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MSc Mathematics and the Foundations of Computer Science (2025-2026 Entry)

4. The MSc Course

4.1 Overview  

The 12-month Master of Science in Mathematics and the Foundations of Computer Science course (FHEQ Level 7) focuses on the interface between pure mathematics and theoretical computer science. The course is suitable for those who wish to pursue research in pure mathematics (especially algebra, number theory, combinatorics, general topology and their 
computational aspects), mathematical logic, or theoretical computer science. It is also suitable for students wishing to enter industry with an understanding of mathematical and logical design and concurrency.

It builds on Oxford’s traditional strength in the foundations of theoretical computer science and in the related areas of mathematics that stem from the early days of the Programming Research Group in the Computing 
Laboratory. 

4.2 Aims 

The aim of this MSc is to provide a wide grounding over a range of mathematics and computing science and the regulations are designed to ensure that this is achieved without too much specialisation, while giving students a good choice of options. 

4.3 Learning Outcomes 

During the course you will develop a knowledge and understanding of:

  • several topics in advanced mathematics and theoretical computer science 
  • some significant applications of modern mathematical and computational methods. 
  • a general perspective on mathematics and the foundations of computer science as active areas of research. 

You will also have the opportunity to develop the following skills: 

Intellectual Skills 

  • A working knowledge of high-level mathematical methods and their applications. 
  • The ability to develop mathematical ideas and investigations in an open-ended fashion. 

Practical Skills 

  • Ability to apply abstract mathematical concepts to substantial specific examples. 
  • Ability to construct, write-up and communicate logical arguments of some complexity.  

Transferable Skills 

  • Ability to solve problems effectively and to apply high-level mathematical and computational methods to a 
    wide range of problems. 
  • Ability to manage your time and to acquire a complex body of knowledge in a limited time. 
  • Ability to manage your own learning and study for research or other professional qualifications. 
4.4 Course Structure 

The mathematical side of the course concentrates on areas where computers are used, or which are relevant to computer science, namely algebra, general topology, number theory, combinatorics and logic. Examples from the 
computing side include computational complexity, concurrency, and quantum computing.

The course will consist of examined lecture courses and a written dissertation. The lecture courses will be divided into two sections:

  • Schedule I – Basic Courses 
    The lectures may serve also as advanced undergraduate lectures, though students for an MSc should expect to read more widely around the material than would an undergraduate, and the written assignments set at the end of the course will be more searching than undergraduate examination questions, and will often allow the 
    student to develop a theme.
  • Schedule II – Advanced Courses 
    These courses can be expected to lead into areas where students may choose to write dissertations. Some Schedule II courses will be offered as directed reading, rather than by lectures. Their content will be the 
    equivalent of a standard course of sixteen lectures. 

It is intended that a major feature of this course is that candidates should show a broad knowledge and understanding over a wide range of material. Consequently, each lecture course taken will receive an assessment upon its completion by means of mini projects. Candidates will be required to pass five courses, of which at least two shall be from Schedule II. Details regarding the syllabus for each course are published online. Candidates must offer at least four courses from among those available in Michaelmas and Hilary Terms.

While it is necessary to pass five courses, and not more than four may be offered in any one term, the normal 
expectation is that students will take three or perhaps four courses in each of Michaelmas and Hilary terms. It should be noted that Schedule I courses will mainly be given in Michaelmas and Hilary terms, and Schedule II courses in Hilary and Trinity terms. Many courses provide problem sheets and associated classes; completion of such work (and its marking) forms an integral part of the course, and students are expected to enroll in and attend such classes.

Where this is not the case, either the lecturer or the supervisor (see below) will arrange a limited amount of ‘tutorial style’ teaching to supplement lectures. (See also ‘Reading Courses’, section 3.5)

The Geometric Deep Learning and Graph Representation Learning courses will have a practical assessment assigned to them and attendance to these practicals will be compulsory for all students taking these courses. While the marks for these practicals will not contribute towards the final mark for the mini-projects, attendance at these practicals will be marked, and a pass/fail/distinction line will appear on the transcript of students taking these courses. Students must ensure that they enter for the ‘Practicals’ assessment in the Michaelmas or Hilary Examinantion Entry windows if they are taking either or both of these courses. More information is given in ‘Practicals’, section 3.4, and in ‘Examination Entry’, section 4.3.

For the 2025-2026 academic year, candidates may, with the permission of the course lecturer and the MFoCS Course Director, substitute no more than one of the five required written assignments with an appropriate course of study 
from outside the published list (Approved Subject), which need not be examined by written assignment - i.e. permission may be requested to take a course assessed by examination, in place of one mini-project.  

The majority of these courses will be given in the first two terms. During Trinity term and over the summer students should complete a dissertation on an agreed topic. During Trinity Term you should be focusing primarily on your dissertation, and are unlikely to have time to take more than one course for examination.

All students will be required to attend an oral examination. This will be held in the second half of September.