MSc in Mathematics and the Foundations of Computer Science
Admissions Criteria
Introduction
Over the last 10 years or so, there has been an explosion in the use of computers in helping to solve mathematical problems. Such problems range from the extremes of pure number theory across the spectrum of mathematics to solving differential equations originating in biology and engineering. In this course the emphasis is on combining those parts of mathematics which both gain from and contribute to the theoretical aspects of computer science. The mathematical content of this MSc has been deliberately chosen to complement those areas of Computer Science which make up this course. For this reason, the mathematical schedules in this MSc concentrate on Algebra, General Topology, Number Theory, Logic and Combinatorics. Every student concentrating on the mathematical side of this MSc will be expected to study at least one course involving either the theory or experimental uses of computers. This course will be of great benefit to those graduate students hoping to do research on the frontiers of mathematics and computer science. The ideal product will be well equipped either to start work on a doctorate or to enter the research side of industry.
Students take courses from two sections: Section A (Mathematical Foundations) and Section B (Applicable Theories). 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 the mathematical and logical basis to many modern techniques in information technology (for example, machine learning, programming language design and concurrency). Applicants should have a strong mathematical background, that is, a good honours degree in Mathematics or a good honours degree in Mathematics or in Computer Science containing a significant mathematical component.
Outline of Structure
The course will consist of examined lecture courses and a written dissertation. The lecture courses will be divided into two sections:
Section A: Mathematical Foundations
Section B: Applicable Theories
Each section shall be divided into Schedules I (basic) and Schedule II (advanced). Candidates shall be required to satisfy the examiners in at least two courses taken from Section B and in at least two courses taken from Schedule II.
The majority of these courses will be given in the first two terms.
During Trinity Term and over the summer the student should complete a dissertation on an agreed topic. The dissertation must bear regard to course material from Section A or Section B, and it must demonstrate relevance to some area of science, engineering, industry or commerce.
Examinations
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 a test based on written work. Candidates will be required to pass five courses, of which at least two shall be from Schedule II, and not all of which may be from the same section.
Candidates should complete their dissertation by the middle of September, and will be orally examined on the dissertation and the background material to it.
The written assessment on each lecture course will be made by giving the candidate a mini-projects to develop and candidates will be required to sign a statement that the work offered for assessment is theirs alone. The mini-projects will be set at the start of the last week of the relevant lecture course and will be suggested by the course lecturers.
Facilities
Lectures and classes take place in the Mathematical Institute and in the Department of Computer Science, both of which are close to the Radcliffe Science Library, the scientific section of the University Library (the Bodleian). All students have access to this library, which holds, or can readily obtain, all books and periodicals of interest, and also to the Whitehead Library in the Mathematical Institute. The Department of Computer Science has its own library comprising mainly books on numerical analysis and computation.
Students have access to a wide range of computing facilities. These include an extensive network of Linux workstations at the Mathematical Institute and two powerful parallel computing systems that are installed in the Department of Computer Science. All of the machines are connected to the University-wide network, and the Internet, so it is possible to access many of them from terminals and workstations in the Department of Computer Science, Mathematical Institute, University Colleges and Departments, and from home.
Every office in the Mathematical Institute has at least one Unix workstation. In addition, there are four public access computer rooms available for use 24 hours a day, 7 days a week.
Nearly every office in the Department of Computer Science building contains some computing facility, most commonly in the form of a Sun workstation or PC which can be used as a local resource or to access other nodes on the Departmental network. In addition there are a number of public terminal rooms and printer rooms. A wide variety of commercial software and public domain software is available online, as well as software developed within the Department.
The Oxford University Computing Service also has computer rooms for student use, as well as a help desk and a shop for purchasing software for use at home.
Oxford University is a collegiate university and each College forms an autonomous community with its own social, cultural and sporting facilities. The older, undergraduate colleges have a substantial number of graduate students: the younger, graduate colleges admit only graduates. Every student on the course is required to become a member of a college and may offer a list of preferences at the time of application.
List of Lecture Courses 2010/2011
Section A: Mathematical Foundations
Schedule I
| Title | Lecturer | Term |
| Algebraic Number Theory | Prof Flynn | HT |
| Analytic Number Theory | Prof Heath-Brown | MT |
| Analytic Topology | Dr Suabedissen | MT |
| Axiomatic Set Theory | Prof Zilber | HT |
| Godel's Incompleteness Theorems | Dr Isaacson | MT |
| Group Theory | Prof Collins | HT |
| Introduction to Representation Theory | Dr Henke | MT |
| Lambda Calculus and Types | Dr Tzevelekos | MT |
| Lie Algebras | Prof J Wilson | MT |
| Model Theory | Dr Koenigsmann |
Schedule II
| Title | Lecturer | Term |
| Algebraic Geometry | Dr Berczi | MT |
| Building Infinite Groups | Prof Wilson | HT |
| Recursion Theory* | Dr Koenigsmann | HT |
Section B: Applicable Theories
Schedule I
| Title | Lecturer | Term |
| Applied Probability | Dr Hammond | MT |
| Categories, Proofs and Programs | Dr Doering | MT |
| Communication Theory | Dr Stirzaker | MT |
| Computational Complexity | Dr Kreutzer | HT |
| Concurrency | Prof Roscoe | HT |
| Foundations of Computer Science | Prof Benedikt | MT |
| Graph Theory | Prof McDiarmid | MT |
| Reasoning about Information Update | Dr Sadrazadeh | HT |
Schedule II
| Title | Lecturer | Term |
| Automata, Logic and Games | Prof Ong | HT |
| Computational Number Theory* | Prof Heath-Brown | TT |
| Computer Aided Formal Verification | Prof Melham | MT |
| Elliptic Curves | Prof Heath-Brown | HT |
| Probabistic Combinatorics | Prof Riordan | HT |
| Probability and Computing | Dr Worrell | MT |
| Quantum Computer Science | Dr Doering | HT |
| Random Graphs | Prof Riordan | TT |
| Representation Theory of Symmetric Groups | Dr Danz | HT |
| Theory of Data and Knowledge Bases | Prof Gottlob | HT |
*These courses are offered as directed reading courses, with syllabuses provided as in the case of lecture courses.
It is possible that some additional courses will be added or repeated as reading courses, especially for Trinity term. Full synopses will be available in September, but where the title of a course is the same as a course given in 2009/10, it is likely that only minor changes will be made from that synopsis.
A full course synopsis is also available in the Handbook
APPLICATION
Further information regarding the course can be obtained from graduate [dot] studies [-at-] maths [dot] ox [dot] ac [dot] uk.">Margaret Sloper.
Formal details of admission to the University and to the Colleges are contained in the Graduate Studies Prospectus, which is published annually. A copy of this can be found on the University web pages at www.admin.ox.ac.uk/gsp.