MSc

Overview

These are the modules taught in 2023/2024 - not all of them will be available in each following year but similar modules will be provided. Note that at least four modules need to be chosen at MA4 level but this can also include two modules from other departments at this level in consultation with the Director of studies. For details on required background for each module see the module descriptions (follow the links) for details.

Algebra

MA3 Modules

Code	Name
MA3A6	Algebraic Number Theory
MA3B8	Complex Analysis
MA3D5	Galois Theory
MA3F1	Introduction to Topology
MA3G6	Commutative Algebra
MA3H3	Set Theory
MA3H5	Manifolds
MA3K4	Introduction to Group Theory
MA377	Rings and Modules
MA3E1	Groups and Representations
MA3H6	Algebraic Topology
MA3K6	Boolean Functions

MA4 Modules

Code	Name
MA453	Lie Algebras
MA4A5	Algebraic Geometry
MA4H4	Geometric Group Theory
MA426	Elliptic Curves
MA442	Group Theory
MA473	Reflection Groups
MA4E0	Lie Groups
MA4H8	Ring Theory
MA4H9	Modular Forms
MA4J7	Cohomology and Poincare Duality
MA4J8	Commutative Algebra II
MA4M6	Category Theory

Analysis & PDEs

MA3 Modules

Code	Name
MA359	Measure Theory
MA398	Matrix Analysis and Algorithms
MA3B8	Complex Analysis
MA3G7	Functional Analysis I
MA3H5	Manifolds
MA3J4	Mathematical Modelling and PDEs
MA3K8	Variational Principles, Symmetry and Conservation Laws (note restriction)
MA3D1	Fluid Dynamics
MA3D4	Fractal Geometry
MA3G1	Theory of PDEs
MA3G8	Functional Analysis II
MA3H0	Numerical Analysis and PDEs
MA3H7	Control Theory
MA3J3	Bifurcations, Catastrophes and Symmetry

MA4 Modules

Code	Name
MA424	Dynamical Systems
MA433	Fourier Analysis
MA4A2	Advanced PDEs
MA4C0	Differential Geometry
MA4L3	Large Deviation Theory
MA4L6	Analytic Number Theory
MA4M2	Mathematics of Inverse Problems
MA4F7	Brownian Motion
MA4J0	Advanced Real Analysis
MA4J1	Continuum Mechanics
MA4N3	Hyperbolic Dynamics
MA4N5	Symmetric Functions and Integrable Probability

Applied and Computational Maths

MA3 Modules

Code	Name
MA359	Measure Theory
MA390	Topics in Mathematical Biology
MA398	Matrix Analysis and Algorithms
MA3J4	Mathematical Modelling and PDEs
MA3K9	Mathematics of Digital Signal Processing
MA3D4	Fractal Geometry
MA3G1	Theory of PDEs
MA3H7	Control Theory
MA3J3	Bifurcations, Catastrophes and Symmetry
MA3K0	High-dimensional Probability
MA3K1	Mathematics of Machine Learning

MA4 Modules

Code	Name
MA4A2	Advanced PDEs
MA4H0	Applied Dynamical Systems
MA4J5	Structures of Complex Systems
MA4L0	Advanced Topics in Fluids
MA4L3	Large Deviation Theory
MA4M2	Mathematics of Inverse Problems
MA482	Stochastic Analysis
MA4A7	Quantum Mechanics: Basic Principles and Probabilistic Methods
MA4E7	Population Dynamics: Ecology and Epidemiology
MA4F7	Brownian Motion
MA4J1	Continuum Mechanics
MA4M1	Epidemiology by Example
MA4M9	Mathematics of Neuronal Networks

From Other Departments

Code	Name
ST419	Advanced Topics in Data Science
ST420	Statistical Learning and Big Data
ST405	Bayesian Forecasting and Intervention with Advanced Topics
ST413	Bayesian Statistics and Decision Theory with Advanced Topics
CS424	Computational Biology
CS402	High Performance Computing
CS416	Optimisation Methods
PX457	High Performance Computing

Biomaths & Epidemiology

MA3 Modules

Code	Name
MA390	Topics in Mathematical Biology
MA398	Matrix Analysis and Algorithms
MA3J4	Mathematical Modelling and PDEs
MA3K9	Mathematics of Digital Signal Processing
MA3H0	Numerical Analysis and PDEs
MA3K1	Mathematics of Machine Learning

MA4 Modules

Code	Name
MA4H0	Applied Dynamical Systems
MA4J5	Structures of Complex Systems
MA4M2	Mathematics of Inverse Problems
MA4E7	Population Dynamics: Ecology and Epidemiology
MA4M1	Epidemiology by Example
MA4M9	Mathematics of Neuronal Networks

