (in French) Jan Johannes 30h  5credits  1q  x x
Optional LSTAT2030

Statistical analysis  Anouar El Ghouch, Rainer von Sachs 30h + 22.5h  5credits  2q  x x
Optional LMAT2510

Wiskundige logica (KUL)  (in French) N. 30h  6credits  2q  x x
Optional LMAT2520

Algebraische getaltheorie (KUL)  (in French) N. 30h  6credits  2q  x x
Optional LMAT2530

Asymptotiek en speciale functies (KUL)  (in French) N. 30h  6credits  2q  x x
Optional LMAT2540

Submanifolds, Riemannian and sympletic spaces (KUL)  (in French) N. 30h  6credits  1q  x x
Optional LINMA2380

Matrix theory  (in French) Paul Van Dooren 30h + 22.5h  5credits  2q  x x
Optional LINMA1170

Numerical analysis  Pierre-Antoine Absil, Paul Van Dooren (coord.) 30h + 22.5h  5credits  1q  x x
Optional LINMA2345

Differential equations  (in French) Abdou Kouider Ben-Naoum, Jean Van Schaftingen (coord.) 30h + 22.5h  5credits  2q  x x
Optional LINMA2725

Financial mathematics   (in French) Pierre Devolder 30h + 22.5h  5credits  1q  x x
Optional LACTU2020

MATHEMATICS OF FINANCIAL MARKETS  Pierre Devolder 30h + 15h  5credits  1q  x x
Optional LACTU2030

LIFE INSURANCE 1  Michel Denuit, Françoise Gilles 30h + 15h  5credits  1q  x x
Optional LACTU2070

STOCHASTIC FINANCE 1  Pierre Devolder 30h  5credits  2q  x x
Optional LACTU2010

NON LIFE INSURANCE 1  Michel Denuit 30h + 15h  5credits  1q  x x
Optional LACTU2040

PENSION FUNDING  Pierre Devolder 30h + 15h  5credits  2q  x x
Optional LACTU2060

LIFE INSURANCE 2  Michel Denuit 30h  5credits  2q  x x
Optional LACTU2080

REINSURANCE  Jean-François Walhin 30h  5credits  2q  x x
 


Option statistique [30.0]
Legend
Mandatory Optional
Courses not taught this academic year Periodic courses not taught this academic year
Periodic courses taught this academic year Two year courses

Click on the course code to see detailed informations (objectives, methods, evaluation...)
Year
1 2
Mandatory LMAT2470

Processus stochastiques (statistique)  (in French) Jan Johannes 30h  5credits  1q  x  
Mandatory LSTAT2030

Statistical analysis  Anouar El Ghouch, Rainer von Sachs 30h + 22.5h  5credits  2q  x  
Mandatory LSTAT2200

Survey and Sampling  Marie-Paule Kestemont 15h + 5h  4credits  2q  x  
Mandatory LSTAT2020

Statistical computing  Céline Bugli (supplée Bernadette Govaerts), Bernadette Govaerts 20h + 20h  6credits  1q  x  
Mandatory LSTAT2110

Data Analysis  Christian Hafner, Johan Segers 22.5h + 7.5h  5credits  1q  x  
Mandatory LSTAT2120

Linear models  Christian Hafner 22.5h + 7.5h  5credits  2q  x