# The Mathematician and the Applied Mathematician

It has always been the case, but particularly since the 17th century, general scientific development has been intimately linked to that of Mathematics. Historical examples are numerous: Newton, Euler, Lagrange, concurrently conducted their studies in Mathematics, Physics, Mechanics and Astronomy. The development of the general theory of relativity would not have been possible without the Riemannian geometry mathematical tool, established some fifty years before. Conversely, natural sciences are nowadays, as always, an inexhaustible source of inspiration to Mathematicians; three out of the four 1990 Fields Medal Laureates (“equivalent” to the Mathematics Nobel Prize) were rewarded for work inspired by the Field Theory.

In the nineteenth century, mathematical applications were essentially limited to Physics, Astronomy, and Engineering sciences. Nowadays it extends to fields as diversified as Economics, Biology, Business Management, Medicine, etc. .

The Mathematics Section at EPFL was created in 1970, after the Federalization of the school. Its mission is to educate mathematicians, directed towards fundamental mathematics or to its applications. It welcomes around 150 new students each year; adding up to a total of nearly 450 students. Significantly, young women are particularly well represented, as the female share of the Section regularly reaches 25 to 30% of the faculty.

### The Bachelor in Mathematics

The Mathematics Section has shaped its Bachelor program to provide a fundamental base in the domains of pure and applied mathematics. It is a foundation course in mathematics, complimented with courses in Physics, Informatics and Social Sciences. In the Bachelor third year, courses can be chosen from a list of options, and the student must also carry out two one-semester long projects. Thus the student is allowed to give his Bachelor a personal touch, which will help him chose his Masters, and its professional path later on.

### Master in Mathematics

Nowadays, more than ever, knowledge advances often rely on modern mathematical tools. The Master in Mathematics is oriented towards high level pure mathematics (algebra, analysis, probability, geometry and topology) or applied mathematics (applied analysis, numerical analysis, probability, statistics, optimization). This degree leads to various careers in teaching, private companies, and governmental institutions. It is also an excellent preparation for students planning to follow a PhD program in mathematics.

The mathematician is a specialist in the analysis, abstraction and reflection necessaries to solve complex problems. In the professional world, this broad, general, competences are highly appreciated.

The level and variety of subjects studied allow the mathematician to acquire great mastery of fundamental mathematical tools and abstract reasoning. These tools are useful in a variety of fields. Just a few examples are: the modelling of DNA chains require innovative differential equations; communication systems of the future require powerful data compression algorithms; cryptography and coding require deep knowledge of modern algebra.

### Master in Applied Mathematics

Nowadays, more than ever, knowledge advances often rely on modern mathematical tools. The Master in Applied Mathematics (Master en Ingénierie Mathématiques) is oriented towards the applications for mathematics at a high level (operations research, applied probability and stochastic processes, numerical analysis and scientific calculus). The curriculum includes an engineering internship of 4 to 6 months. This degree forms an excellent basis for various professional careers such as financial mathematics, insurance, statistics, data analysis, scientific calculus and industrial modelling.

The applied mathematician is a specialist in the analysis of complex problems requiring abstraction, identification and extraction of relevant parameters; simulations of the system under consideration; forecasting and comparing expected results with factual data. In the professional world, these technical competences are highly appreciated.

The level and variety of subjects studied allow the applied mathematician to solve complex organizational problems. These competencies are useful in a variety of fields. Just a few examples are: the conception of predictive models in the financial and insurance domains; the optimization needed to implement those models; the calculations for an optimal mobile telephony network; statistical analysis of complex data, which is necessary in many domains.