The MSc Pure Mathematics offers a modern research-oriented taught course, providing students with a broader and deeper understanding of several core areas of pure mathematics that are of strong current interest and with a solid foundation for a career in research in pure mathematics. The programme covers a wide range of topics in algebra, analysis and number theory.
The course is informed by the research interests of the members of the Division of Pure Mathematics
- The School of Mathematical Sciences is one of the largest and strongest mathematics departments in the UK, with over 60 full-time academic staff
- In the latest independent Research Assessment Exercise, the school ranked eighth in the UK in terms of research power across the three subject areas within the School of Mathematical Sciences (pure mathematics, applied mathematics, statistics and operational research)
Advanced Linear Analysis
Algebraic Number Theory
Combinatorial Group Theory
Further Topics in Analysis
Further Topics in Rings and Modules
Pure Mathematics Dissertation
IELTS: 6.0 (with no less than 5.5 in any element)
Postgraduate combined research and teaching degree programme Pure Mathematics MRes:
This programme involves both taught classes in Pure Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree.
The MRes can be used as the first phase of our fast track PhD programme, in which the MRes thesis is extended over a further period of two years into a PhD thesis.
This programme involves both taught classes in Pure Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. The minimum period of registration is 12 months.
The MRes is an ideal preparation for entry into the PhD programme at Birmingham or at any other UK university. Indeed, the MRes programme can be used as the first phase of our fast track PhD programme. This is an excellent option for well-qualified mathematics students who do not have all the necessary mathematical background to start immediately on a PhD in their area of choice. In the fast track programme the MRes thesis is extended over a further period of two years into a PhD thesis.
Each MRes student is assigned a project supervisor who will act as director and mentor in the preparation of the MRes thesis. This gives each student the opportunity to work one-to-one with mathematicians who are international experts in their fields.
In addition to the assessed elements of the course, students are expected to play a full part in the research life of the School. The School has an active seminar programme, and organises international conferences in all areas of mathematics.
These courses are approximately one-third course work and two-thirds dissertation. The dissertation is completed under the direction of a project supervisor which gives our students the opportunity to work one-to-one with a leading expert in their field.
A regular programme of seminars and conferences takes place within the School in a wide range of subjects. Currently thriving at Birmingham are the following research groups:
This programme gives comprehensive training in mathematics and areas appropriate to professional development and research foundations. The MRes is an ideal preparation for entry into the PhD programme at Birmingham. In fact, the MRes programme can be used as the first phase of our ?Fast-track? PhD programme.
University Careers Network
Preparation for your career should be one of the first things you think about as you start university. Whether you have a clear idea of where your future aspirations lie or want to consider the broad range of opportunities available once you have a Birmingham degree, our Careers Network can help you achieve your goal.
Our unique careers guidance service is tailored to your academic subject area, offering a specialised team (in each of the five academic colleges) who can give you expert advice. Our team source exclusive work experience opportunities to help you stand out amongst the competition, with mentoring, global internships and placements available to you. Once you have a career in your sights, one-to-one support with CVs and job applications will help give you the edge.
If you make the most of the wide range of services you will be able to develop your career from the moment you arrive.
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 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