Mathematics

The language of science

Mathematics: The Language of Science

Mathematics is a vibrant, multifaceted and versatile field, in which the focus is on the study and development of techniques to tackle pure and applied mathematical questions. Often, the dividing line between theory and practice is merely an illusion. Mathematical theory, developed for a specific problem, often finds its way to unexpected  applications. For example, modern cryptography makes essential use of prime numbers, bacterial growth is governed by differential equations, and the spread of forest fires and infections can be predicted by stochastic models.

In research and teaching, the Vrije Universiteit Amsterdam combines pure and applied mathematics in a way that is unique in the Netherlands. We develop fundamental theory in algebra, number theory, geometry, analysis, dynamical systems, probability, and statistics. But we also apply this theory in business analytics, big data, forensic statistics, systems biology, neuroscience, and complex systems. Our Master’s programme in Mathematics provides you with excellent opportunities to specialize in one or more areas, and at the same time further deepen your general mathematical knowledge and skills.

Msc Mathematics in Amsterdam

The Master’s programme in Mathematics is a two year programme, divided into four semesters. It consists of specialized courses, optional courses and seminars, and concludes with the Master’s Project, which is either a research project or an external internship.

Courses and Tracks
During your Master's you specialise in one of the tracks Algebra and Geometry, Analysis and Dynamical Systems, Stochastics, Biomedical Mathematics, or an educational track. Each track comes with its own set of courses, but the tracks are not strictly separated, and you have a lot of freedom to choose your own study path (see Tracks below for more information).

Our programme is offered in full collaboration with the University of Amsterdam (UvA). Thus, you benefit from the expertise, networks, partnership projects, and international reputation of both VU Amsterdam and UvA. Moreover, you may choose from about 40 courses in the nationwide Mastermath programme (offered jointly by nine Dutch universities). Many of these courses are given at our campus.

Master Seminar
During the entire first year, you will participate in the weekly Master Seminar. The seminar is led by active mathematicians who will introduce you to the local research groups in your field of specialisation. You will also learn about possible thesis projects, practice giving advanced mathematical presentations, and experience what it means to be part of an active research community.

Master's Project
The last semester is dedicated to the Master’s Project, which is either a research project under the supervision of a staff member, or an external internship at a company or research facility. In the latter case, you will have an on-location advisor and a supervisor from the Department of Mathematics. The Master's Project is completed by writing a thesis and presenting your results in a colloquium.

In 2016, the ASML prize for best Mathematics Master's thesis of the Netherlands was won by VU student Madelon de Kemp.

For more information on internships and work placement opportunities, you can consult the website of the Internship Office for Mathematics and Computer Science. Further information about the Master’s programme in Mathematics and descriptions of course module can be found in the study guide.

In the Master's programme you choose one of the following six tracks:

  • Algebra and Geometry
  • Analysis and Dynamical Systems
  • Stochastics
  • Biomedical Mathematics
  • Education
  • Teachers

To get an idea about the (past) courses and people involved in these tracks, see this manual. Below we provide examples of research directions and recent thesis topics for each track.

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 generalization 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.

Titles of recent Master's theses
- Hilbert's Tenth Problem over large subrings of number fields
- Brauer groups

Analysis and Dynamical Systems
The second major area of expertise at VU Amsterdam is dynamical systems. Researchers span a broad class of topics in differential equations and analysis.

Computational dynamics
We often do simulations of a dynamical system on a computer, or calculate numerical solutions to a nonlinear differential equation. This gives very detailed, stimulating information, but from a mathematical perspective, the outcomes are at best conjectures about solutions. Rigorous validation of the computations allows such objects to be used as ingredients of theorems. In this rapidly developing research area mathematical theorems are intertwined with computational algorithms to obtain results about nonlinear dynamics that are not otherwise accessible.

Network dynamics
Networks of coupled nonlinear dynamical systems often display unexpected phenomena such as synchronisation. Examples include social cooperation and the simultaneous firing of neurons. We try to understand the scenarios by which synchrony emerges or breaks, using techniques from bifurcation theory, representation theory and singularity theory.

Topology and geometry in dynamical systems
In order to understand the global behaviour of dynamical systems, it is very fruitful to exploit their geometric and topological properties. Examples include the way orbits can be knotted or braided with each other, as well as the intimate relation between Hamiltonian dynamics and symplectic geometry.

