General presentation of the second year master
1.1 Goals and career opportunities
The second year master in Pure and Applied Mathematics, research specialization (M2R for
shortness) offers a high level training in mathematics and their applications, as well as an
introduction to research. More precisely, the following topics are taught: algebra, geometry,
topology, complex analysis, dynamical systems, partial differential equations, optimisation,
numerical analysis, probability and statitics. The degree also presents a wide range of applications
of these mathematical tools to the study, the modeling and simulation of complex
phenomena occuring in Physics, Biology, Mechanics, Signal Processing, Finance, Aeronautics,
The natural, but not the only, continuation of the M2R is the preparation of a PhD thesis
in mathematics or in applied mathematics. Such a PhD gives access to the careers in academic
research as well as in research and development in the corporate and public sectors. The M2R
is also a very good preparation to the career of teacher (for instance in preparatory schools).
It is also a complement to engineer studies. In particular the students of ISAE and INSA can
benefit from a joint curriculum which allows them to combine the M2R with the last year of
training in their engineer school.
1.2 The environment
Research activity in Toulouse. The M2R Pure and Applied Mathematics benefits from a
very stimulating environment. It is supported by researchers from the Institute of Mathematics
of Toulouse, which gathers most of the mathematicians in the Toulouse area (UT1-UT2-UT3-
INSA-ISAE) and has the status of CNRS laboratory (Unité Mixte de Recherche du CNRS). The
research activities of the institute cover a wide mathematical range, from theory to applications
(learn more at http://www.math.univ-toulouse.fr). Besides, several research institutions,
applied research centers and a network of companies of various size are present in the Toulouse
area and develop activities in which mathematics play an important role. Among them are
EADS, CNES, ONERA, Météo-France, INRA, INSERM, ELF-SANOFI, MOTOROLA, ASTRIUM,
ALCATEL-ESPACE, etc. These institutions regularly offer internships for M2R
students, as well as PhD grants.
Partner institutions. Three universities and two engineer schools are associated to the
M2R: Université Paul Sabatier (UPS), Institut Supérieur de l’Aéronautique et de l’Espace
(ISAE), Institut National des Sciences Appliquées de Toulouse (INSA), Université de Toulouse
1 (UT1), Université de Toulouse 2 (UT2).
The M2R leads to a common certification of UPS-UT1-INSA-ISAE. Researchers from the
above five institutions teach courses for the second year master.
The Doctoral School. Since M2R students should be ready to start a PhD thesis the
next year, the M2R is closely connected to the Doctoral School EDMITT (Ecole Doctorale
de Mathématiques, Informatique et Télécommunications de Toulouse). More information is
available at http://www.edmitt.ups-tlse.fr.
1.3 Organisation of the studies
The courses. The second year Master in Pure and Applied Mathematics
offers a choice of courses but it is possible though,
with the approval of the faculty in charge, to choose one or even two courses from
another Master in Mathematics. The detailed rules are explained later on.
Curriculum. All courses are taught in English (during examinations students may use English
or French). The general structure is as follows:
– basic courses, of 30h each, during the fist term (students should pass 3 of them)
– advanced courses, of 24h each, during the second term (students should pass 2)
– a reading seminar, during the two terms, including participation to seminars and conferences
– an English course of 24h (see http://langues.ups-tlse.fr > Enseignement > Master
– an individual dissertation on a research topic.
Structure, length and ECTS credits of the courses in the standard curriculum.
Basic course 1 8 ECTS 30h first term
Basic course 2 8 ECTS 30h first term
Basic course 3 8 ECTS 30h first term
Reading seminar 6 ECTS 36h first term
Advanced course 1 6 ECTS 24h second term
Advanced course 2 6 ECTS 24h second term
English course 1 3 ECTS 24h second term
Dissertation 15 ECTS 4 months second term
TOTAL 30 ECTS first term and 30 ECTS second term
Dissertation and/or internship. The M2R curriculum comprises a dissertation. It is
prepared under the supervision of a researcher (usually from one of the 5 institutions associated
with the M2R). The dissertation often consists in understanding a few recent research articles
and can lead to the study of open questions. It can also be an internship in an applied research
center (in the public or the corporate sector). The preparation of the dissertation will start
in March, and lasts for at least 4 months. The possible topics are announced in December and
the students should make ther choice by the end of January. A public defense is organized at
the end of the year (usually in June, sometimes in September).
