Masters degrees in Pure Mathematics involve advanced, abstract analysis of quantities, magnitudes, forms and their relationships, predominantly using symbolic logic.
Related subjects include Mathematical Logic and Interdisciplinary Mathematics. Entry requirements usually include an undergraduate degree in an appropriate Mathematics discipline.
Professionals within the field of Pure Mathematics typically draw their inspiration from natural and social phenomena to develop accurate models for describing the real world. As such, methodologies within this field are significant in many other fields (including Architecture, Civil Engineering, Mechanical Engineering, Aerospace Engineering, and Space Science, to name a few).
Careers are therefore highly varied for graduates of this subject. For example, you may be employed within the manufacturing industries to develop prototypes of various products, particularly vehicles and other automotives.
Alternatively, you may become involved within professional practices related to mining and deep sea investigations, such as defence systems and the design of technology such as submarines for environmental surveillance.
Other careers may include consultation on celestial mechanics and the development of satellites and space travel. Or, you may even undertake assessment of economic practices on behalf of government departments and large corporations.
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.
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.
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)
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.
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.
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.
The approval from the Institute of Mathematics and its Applications is currently being sought.
A student obtaining an approved IMA award can qualify as a Chartered Mathematician once they have completed 5 years employment in a relevant occupation after graduating.
The MSc in Mathematics is a one-year taught programme run by the School of Mathematics and Statistics. This programme is particularly suited for those seeking a career in academic mathematical research or a mathematics-related career in the private sector.
The programme consists of two semesters of taught courses followed by a dissertation (15,000 words) over the summer months. Most modules for the MSc in Mathematics are traditional semester-long lecture courses with end of semester exams, but some modules have a large element of continuous assessment. Class sizes range from 10 to 60 students, depending on the module.
The School of Mathematics and Statistics is well equipped with computing facilities (including a large parallel computing cluster) and an on-site library.
For an MSc in Mathematics, students take at least 90 credits at 5000-level Mathematics and Statistics modules. The remaining 30 credits can be taken from the School's 3000-level and 4000-level modules. At least 90 credits of the total of 120 credits of the taught part should be Pure Mathematics or Applied Mathematics modules.
The modules in this programme have varying methods of delivery and assessment. For more details of each module, including weekly contact hours, teaching methods and assessment, please see the latest module catalogue which is for the 2017–2018 academic year; some elements may be subject to change for 2018 entry.
This programme reflects and benefits from the strong research activities of the Department of Mathematics.
The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:
During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.
This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation.
Example module listing
The following modules are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.
Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management.
There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.
As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.
Knowledge and understanding
Intellectual / cognitive skills
Professional practical skills
Key / transferable skills
We often give our students the opportunity to acquire international experience during their degrees by taking advantage of our exchange agreements with overseas universities.
In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.