Titles of recent Master's theses
- Dynamics on time-dependent networks
- Floer homology for travelling waves in reaction-diffusion equations

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

Statistics
Statistics is the science of learning from data, and it plays an increasingly important role in many research fields as well as in modern society. Our mathematical research on high-dimensional statistics, such as nonparametric Bayesian inference, adaptive procedures and statistics for networks, provides the theoretical backbone for statistical methodology, machine learning tools, and data analytic algorithms that are used in a wide variety of applications.

Spatial probability
How do forest fires spread, how can we model magnetization, and how is it possible that large system organise themselves? These are typical questions addressed in the research field called spatial probability.

Probability in forensic science
How can probability help in interpreting the evidential value of (partial) DNA matches? This is not only a practical issue, but also connected to philosophical debates about the meaning and interpretation of chance.

Stochastic optimization
Many decision problems in organizations are stochastic in nature, simply because the future is uncertain. As organizations innovate, new optimization problems come to see the light, that only wait for skilled mathematicians to solve them. We are both interested in further developing the theory of stochastic optimization, and in its applications in companies and other organizations.

Titles of recent Master's theses
- Limit theorems for some Markov-modulated processes
- Robust appointment scheduling and sequencing for many patients

Biomedical Mathematics
The department has long-standing collaborations with the VUmc and the systems biology group of the Vrije Universiteit Amsterdam.

Stochastic modelling and statistical analysis of biological processes
What do EEG- and fMRI recordings tell us about the dynamics of brain networks? How do we find which genes interact in causing a disease like cancer? The biomedical sciences are the great frontier of statistics, and plenty of fascinating open problems remain.

Mathematical biology
The department is also involved in more mechanistic modelling approaches to biological systems, using ordinary and partial differential equations. Examples include optimal growth strategies by microbial cells such as bacteria and yeasts, and collective behaviour in ants.

Titles of recent Master's theses
- Information processing in stochastic two-component signal transduction

Education
The Education track leads to a Master's degree in Mathematics with a Teaching Qualification (“eerstegraads bevoegdheid Wiskunde”). The programme consists of master courses in mathematics (36 EC), a Master's Project (24 EC), and 60 EC related to the Teaching Qualification (including an external internship). The part of the programme leading to the Teaching Qualification has the same content as the Master “Leraar VHO Wiskunde”, and is taught in Dutch. Students who already completed an “educatieve minor” during their Bachelor's attend less courses for their Teaching Qualification, and instead follow more mathematics courses.

Teachers
This track leads to a Master’s degree with an “eerstegraads bevoegdheid” for teaching mathematics. It has a special entry requirement: HBO students from the “lerarenopleiding wiskunde” with a “tweedegraads bevoegdheid” can enter this track after having followed a premaster programme, consisting of a specific selection of 30 EC of first year bachelor courses. The Teachers track itself consists of 42 EC of mandatory bachelor courses in mathematics, 24 EC of master courses, a Master's Project (24 EC), and 30 EC related to the Teaching Qualification.

An MSc in Mathematics prepares you for an exciting (international) career. Professional mathematicians work in research, education, business, finance, technology, healthcare, et cetera. Your analytic and problem solving skills make you a valuable asset for employers. If you graduate with excellent academic achievements, you are encouraged to apply for one of our PhD student positions and pursue an academic career.

We offer a special programme in Mathematics for outstanding students from our partner universities. The short track programme consists of one full year of study. You should be able to obtain at least 66 EC in courses (30 EC) and a Master’s project (36 EC) in this one year. Application for this programme is possible if you have finished at least 60 EC of courses at Master's level at one of our partner universities that entitle you to exemptions for master's courses at VU Amsterdam.

Partner universities
Students from our partner universities are encouraged to opt for this programme through their respective contact persons:

Partner universityContact person
Eötvös Loránd University (Budapest, Hungary)Prof. G. Michaletzky
University of Warsaw (Warsaw, Poland)Prof. A. Bojanowska
Jagiellonian University (Krakow, Poland)Prof. K. Ciesielski
Charles University (Prague, Czech Republic)please contact admissonsfs@vu.nl
University of Silesia (Katowice, Poland)Dr Michał Baczyński
Comenius University (Bratislava, Slovakia)Prof. Marek Fila


Courses
More information about the courses can be found in the study guide.

