# Mathematics

## The programme in a nutshell

The Master’s programme in Mathematics is a two year programme, divided in four semesters. The last semester is dedicated to the Master’s project, which is either a research project or an external internship.

## Programme outline

The Master’s programme in Mathematics consists of specialized courses, optional courses and a Master's project. Courses can be taken throughout, culminating in the Master’s project in your second year. This project can be carried out under the supervision of a staff member from the mathematics institute, or externally at a company or research facility. In the latter case, you will have an on-location advisor and a supervisor from the institute. The Master's project is completed by writing a thesis and presenting your results in a colloquium.

## Courses

The collaboration with the University of Amsterdam on the entire Master’s programme and with all Dutch universities in MasterMath allows students to choose from a long and varied list of courses. Below a small selection:

- Algebraic Geometry
- Asymptotic Statistics
- Financial Stochastics
- Measure Theoretical Probability
- Functional Analysis
- Partial Differential Equations
- Algebraic Topology
- Mathematical Biology
- Modular Forms

Further information about the Master’s programme in Mathematics and course module descriptions can be found online in the study guide and at MasterMath.

## Professional profiles

Students in the Master’s programme in Mathematics can choose to follow the programme with an emphasis on research, on communication and education skills or on society-oriented skills. In the research and society-oriented profiles, the focus is on deepening your mathematical foundation, and includes an internship of Master’s project, lasting about six months. The communication and education profiles have, in comparison, less mathematical courses, but include a full year of courses on communication, science writing, teaching and/or an internship in a school.

## Specializations and Master’s Thesis

The Master’s programme concludes with a research project or with an external project carried out at a business or research facility outside the Department of Mathematics. This final project will fill the last semester. Your mentor can help you to find a suitable project. The project culminates in writing your Master’s thesis and giving an oral presentation of the results. VU University Amsterdam maintains close contact with many financial businesses, yielding internship possibilities in plenty. For more information on internships and work placement opportunities, you can consult the website of the Internship Office for Mathematics and Computer Science.

Examples of research topics for a Master’s project are most likely chosen close to the areas in which the Department conducts most of its research: Stochastics, Mathematical Analysis, and Algebra and Geometry.

**Stochastics
** VU University Amsterdam has the largest group of mathematicians in the Netherlands working in the three main disciplines in stochastics, statistics, probability and operations research. Topics of active research vary from the truly theoretical to the very applied.

- Percolation theory

How do forest fires spread, and can we predict the size of such fires to better control them? Modern probability theory allows us to better understand how small events may stochastically snowball and spread throughout a system. - Stochastic modeling and statistical analysis of biological processes

How do we find mutant genes responsible for particular diseases? How does one use studies on twins to get better understanding of the biological processes causing a disease? The biomedical sciences are the great fronteer of statistics, and plenty of fascinating open problems remain. - Queuing theory

How can one make sure waiting times in call centres or hospitals are minimized? There are still many open questions in Operations Research to deal with common problems in our everyday life.

**Differential Equations and Dynamical Systems**

The second major area of expertise at VU University Amsterdam is mathematical analysis. Researchers span a broad class of topics in differential equations and analysis.

- Blowup phenomena in partial differential equations

Can one predict when and at what speed gas balls ignite when lit? Functional analysis, perturbation methods and scaling techniques allow you to follow such fast-reacting systems. - Braids in dynamical systems

Solutions of differential equations are often knotted or braided inside the state space. Understanding the toplogy of such braids often allows you to infer existence and structure of new solutions which are forced by old ones. - Mathematical Biology

Next to the stochastic approaches to the life sciences, the department is involved in modelling biological systems using ordinary and partial differential equations. Examples include cell growth and collective behaviour in ants.

**Algebra and Geometry**

The department has a strong and active group in algebra and geometry, two important subjects in modern mathematics. Research is done in a wide spread of topics.

- Algebraic K-theory

This is a far-reaching generalisation of the notion of a dimension of a vector space. It has connections with number theory, algebraic geometry, and even theoretical physics. - Number theory

Finding all integer solutions to polynomial equations is an important research topic. A crucial role is played by prime numbers and associated number systems such as p-adic numbers. Besides their theoretical importance, these p-adic numbers also have applications in modern cryptography. - Toric topology

Toric topology lies on the borders between topology, algebraic and symplectic geometry, and combinatorics. Spaces with "nice" torus actions are studied, which can be described by purely combinatorial means. Main examples come from algebraic and symplectic geometry. - Classifying spaces

For any group there exists an associated topological space, the so-called "classifying space", which, in several cases, contains a lot of information about the underlying group. The goal of this subject is the study of these spaces from a homotopy theoretic point of view.