This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics and Mathematical Logic. The programme is suitable not only for students who wish to improve their background knowledge prior to applying to undertake a PhD by research, but also for students who wish to enhance their knowledge of postgraduate-level abstract mathematics.
The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from May until September.
During the taught component of the course, you will normally take five units together with a written project. You may choose exclusively pure topics, or mainly logic modules with a few pure modules. Alternatively, students can choose a mixture of the two. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.
After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor.
You can also take the programme part-time, over a period of two years. There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.
The aims of the programme are to provide training in a range of topics related to pure mathematics and mathematical logic, to encourage a sophisticated and critical approach to mathematics, and to prepare students who have the ability and desire to follow careers as professional mathematicians and logicians in industry or research.
The taught component is assessed by coursework, project work and by written examination. The written exams take place at the end of January (for the first semester course units) and the end of May (for the second semester course units). The dissertation component is assessed by the quality and competence of the written dissertation.
The Postgraduate Diploma and Postgraduate Certificate exist as exit awards for students who do not pass at MSc level.
The taught courses cover material related to the research interests of the academic staff. Topics covered in lectured course units normally include: set theory, group theory, dynamical systems and ergodic theory, measure theory, functional analysis, algebraic topology, Godel's theorems, hyperbolic geometry, Lie algebras, analytic number theory, Galois theory, predicate logic, computation and complexity, and other topics relevant to current mathematics.
The Master of Science in Mathematics (120 ECTS) is a research-based master’s programme in which you can specialize in the following fields of mathematics: Pure Mathematics: Algebra, Analysis and Geometry; and Applied Mathematics: Statistics, Financial Mathematics, Computational Mathematics, Plasma-Astrophysics.
Besides a solid, all-round education in mathematics, the programme offers you the possibility to focus on either pure or applied mathematics. This allows you to acquire both breadth of knowledge and depth in your own areas of interest. Pure and applied mathematics courses are firmly grounded in the core research activities of the Department of Mathematics. Gradually, you will gain experience and autonomy in learning how to cope with new concepts, higher levels of abstraction, new techniques, new applications, and new results. This culminates in the Master’s thesis, where you become actively involved in the research performed in the various mathematical research groups of the Departments of Mathematics, Physics, Astronomy and Computer Sciences.
This is an initial Master's programme and can be followed on a full-time or part-time basis.
The programme of the Master of Science in Mathematics consists of 120 ECTS. You choose one of the two profiles – Pure Mathematics or Applied Mathematics (54 ECTS) – and one of the two options – Research Option or Professional Option (30 ECTS). The profile allows you to specialize either in pure mathematics (algebra, geometry, analysis), or in applied mathematics (statistics, computational mathematics, fluid dynamics).
There is one common course: ‘Mathematics of the 21st Century’ (6 ECTS). To complete the programme, you carry out a research project that results in a master’s thesis (30 ECTS).
All staff members of the Department of Mathematics are actively involved in the two-year Master of Science in Mathematics programme. The academic staff at the Department of Mathematics consists of leading experts in their fields. Researchers in pure mathematics focus on algebraic geometry, group theory, differential geometry, functional analysis, and complex analysis. Researchers in mathematical statistics deal with extreme values, robust statistics, non-parametric statistics, and financial mathematics. Research in the applied mathematics group is in computational fluid dynamics and plasma-astrophysics.
Mathematicians find employment in industry and in the banking, insurance, and IT sectors. Many graduates from the research option pursue a career in research and start a PhD in mathematics, mathematical physics, astrophysics, engineering, or related fields.
The master’s programme Mathematics focuses on analysis and number theory. From applied to fundamental research, and from algebra to data science, our master’s programme spans these fields entirely.
The two-year master's programme Mathematics has two components: an analysis-oriented component with topics such as dynamical systems, differential equations, probability theory and stochastics, percolation and mathematics in the life sciences, and an algebra/geometry-oriented component with topics such as algebraic number theory, algebraic geometry, algebraic topology and cryptology. The goal of each programme is to train the student as an independent researcher, and to develop the necessary skills and proficiency to advance your career.
Read more about our Mathematics programme.
Find more reasons to choose Mathematics at Leiden University.
The master’s programme in Mathematics in Leiden focuses on analysis, probability and statistics, number theory and (arithmetic) geometry. If you are looking for an opportunity to specialize in one of these areas, Leiden is an excellent possibility. Students who have obtained a Master of Science degree in Mathematics possess a thorough theoretical basis, know how to work in a multinational environment, and are able to operate well on the international market.
Read more about the entry requirements for Mathematics.
The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. It is the medium for expressing knowledge about many physical phenomena and is concerned with patterns, systems, and structures unrestricted by any specific application, but also allows for applications across many disciplines.
Modes of delivery of the Masters in Mathematics/Applied Mathematics include lectures, laboratory classes, seminars and tutorials and allow students the opportunity to take part in project work.
If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).
You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.
The project titles are offered each year by academic staff and so change annually.
Career opportunities are diverse and varied and include academia, teaching, industry and finance.
Graduates of this programme have gone on to positions such as:
Maths Tutor at a university.