Admission and application
The Examination Board of the Faculty of Sciences will decide which applicants will be admitted to the Short track Master's programme in Mathematics.

  • Please note that you can only apply for the Short track Master's programme if you are a student from one of the above mentioned partner universities.
  • Contact your coordinator to discuss your study plans. You will need a formal approval from your coordinator stating that you are selected for the Short track Master. We will be informed by your coordinator if you have been selected.
  • Apply online as described here. Please note that you will not find the option “Short track Master” in Studielink, so just select the regular master programme of your choice. Application deadline is 1st of April. However, if you also would like to apply for the VU Fellowship Programme (VUFP), you should send in both applications before 1st of March.
  • You will have to upload a set of documents for your online application. If you have any questions about the requested documents, please contact the International Office. Please start your application, even if you cannot provide all documents.
  • Send the following documents (also) by regular mail to: 

    VU Amsterdam
    International Office/Degree Mobility Unit
    De Boelelaan 1105
    1081 HV Amsterdam
    The Netherlands

    1. A completed application form signed by a senior faculty representative at your home university; please mention your VU student number (which you will receive once you have started your online application) ;
    2. Your CV / Resume in English;
    3. A form with a list of completed courses (transcript of records) taken at your home university and a list of courses that you still intend to take at your home university. Please have these lists signed by a faculty representative from your home university;
    4. Recommendation letters from a senior member of your faculty (a professor in your department).

More information
For practical matters, like accommodation, living costs, financial aid, work, and so on, please contact our International Office.

Excellent reputation
The Department of Mathematics at VU Amsterdam has an excellent reputation as a training and research institute. The Netherlands Organization for Scientific Research (NWO) regularly awards prestigious VENI-VIDI-VICI grants to our researchers.

Location
We are located at the Zuidas campus in Amsterdam, which is very well connected to the inner city of Amsterdam, Schiphol international airport, and the rest of the Netherlands.

Close to where mathematics is applied
The mathematical department at VU Amsterdam maintains close ties with companies in the financial epicentre of The Netherlands, located at a stone’s throw from the university campus. The campus also houses the VUmc academic hospital, and mathematical research is conducted in a variety of biomedical collaborations. In addition, the university programmes in other fields of science provide opportunities for combining mathematics with key areas of application, such as economics and the modern natural and life sciences.

Mathematics in the Netherlands: nationwide courses
The Departments of Mathematics at the Dutch universities have combined their efforts by offering courses open to all Master's students in Mathematics. This Mastermath initiative offers students the highest quality of instruction and opens opportunities for interaction with students from other mathematics institutes. The joint courses widen the options for students who intend to pursue a PhD programme after completing their Master's programme. All Master's students in Mathematics are required to follow at least 30 EC of Mastermath courses.


 

Thierry Mondeel

Graduate in Mathematics (Biomedical Mathematics track)

Thierry Mondeel
"In my final preparatory year I was undecided about whether to study Physics or Mathematics. Attending several open days finally made me decide for Mathematics. Once at VU Amsterdam, I found that the track Biomedical Mathematics was being offered within the programme. I applied for it out of curiosity: it proved a great move!"

Student experiences


Martijn Zaal‘The high-tech industry is highly knowledge-intensive and research-oriented’

What exactly is the role of a physical model designer at ASML?
‘ASML produces lithography machines for the largest electronics companies in the world. Our customers use these machines to make chips. Stronger and more durable chips require ever more precise machines. As a physical model designer, I’m working every day to improve the software and algorithms. I’m working on the software for YieldStar, a metrology machine. With this machine you can measure what has been created on a “wafer” (a disc on which chips are made) after certain production steps. Algorithms can be thought of as mathematical recipes: they tell you how to use certain “ingredients” to achieve a result. We work on subproblems, pieces of a larger puzzle, in multidisciplinary teams that include physicists and others. My work is highly exploratory and there’s a lot of mathematics and physics to it.’

How did you end up at ASML?
‘After my doctoral research I worked in Bonn as a postdoc. I had a temporary contract and the subjects I was really interested in were not the subjects that would earn you grants. That’s when I reached a tipping point; I wanted to have some hands-on experience again. The high-tech industry is highly knowledge-intensive and research-oriented, so I knew which sector it had to be. ASML has attractive programmes and gives a lot of attention to your personal development, for instance by developing your management expertise.’