Combinatorics & Discrete Maths

MA3 Modules

Code	Name
MA359	Measure Theory
MA3B8	Complex Analysis
MA3F1	Introduction to Topology
MA3G7	Functional Analysis I
MA3K4	Introduction to Group Theory
MA3D9	Geometry of Curves and Surfaces
MA3G1	Theory of PDEs
MA3H2	Markov Processes and Percolation Theory
MA3J2	Combinatorics II
MA3K0	High-dimensional Probability
MA3K6	Boolean Functions

MA4 Modules

Code	Name
MA453	Lie Algebras
MA4J3	Graph Theory
MA442	Group Theory
MA473	Reflection Groups
MA4M8	Theory of Random Graphs
MA4M9	Mathematics of Neuronal Networks *

Differential Geometry & Geometric PDEs

MA3 Modules

Code	Name
MA359	Measure Theory
MA3B8	Complex Analysis
MA3F1	Introduction to Topology
MA3H5	Manifolds
MA3K8	Variational Principles, Symmetry and Conservation Laws (note restriction)
MA3D9	Geometry of Curves and Surfaces
MA3G1	Theory of PDEs

MA4 Modules

Code	Name
MA448	Hyperbolic Geometry
MA4A2	Advanced PDEs
MA4C0	Differential Geometry
MA4J0	Advanced Real Analysis

Dynamical Systems & Ergodic Theory

MA3 Modules

Code	Name
MA359	Measure Theory
MA398	Matrix Analysis and Algorithms
MA3B8	Complex Analysis
MA3G7	Functional Analysis I
MA3H5	Manifolds
MA3J4	Mathematical Modelling and PDEs
MA3K8	Variational Principles, Symmetry and Conservation Laws (note restriction)
MA3D1	Fluid Dynamics
MA3D4	Fractal Geometry
MA3G1	Theory of PDEs
MA3G8	Functional Analysis II
MA3H0	Numerical Analysis and PDEs
MA3H7	Control Theory
MA3J3	Bifurcations, Catastrophes and Symmetry

MA4 Modules

Code	Name
MA424	Dynamical Systems
MA433	Fourier Analysis
MA4A2	Advanced PDEs
MA4C0	Differential Geometry
MA4L3	Large Deviation Theory
MA4L6	Analytic Number Theory
MA4M2	Mathematics of Inverse Problems
MA4F7	Brownian Motion
MA4J0	Advanced Real Analysis
MA4J1	Continuum Mechanics
MA4N3	Hyperbolic Dynamics
MA4N5	Symmetric Functions and Integrable Probability

Geometry & Topology

MA3 Modules

Code	Name
MA359	Measure Theory
MA3F1	Introduction to Topology
MA3G6	Commutative Algebra
MA3H5	Manifolds
MA3D4	Fractal Geometry
MA3D9	Geometry of Curves and Surfaces
MA3E1	Groups and Representations
MA3H6	Algebraic Topology

MA4 Modules

Code	Name
MA448	Hyperbolic Geometry
MA453	Lie Algebras
MA4A5	Algebraic Geometry
MA4C0	Differential Geometry
MA4H4	Geometric Group Theory
MA426	Elliptic Curves
MA473	Reflection Groups
MA4E0	Lie Groups
MA4J7	Cohomology and Poincare Duality
MA4J8	Commutative Algebra II
MA4L7	Algebraic Curves
MA4M6	Category Theory

Number Theory

MA3 Modules

Code	Name
MA359	Measure Theory
MA3A6	Algebraic Number Theory
MA3B8	Complex Analysis
MA3F1	Introduction to Topology
MA3G6	Commutative Algebra
MA3H3	Set Theory
MA377	Rings and Modules
MA3D1	Fluid Dynamics
MA3D9	Geometry of Curves and Surfaces

MA4 Modules

Code	Name
MA424	Dynamical Systems
MA433	Fourier Analysis
MA453	Lie Algebras
MA4A5	Algebraic Geometry
MA4L6	Analytic Number Theory
MA426	Elliptic Curves
MA427	Ergodic Theory
MA4H8	Ring Theory
MA4H9	Modular Forms
MA4J8	Commutative Algebra II
MA4L7	Algebraic Curves

Probability & Stochastic Analysis

MA3 Modules

Code	Name
MA359	Measure Theory
MA398	Matrix Analysis and Algorithms
MA3G7	Functional Analysis I
MA3G8	Functional Analysis II
MA3H2	Markov Processes and Percolation Theory
MA3J2	Combinatorics II
MA3K0	High-dimensional Probability
MA3K1	Mathematics of Machine Learning
MA3K6	Boolean Functions

MA4 Modules

Code	Name
MA4J3	Graph Theory
MA4L3	Large Deviation Theory
MA482	Stochastic Analysis
MA4A7	Quantum Mechanics: Basic Principles and Probabilistic Methods
MA4E7	Population Dynamics: Ecology and Epidemiology
MA4F7	Brownian Motion
MA4M8	Theory of Random Graphs
MA4M9	Mathematics of Neuronal Networks
MA4N5	Symmetric Functions and Integrable Probability