Reading seminar. The goal of this activity will be to enlarge the mathematical perspectives
of the students through active participation to mini courses, seminars and conferences.
Seminars and conferences. It is important to complete the curriculum with the regular
attendance to conferences, seminars or working groups. The Institute of Mathematics of
Toulouse features several of them every week; it organizes also some winter/summer schools (for instance
a yearly winter school in La Llagone). The advisors help the students to select the most relevant activities.
Moreover, M2R students attend lectures provided by the Doctoral School on careers
1.4 Pedagogic information
Individual advice and choice of the courses. Every student will propose his own list of courses.
This proposal has to be accepted by the faculties in charge before to be definitive.
This will be done at the beginning of the first term. The faculties in charge meet the
students individually at the beginning of the first and second term in order to help them to
make the right choices according to their projects. This can lead them to allow some students
to choose a course (or two) in another master 2.
Examinations. The precise modalities of examinations (called MCC for ”modalités de contrôle
des connaissances”) are officially declared every year. They have to be approved by the university
council. Students can answer to the tests in English or in French. Usually the exams
consist either in a written test of 4 hours, or in a combination of a written test, counting for
4/5 of the grade, and an individual oral or practical test counting for 1/5 of the grade.
For students who did not reach a grade of at least 10 (over 20) at the first examination,
a second examination is organized, no later than early September. In practice, it is often
organized much earlier (in April or May) provided that all interested students are available.
The M2R Jury meets by July and mid-september.
Continuation of studies and application to a PhD grant. The M2R provides the
students with a high-level training and a first contact with active research. For students who
think of PhD studies, it also gives a better idea of the various possible research topics.
The registration to a PhD is not automatic after the M2R: the student should get good
grades in M2R, find a researcher willing to serve as a PhD advisor in the framework of the
Doctoral School and obtain a PhD grant (there are various fundings: Doctoral contracts provided
by the university, PhD grants of CNRS, INRA, M´et´eo-France,…, as well as PhD grants
allowing to complete a PhD in the corporate sector with an academic co-advisor (usually called
”bourses CIFRE”). Some of the offers come with a prescribed topic, some do not.
It his higly recommended to meet with the M2R instructors, the director of the doctoral
school and the directors of the laboratories where the work will be done in order to build
a PhD project. The doctoral school receives offers of PhD grants from the university and
other institutions starting from January. Several internships (advertised in December) allow a
continuation of the work by a PhD thesis and are coupled with a PhD grant. Please visit the
website http://www.edmitt.ups-tlse.fr/ for more details.
1.5 How to apply to the M2R?
Conditions of admission. The M2R admission jury studies the application folders and sets
up the list of accepted students.
Applicants should have completed a first year master in Mathematics or in Applied mathematics,
or a cursus of equivalent level (e.g. an engineer school). The students of ISAE or INSA
who will start the last year of their school can apply and benefit from a mixed curriculum.
Student who already have a job or mothers of young children may complete a M2R curriculum
over two years instead of one.
Registration procedure. This is only an indicative text: the precise procedure and deadlines
are described on the web site of Universit Paul Sabatier.
Applicants should make a pre-registration on the website of Université Paul Sabatier:
http://www.ups-tlse.fr between March and June of the preceding academic year. Foreign
students should apply through the Campus France procedure (or CEF for ”Centre pour
les Etudes en France”) in their country, as early as possible.
After completing the pre-registration, applicants prepare a complete admission folder and
send it to the administrative office of the M2R, for mid-JUNE. Please include a detailed
CV, letter of motivation, copies of diplomas, and all grades of the previous years (especially
Bachelor and first year Master). For foreign students or for students who do not have a Master
1 in mathematics or applied mathematics, the application folder should contain a detailed
description of the curriculum of the last two years, and especially of the courses in mathematics.