What do you like most about your work and what do you like least?
‘Putting the puzzle together, problem-solving, is immensely enjoyable. Working together on one team with people from entirely different disciplines is very instructive. The time-pressure is not so enjoyable. Sometimes it prevents you from achieving the perfect solution, as you don’t want to keep customers waiting for days. I’m a perfectionist and I prefer to keep fiddling until I’m completely satisfied myself.’

You did doctoral research first; why didn’t you start in a company straightaway?
‘The decision wasn’t obvious to me from the start. After graduating I hesitated for a while about starting in a company. The freedom to investigate problems you find interesting is what attracted me to the academic world. I was lucky: after my Master’s research I was immediately offered a doctoral position. So I didn’t take long to decide.’

What are you most proud of in your career?
‘Before I started on my doctoral programme, my supervisor was sceptical about what I wanted to do research on. Apparently, my subject was very out-of-the-box. I was working on a simple mathematical model for the swelling of a cell because of osmosis. The novelty about the research was that I used a so-called “gradient flow” to describe the problem. In the end I managed to prove the central thesis. When I talk about my research people are still amazed that I managed it, and I’m proud of that.’

Why did you choose to study Mathematics?
‘When I was sixteen I wanted to be a judge. This dream was shattered when I attended a case study during a taster session of the Faculty of Law; I was bored stiff. In secondary school I was good at maths, so I started on the Bachelor’s programmes in Mathematics and Econometrics, and I saw them both through. ’

Is there someone or something at VU Amsterdam you look back on especially fondly?
‘Riekus Kok, now an emeritus professor, has a gift to make difficult course material understandable. On top of that his lectures were fun; this man is an icon. He also encouraged me to continue doing two Bachelor’s programmes and to obtain higher marks.’

What would you say to current or prospective mathematics students?
‘Do something beside your study. It’s great if it’s related to what you are studying, but that’s not essential. Look beyond your specialisation from time to time. I myself taught support classes and contributed to planning software during my student days. Doing extracurricular activities teaches you interdisciplinary skills, gives you a feeling for applied science and will allow you to stand out in the job market.’


VU Wiskunde alumnus Rick Boere‘Doing doctoral research is like studying’

You currently work as a doctoral researcher at Eindhoven University of Technology. How did you end up there?
‘Before graduating and doing my Master’s thesis I did a ten-month work placement at TNO. After that it was time to take a breather. I decided to take it easy for a few months to figure out what I wanted to do. In January I ended up at Eindhoven University of Technology and also moved to Eindhoven. It takes time to get used to a new city. Fortunately, I have a nice house for myself: in Amsterdam I had no fewer than twenty housemates.’

What is your research about?
‘Briefly put, it’s about how to optimise traffic flows using stochastic models. A stochastic model is a process in which a phenomenon takes place in time or space with stochastic variables as outcomes, i.e., random quantities.’

What did you have to get used to after graduating?
‘At the end of the day, doctoral research is not unlike studying. For instance, I still take subjects, I’m always learning new things and even the environment (a University!) is still the same. So for me, it wasn’t that big of a transition. It must be a different story if you take up a mega commercial company job.’

Why did you choose to study Mathematics at VU Amsterdam?
‘After secondary school I actually wanted to be an air traffic controller, but I was too young to enter into the selection process. So I decided to study maths because I was good at it and I always found it an interesting subject at school.’

What do you learn in practice that you do not learn from lectures?
‘I’m lucky to have a nice supervisor who helps me decide on the course for my doctoral research. Thanks to this, I haven’t really got stuck yet. I can imagine that without such supervision it would be hard to plot the course of your research.’

How is your study useful to you in practice?
‘Above all the Mathematics programme teaches you to think logically, to have a certain way of thinking. This enables you to apply new theories easily in your work and to solve things quickly. It’s really not the case that I can now rattle off certain formulas. But in my doctoral research I do still benefit a lot from my specific mathematical knowledge.’

What do you want to do after obtaining your PhD?
‘I do think I’ll want to make the switch from the academic setting to the commercial one. I sometimes miss working on really practical issues, even though the research I’m doing is quite practical and non-theoretical already. This is because we also work with a consultancy firm which offers advice in the field of traffic flows.’

What was your favourite hangout at VU Amsterdam?
‘The clubhouse of STORM, the study association of Mathematics among other studies. I often spent time there during breaks; it was the spot at university where I really felt at home. The good atmosphere at STORM was also a reason why I moved into a student house.’
 

