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The University of Southampton

MATH3089 Mathematics for the Modern World

Module Overview

This module will teach you about the mathematical modelling for contemporary real world problems. The module will consist of four sets of lectures, on four distinct but related mathematical topics. The main aim is to give students an introduction to cutting edge techniques in mathematical modelling. The four topics will be scaling and critical behaviour in real world systems (including financial markets); information theory; machine learning and networks (including the spread of information across social networks such as Twitter).

Aims and Objectives

Module Aims

This module will explore modern mathematical research topics, and their relevance to key developments and challenges in society.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Demonstrate knowledge of a range of applications of the mathematical ideas introduced in this module
  • Understand modern mathematical theory, such as information theory and critical phenomena, and have an ability to apply such theory to real world phenomena such as stock market behaviour.


1. Scaling behaviour Scaling in temporal and spatial behaviour; examples of systems exhibiting scaling behaviour; short time and long time scaling of financial time series. 2. Information Theory Shannon's theory of information; entropy; relevance of information theory to transmission; errors in transmission and their correction. 3. Machine Learning Introduction to artificial neural networks and ensemble learning methods for pattern recognition. 4. Social Networks Mathematics of spreading on networks (examples could include viruses, rumours, memes, etc. in online and physical human social networks).

Learning and Teaching

Teaching and learning methods

The lecturers will provide a structured week-by-week study programme. Each week there will be three hours of lectures and there will be tutorials every week, each lasting one hour. The tutorial classes will be used to explore problems illustrating the lecture material. Students should spend their private study time studying the lecture notes and working through problems.

Independent Study90
Total study time150



MethodPercentage contribution
Coursework 20%
Exam 80%


MethodPercentage contribution
Exam 100%

Repeat Information

Repeat type: Internal & External

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