## 400 level (postgraduate) papers and modules

Not all papers/modules shown here will be available in any one year. Additional papers/modules may be offered. Check with the

Director of Studies for a confirmed list of modules that are running, their prerequisites and semester.

COMO480 Project 36 points

Full yearA 36-point project in an agreed topic, supervised by one or more staff.

MATH401 Special topic (two 10-point modules) 20 points

First SemesterA combination of two 10-point modules.

MATH402 Special topic (two 10-point modules) 20 points

Second SemesterA combination of two 10-point modules.

MATH403 Special topic (two 10-point modules) 20 points

First SemesterA combination of two 10-point modules.

MATH404 Special topic (two 10-point modules) 20 points

First SemesterA combination of two 10-point modules.

MATH406 Special topic (two 10-point modules) 20 points

Second SemesterA combination of two 10-point modules.

MATH485 Honours Project 36 points

Full yearA 36-point project in an agreed topic, supervised by one or more staff.

MATH490 Honours Project 40 points

Full yearA 40-point project in an agreed topic, supervised by one or more staff.

MATH495 MSc Preparation 18 points

Full yearMSc Preparation.

Module

MATH4AP Advanced Probabillity 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Introduction

Module

MATH4AR Advanced Topics in General Relativity 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

General relativity, Albert Einstein’s theory of gravitation, is one of the most elegant theories of mathematical physics. It gives a geometric description of gravitation in terms of the curvature of space and time, using mathematical methods like tensor algebra, differential geometry and the theory of ordinary and partial differential equations.

Module

MATH4CA Complex Analysis 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4CO Graph Theory 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4DE Differential Equations 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

This paper gives an introduction to the theory of partial differential equations by discussing the main examples (Poisson's equation, transport equation, wave equation) and their applications.

Module

MATH4DG Differential Geometry 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Since the time of the ancient Greeks, mathematicians and philosophers have been interested in the geometry of curves and surfaces, for example the Euclidean plane and the surface of the earth. From the end of the 19th century onwards with the work of Riemann, however, a powerful mathematical theory of much more general classes of curved spaces arose; this is what is nowadays understood as differential geometry.

Module

MATH4ET Evolutionary Trees 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4FA Functional Analysis 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

The main focus of this course is the analysis of linear mappings between normed linear spaces. It turns out that many problems in analysis can be studied from this abstract point of view, which recognizes important underlying principles without getting lost in technical details. The applications of the approach ranges from differential and integral equations through problems in optimal control theory and numerical analysis to probability theory to name a few. This introductory course covers some of the basic constructions and principles of functional analysis: completions of metric/normed spaces, the Hahn-Banach Theorem and its consequences, dual spaces, bounded linear operators and their adjoints, closed operators, the Open Mapping and Closed Graph Theorems, the Principle of Uniform Boundedness and some elements of the spectral theory for closed linear operators. The applications of the abstract concepts are demonstrated through various examples from different branches of analysis.

Module

MATH4GR Introduction to General Relativity 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

This module is an introduction to General Relativity, the theory of gravity by Albert Einstein. Building on the module Differential Geometry (MATH4DG), which takes place in the first half of semester 1, we develop Einstein’s idea that “space” and “time” form a continuum “spacetime” described by a 4-dimensional Lorentzian manifold.

Module

MATH4GS Geometry of Curves and Spaces 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Introduction

Module

MATH4GT Group Theory 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Introduction

This is a short course on group theory.

Module

MATH4HS Hilbert Spaces 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Introduction

Module

MATH4ID Integral Domains 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4MA Modern Algebra 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4MI Measure and Integration 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

This course introduces a modern theory of integration of real-valued functions via measure theory.

Module

MATH4NM Numerical Methods 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Introduction

Module

MATH4OA Operator Algebras 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4OP Optimization 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Optimization is a core tool of applied mathematics, computational modelling, statistics, operation research, finance, engineering, indeed almost any application of the mathematical sciences. This paper focuses on convex optimization, covering a few key algorithms, the theory behind them, and applications.

Module

MATH4PD Numerical Solution of PDEs 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4PT Probability Theory 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

This course is an introduction to probability theory based on measure theory.

Module

MATH4RM Rings and Modules 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4SL Data Mining, Inference and Prediction 10 points

Second SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4ST Set Theory 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

Not available in 2017

Module

MATH4TO Topology 10 points

First SemesterThis 10-point module makes up one half of a 400-level paper

This paper is an introduction to point-set topology, which underlies differential topology and algebraic topology, and is used all over mathematics (for example, operator algebra, functional analysis, topological group theory...). The main ideas are continuity of functions, and compactness and connectedness of sets. For example, you know that continuous functions take “nearby'” points to “nearby” points. In topology, there is a way to formulate what “nearby” is without using a distance function. The purpose of this module is to give students the background in topology that they need to pursue higher level mathematics.