This course provides you with a sound general knowledge of advanced mathematics through study in several pure and applied areas of the subject, including Statistics and Operational Research. A wide choice of topics is available for your dissertation, taken under the supervision of a member of the academic staff.
If you wish to enter employment within the field of Mathematics then this course will enhance your career prospects by promoting a professional attitude to Mathematics. Mathematicians are warmly welcomed in industry, business and commerce for their analytical ability and logical approach to problem solving. The course is particularly suitable if you are planning a career in teaching Mathematics or are already a qualified teacher seeking to enhance your promotion prospects.
Research Methods and professional Skills
Introduction to Cybermetrics
Advanced Topics in Mathematics
The Mathematics department includes a team of researchers in the field of Introduction to Cybermetrics, led by a professor who has been recognised as a leading international authority on the subject and who achieved a very high rating in the latest Research Assessment Exercise.
We pride ourselves on the academic support and guidance given by our friendly and approachable staff. Students have shown their appreciation for this by the exceptionally high ratings they have given us in the National Student Survey in recent years.
Students will have developed advanced technical skills within the field of Mathematics together with an ability to critically analyse and evaluate complex problems. These skills should equip students to enter careers in Mathematics in a variety of roles.
There is a shortage of Mathematics-related skills both nationally and regionally, and in particular there is a recognised severe shortage of qualified Mathematics teachers. Hence the Mathematics qualification that this course offers will make its graduates highly employable.
Excellent career opportunities will also be open in operational research, statistics, information analysis, financial advising, actuarial work and accountancy.
You will be able to demonstrate a full understanding, knowledge and experience of complex and specialised areas of mathematics; Select and apply appropriate techniques to the analysis, design and synthesis of solutions to problems which require mathematics for their resolution.
Within this course, you will apply knowledge of mathematics with particular reference to its applications in other subject areas (e.g. mathematical education, analysis and modelling of business and finance, computing and scientific systems).
You will be able to demonstrate originality in the application of knowledge, together with a practical understanding of how established techniques of research and enquiry are used to create and interpret knowledge in mathematics.
Conduct research into current mathematical literature; review, analyse and evaluate findings in a professional manner.
This course will enable you to deal with complex issues both systematically and creatively, making sound judgements in the absence of complete data, and communicating conclusions clearly to specialist and non-specialist audiences.
Faculty of Science and Engineering on Facebook
Faculty of Science and Engineering on Twitter
The Algebra and Topology section is an active research group consisting of renowned experts covering a remarkably broad range of topics. The group consists of two full professors (I. Moerdijk, Spinoza Laureate 2012, and B. Moonen), four permanent members, and a large number of post-docs and PhD students. More information about the research activities of the group can be found at http://www.math.ru.nl/topology.
The section offers a Master's specialisation in Algebra in Topology, which is a 2-year programme aimed at students with an interest in pure mathematics and its applications.
The Master's programme has a strong focus on current research developments. It introduces students to a broad range of techniques and concepts that play a central role in modern mathematics. In addition to providing a strong theoretical basis, the programme offers excellent opportunities for a further specialisation focusing on applications of pure mathematics or on interactions with other fields.
The programme offers courses in Algebra, Topology, Geometry, Number Theory, and Logic and Computation. There are strong interactions with other Master's specialisations at Radboud University, notably the ones in Mathematical Physics and in Mathematical Foundations of Computer Science.
In addition, the programme offers a variety of seminars from beginning Master's level to research level. Moreover, students have the possibility to incorporate courses from related programmes (e.g. Mathematical Physics and Mathematical Foundations of Computer Science into their programme, as well as individual reading courses. Each student concludes his programme by studying a special topic and writing a Master's thesis about it.
Excellent students having completed this Master's programme or a similar programme elsewhere can in principle continue and enrol in the PhD Programme, but admission for this is limited and highly selective.
See the website http://www.ru.nl/masters/algebratopology
1. A completed Bachelor's degree in Mathematics or related area
Entering the Master’s programme in Mathematics requires a Bachelor’s degree in Mathematics that is the equivalent to a Dutch university diploma (this does not include a Bachelor’s from a university of applied science, in Dutch hbo; in German Fachhochschule). That means we expect you to have a solid background in the core areas groups, rings, fields and topology. We expect students to have passed core mathematics courses during their Bachelor’s in:
The Examination Board will determine if an international student has the required mathematical knowledge to be admitted. The Examination Board will also indicate if the student is required to follow specific courses from the Bachelor's programme to eliminate possible deficiencies.
- Basic notions in Mathematics
- Linear Algebra
- Differential Equations
2. A proficiency in English
In order to take part in this programme, you need to have fluency in both written and spoken English. Non-native speakers of English without a Dutch Bachelor's degree or VWO diploma need one of the following:
- TOEFL score of ≥575 (paper based) or ≥90 (internet based)
- An IELTS score of ≥6.5
- Cambridge Certificate of Advanced English (CAE) or Certificate of Proficiency in English (CPE) with a mark of C or higher
Mathematicians are needed in all industries, including the banking, technology and service industries, amongst many others. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of specialised analytical and problem-solving skills.
The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may not seem initially relevant. This makes your job opportunities very broad and is why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- ICT developer / software developer
- Policy maker
Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world.
See the website http://www.ru.nl/masters/algebratopology