Course Modules

This course begins with the introduction of a new number: the square root of minus 1. Throughout the module, you will see that working with complex numbers can often improve our understanding of certain mathematical processes and greatly simplify calculations. […]

The content of all the mathematics modules follows the overarching principle of developing students’ technical ability, development of knowledge into areas of mathematical structure, proof and formality, continuity, discrete procedures, limiting processes, mathematical modelling and interpretation of space. This module’s

This module provides a grounding in the theory of probability, and is an essential precursor for the subsequent study of mathematical statistics and operations research. The emphasis will be on modelling real situations, including probability calculations motivated by statistical problems.

This module builds on the material covered within the first year calculus courses. Calculus will be extended to functions of more than one variable and applications of partial differentiation and multiple integrals.

This module explores how complex analysis is concerned with extending the familiar notions of differentiation and integration to functions of a complex variable. Perhaps surprisingly, this apparent increase in sophistication results in a host of spectacularly strong results. Applications abound;

This modules explores how groups were introduced in an attempt to study one of the most fundamental aspects of nature: symmetry. As an example, the 6 symmetries of an equilateral triangle form a group: every symmetry has a counterpart inverse

The subject of mathematical analysis puts calculus on a rigorous foundation. The key concept underlying the whole course is that of “limit”. The purpose of analysis is to develop a solid understanding of when familiar techniques of calculus apply and

This module introduces formulating numerical problems and building models to address and derive numerical solutions. It also provides you with the knowledge and understanding of mathematical and statistical principles appropriate to interpret numerical findings and draw justified conclusions.

In recent years, interest in the theory of complex networks has exploded. The advent of social media and progress in artificial intelligence have made network analysis into an indispensable tool. In this course, you will study the mathematical theory that

In this module, you will build on the material introduced in the first-year module to take a more in-depth look at the idea of estimation. You will learn how to compare the relative strengths and weaknesses of estimators and how