“Mathematics and applications” Master's degree: reaching across the boundaries between disciplines to train tomorrow’s experts and researchers


In fall 2018, PSL (Paris Sciences & Lettres) is launching a Master's degree in “Mathematics and applications,” a collaborative effort between Ecole Normale Supérieure, Paris-Dauphine, EHESS, MINES ParisTech, and Observatoire de Paris. We interviewed Marc Hoffmann (Paris-Dauphine) and Patrick Bernard (ENS), program heads, for more information about this cutting-edge degree program in fundamental and applied mathematics.

Patrick Bernard (ENS) et Marc Hoffmann (Paris-Dauphine) dans l'espace Henri Cartan de l'ENS

PSL:  The PSL Master's degree in Mathematics and Applications will open in September 2018. What was the reasoning behind this program?

Patrick Bernard: Our hope is to create a Master's program that embraces every aspect of Mathematics, from so-called “pure” Mathematics to applied Mathematics and even professional applications. These two dimensions of mathematics have historically fed into one another, but today are separated by the organization of research laboratories and educational programs. We intend to bring them together, offering a curriculum focused on mathematics that offers both high-level theoretical courses and a wide range of career options.
Marc Hoffmann: Right, because the ability to develop algorithmic tools paired with advanced knowledge in Mathematics is highly prized in the professional world today. Thanks to PSL University, this Master's degree brings together two major research centers in high-level Mathematics: Université Paris-Dauphine’s CEREMADE for applied mathematics and the ENS DMA laboratory for fundamental mathematics. This important alliance was no easy feat to achieve.

PSL: Is that alliance what makes the Master’s program so unique?

PB: Yes and no. It is unique, but what really makes the Master's program unique, and the main factor that should motivate a student to apply, is that this program offers a foot in the door to the Ile-de-France mathematics community.
MH: True. In Mathematics, the community plays a very important role, and there is a great deal of interaction between laboratories, universities, and research centers. For a Master’s student, working closely with the ENS, Paris-Dauphine, and MINES ParisTech labs, for example, also puts them in contact with the entire Ile-de-France mathematics community (including the laboratories at Saclay, Sorbonne University (UMPC), etc.).
PB: Not to mention that the program is also connected with PSL-Maths, the major research program launched in 2017 to bring together all of PSL’s mathematicians and encourage interdisciplinary relationships. In concrete terms, it offers students an opportunity to interact with astrophysicists, biologists, chemists, and others whose disciplines are in constant dialogue with Mathematics.

PSL: That response highlights the importance of connections to research. How exactly does a student form connections with the research laboratories? How are the class locations distributed?

Education through research is essential: when students adopt a research question, they reveal their potential, moving on from an academic approach to truly master the material and develop their scientific interests.

MH: To answer the easy part first, the distribution of class locations is extremely simple, despite the many establishments involved. It depends on the chosen curriculum: students taking the M1 track in Fundamental Mathematics have classes at ENS; students taking the M1 track in Applied Mathematics or Advanced Mathematics go to Paris-Dauphine. The career-developing tracks in the second year are taught entirely at the Paris-Dauphine site. The MASH track, meanwhile, is taught at ENS, with a few classes at Observatoire de Paris and MINES ParisTech, which are relatively near to each other.
PB: Connections with research and laboratories form very naturally. Each professor is a researcher, and our offices and classrooms are nearby.  Because it is not always easy for a student to walk into a lab or our offices, we help them take that first step.  
MH: By 2019, we will implement a research credit (UE) for which students in the Advanced Mathematics or Applied Mathematics track will work on a project supervised by a researcher throughout an entire semester. This is essential, because students reveal their potential when they begin to tackle advanced questions. They “take off,” moving on from an academic approach to truly master the material and develop their scientific interests. Our role is to support this process and help them become independent thinkers.

PSL: The Master's degree offers increasing levels of specialization, with 3 tracks in the first year and 5 in the second. How do you help guide a student with a general interest in Mathematics into one of these 3 tracks?

MH: The idea of the Master's program is to open up broad horizons for teaching Mathematics, precisely to help M1 students choose based on their disciplinary interests rather than a previously made, and often somewhat arbitrary, career choice. Naturally, some students will specialize very early on, because they know that they want to go into Actuarial Science (Applied Mathematics track in M1 and Actuarial Science in M2) or Finance (Mathematics of Insurance, Economics, and Finance (MASEF) track in M2), for example. Others will prefer an interdisciplinary approach, like the one offered by the Mathematics, Apprenticeship and Humanities track in M2, which includes data science. The most important thing is that they find their studies fulfilling; I know a student, for example, who wanted to go into machine learning but hesitated at the prospect of a career in academic research. After a CIFRE dissertation, he was hired by a start-up specializing in web traffic management. I consider this a triumph for applied mathematics: his work is central to web issues but retains close ties to academic research.

PSL: How do you recruit your students, and in your opinion, what qualities can set an applicant apart?

PB: In M1, we recruit graduates of PSL (Bachelor's in Applied Mathematics from Paris-Dauphine, CPES multidisciplinary undergraduate degree with a mathematics specialization, ENS) or other universities. For entry into M2, the research tracks also attract a large proportion of international students. In general, our main recruitment criterion is a student’s mathematical ability, which must of course be excellent regardless of track.
MH: For the career-developing tracks, including Actuarial Science, it is important to keep in mind that of the five similar courses offered in France, the Mathematics and Applications Master's degree is the “mathiest”. Applicants must be sufficiently advanced and motivated to take the program. But one thing is certain - it’s exciting! And we have a 100% job placement rate for Master's graduates, not only in traditional actuarial science but also in careers involving machine learning and modeling skills.

PSL: What message would you like to share with incoming students?

MH: Set aside your career worries. You’re going to get to do math, and the fact that you’re here means you love the field--so just follow what you love and you’ll find yourself in an exciting career!
PB: Exactly. Be sure to take advantage of your special situation! Doing math in the heart of Paris, alongside the top researchers in the field, is an incredible opportunity!

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Deadline for applications : June, 18th, 2018