Overview

The 12 month Master of Science in Mathematics and 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.

The courses offered are divided into two sections:
• theoretical
• applicable

Theoretical courses are concerned with those areas of mathematics and computer science which are related to the general goals stated above. The range of courses may vary from year to year.

Courses offered in 2020/2021

Section A

Schedule I:
C3.1 Algebraic Topology
B3.4 Algebraic Number Theory
C3.8 Analytic Number Theory
C1.3 Analytic Topology
C2.7 Category Theory
B2.2 Commutative Algebra
C3.3 Differentiable Manifolds
C1.2 Gödel's Incompleteness Theorems
B2.1 Introduction to Representation Theory
Lambda Calculus and Types
C2.1 Lie Algebras
C1.1 Model Theory
B3.5 Topology and Groups

Schedule II:
C3.10 Additive and Combinatorial Number Theory
C3.4 Algebraic Geometry
C1.4 Axiomatic Set Theory
C3.2 Geometric Group Theory
C2.2 Homological Algebra
C2.4 Infinite Groups
C2.6 Introduction to Schemes
C2.5 Non-Commutative Rings
C2.3 Representation Theory of Semisimple Lie Algebras
Topological Groups

Section B

Schedule I:
Categories, Proofs and Processes
Computational Complexity
Computer-Aided Formal Verification
Concurrency
Foundations of Computer Science
B8.5 Graph Theory
B8.4 Information Theory
B6.3 Integer Programming
Introduction to Cryptology
C7.4 Introduction to Quantum Information
Quantum Processes and Computation

Schedule II:
Analysing Logics using Tree Automata *
Applied Category Theory
Automata, Logic and Games
Categorical Quantum Mechanics
C8.3 Combinatorics
C3.9 Computational Algebraic Topology
Computational Game Theory
Computational Learning Theory
Distributional Models of Meaning *
C3.7 Elliptic Curves
C5.4 Networks
C8.4 Probabilistic Combinatorics
Probability and Computing

* reading courses


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