It is also important to mention which track(s) of the M2R you are most interested in (this is
only a tentative information), the final choices will be done at the beginning of the courses.
It is essential to send the folder in time. Send it even if you are still waiting for the final
results of the current year (e.g. first year Master).
Results of admission will be posted on the website of Université Paul Sabatier in JULY.
The decision will also be notified individually to applicants by surface mail. It is valid only for
the current year.
Accepted students are expected to confirm their registration in July or August. Next, the
students can come to the administrative office, where they will receive an official letter which
allows them to preceed to the formal administrative registration in the central building of
the university. The tuition (which includes social insurance) costs about 500 euros. This
registration to the university is compulsory for all M2R students (but there are no fees for
students of ISAE and INSA for instance).
Late applications (after mid-June) can be send directly to the administrative office of the
Beginning of the year. A meeting of presentation will be organised at the beginning of September
2016. The courses will start on Monday the 12 th of September 2016.
1.6 Fellowships and housing
M2R Fellowships. Master 2 followhips are offered by the Centre International de Math´ematiques
et Informatique de Toulouse (CIMI) as an incentive for high-level students to come and
study mathematics or computer sciences in Toulouse. Applications can be send by email
More details can be found on the website http://www.cimi.univ-toulouse.fr/ .
The University Paul Sabatier offers a few fellowships each year, unfortunately in rather
small number. They are allocated after examination of academic and also social criteria.
Applications should comprise a detailled CV. Foreign students can often ask fellowships from
their home country, or from French organisations in case of cooperation agreements. They can
get more information in their country and in particular from the French embassy or consulate.
Housing. Students who whish to rent a room on campus should contact the C.R.O.U.S.
(Centre Régional des Oeuvres Universitaires):
C.R.O.U.S., 58 RUE DU TAUR, 31000 TOULOUSE, Phone 05 61 12 54 00.
Foreign students can ask directly the university service of international relations: ”Service
des Relations Internationales de l’Université Paul Sabatier”.
UPS – M2R administrative office: Mme Emilie MARUEJOULS
Secrétariat du M2R de Mathématiques Fondamentales et Appliquées
FSI, Bâtiment 1TP1, Université Paul Sabatier, 31062 TOULOUSE Cedex 9
Phone: 05 61 55 60 69.
Faculties in charge of the M2R:
Francesco COSTANTINO e-mail: francesco.costantinoATmath.univ-toulouse.fr
Radu IGNAT e-mail: radu.ignatATmath.univ-toulouse.fr
Clément Pellegrini e-mail : clement.pellegriniATmath.univ-toulouse.fr
Doctoral School ”Mathématiques, Informatique et Télécommunications de Toulouse”
Director: Jean-Michel ROQUEJOFFRE
Administrative office: Agnès REQUIS, e-mail: requisATadm.ups-tlse.fr
Address: Ecole doctorale EDMITT, RdC Bât. 1R1, Université Paul Sabatier, 118 Route
de Narbonne, 31062 Toulouse Cedex 9
Phone: 05 61 55 74 81, Fax: 05 61 55 81 74.
ISAE Administrative office:
Institut Supérieur de l’Aéronautique et de l’Espace
BP 4030 31055 TOULOUSE Cedex
Phone: 05 62 17 80 67
Faculty in charge for the M2R:
Denis MATIGNON e-mail: denis.matignonATisae.fr
ISAE, BP 4030 31055 TOULOUSE Cedex
INSA Administrative office:
Monique SEGERIC Centre de Mathématiques
Institut National des Sciences Appliquées
Complexe scientifique de Rangueil 31077 TOULOUSE Cedex
Phone: 05 26 15 59 93 11
Faculties in charge for the M2R:
Béatrice LAURENT-BONNEAU (statistics), e-mail: beatrice.laurentATinsa-toulouse.fr
Jérôme MONNIER (numerics), e-mail: jerome.monnierATinsa-toulouse.fr
UT1 Administrative office:
Manufacture des Tabacs, 21 Allée De Brienne,
Faculty in charge for the M2R:
Christine THOMAS, e-mail: cthomasATcict.fr.