Overview Mathematics

Language of instruction

English

Duration

2 years

Tuition fee

Application deadline

1 July for Dutch students. 1 April for EU/EEA and non-EU/EEA students.*
* EU/EEA students with an international degree who do not need housing services through VU Amsterdam can apply until 1 June.

Start date

1 September
1 February

Study type

Part-time, Full-time

Specializations

Algebra and Geometry, Analysis and Dynamical Systems, Stochastics, Biomedical Mathematics, and Education

Field of Interest

Health and Movement/Computer Science, Mathematics and Business

Dutch students

The requirements are split up into specific Master's programme requirements and general requirements.

Specific Master’s programme requirements
Direct admission to the Master's programme in Mathematics is possible with a Bachelor's degree in Mathematics or Engineering Mathematics from a university in the Netherlands. If you have a Bachelor's degree in another subject from a university or institute of higher education in The Netherlands or elsewhere, you require the approval of the Examination Board. The main admission criteria are:
- A Bachelor of Science.
- 90 EC (European Credit points) or equivalent of Mathematics courses at the BSc level including some advanced courses.
- English language skills at the level of TOEFL score 580 or above.

Entrants from higher vocational education (HBO) generally have to follow a large part of the Bachelor's programme before they can be admitted to the Master's programme in Mathematics. Students who hold a teacher's degree in mathematics (“tweedegraads bevoegdheid wiskunde”) will likely be admitted to a premaster's programme. For specific questions, please contact the programme coordinator.

General requirements
Please check out the general application information for Dutch students.

Information about the programme

For further information about admission to the programme you can contact the master coordinator:

VU Amsterdam
Faculty of Sciences
Dr. C.M. Quant 
De Boelelaan 1083a, R-319
1081 HV Amsterdam
T +31 (0)20 598 7831
E c.m.quant@vu.nl

General information about VU Amsterdam
empty

Please phone us at +31 (0)20 598 5000 (Monday – Friday, 10:00 to 12:00). You may also email us at study@vu.nl.

Would you like to read the key points of the Master's programme? Order the brochure. Or find out more about the Master's programmes and visit our information days.

International students

The requirements are split up into specific Master's programme requirements and general requirements.

Specific Master's programme requirements
Direct admission to the Master's programme in Mathematics is possible with a Bachelor's degree in Mathematics or Engineering Mathematics from a university in the Netherlands. If you have a Bachelor's degree in another subject from a university or institute of higher education in The Netherlands or elsewhere, you require the approval of the Examination Board. The main admission criteria are:
- A Bachelor of Science.
- 90 EC (European Credit points) or equivalent of Mathematics courses at the BSc level, including some advanced courses.
- English language skills at the level of TOEFL score 580 or above.

Entrants from higher vocational education (HBO) generally have to follow a large part of the Bachelor's programme before they can be admitted to the Master's programme in Mathematics. Students who hold a teacher's degree mathematics (“tweedegraads bevoegdheid wiskunde”) will likely be admitted to a premaster's programme. For specific question, please contact the programme coordinator.

General language proficiency requirements
VU Amsterdam requires international applicants to take an English test and to submit their score as part of the application. Exceptions are made for students who have completed their education in Canada, USA, UK, Ireland, New Zealand or Australia, or who have obtained an international Baccalaureate or European Baccalaureate diploma. Please check out the admission and language requirements for international students for more details.

There are several possibilities for obtaining funding. VU Amsterdam, the Dutch governement and other organisations offer scholarships, fellowships and grants.

Information about the programme

For further information about admission to the programme you can contact the master coordinator:

VU Amsterdam
Faculty of Sciences
Dr. C.M. Quant 
De Boelelaan 1083a, R-319
1081 HV Amsterdam
T +31 (0)20 598 7831
E c.m.quant@vu.nl

Practical information for international students
empty

Would you like to know more about our courses, scholarships and application & registration procedure? Please contact our International Office.

Email: admissionsfs@vu.nl

General information about VU Amsterdam
empty

Please phone us at +31 (0)20 598 5000 (Monday – Friday, 10:00 to 12:00). You may also email us at study@vu.nl.

Would you like to read the key points of the Master's programme? Order the brochure. Or find out more about the Master's programmes and visit our information days.