Mathematics and Artificial Intelligence | Abertay University

Mathematics and Artificial Intelligence


This module builds on the ideas of MAT201 to comprise a more advanced study of mathematical methods and models relevant to Computer Games Technology, and introduces some of the many Artificial Intelligence (AI) techniques which are currently, or could in the near future, be used to enhance the development of applications in video games, or other entertainment related products. These AI techniques can enhance the immersive properties of a game by enabling ‘realistic’ and ‘believable’ game play and character actions, or used to reduce development time by automatically creating content, etc.


The aim of this module is to provide the student with: an appreciation of the advanced mathematical methods required in the study of Computer Games Technology and introduce the underlying techniques used in video games to create the illusion of ‘intelligence’ as well as some real AI techniques which are, or could be, used to enhance the development of these Game AI methods.

Learning Outcomes


1.  Model and solve more advanced problems in rigid body and 2-dimensional particle dynamics.

2.  Use numerical methods to solve equations.

3.  Develop a critical understanding of AI techniques and technologies.

4.  Evaluate the use of AI technologies and techniques in computer games.

Indicative Content

1 Numerical Methods:

Numerical methods for integration (trapezium and Simpson’s rules) and the solution of equations by simple iteration and the Newton-Raphson method. Numerical solution of DE’s, e.g. Euler, predictor/corrector methods (Euler/trapezium/Simpson), Verlet, Runge-Kutta.

2 Motion of a Rigid Body:

Centroids and moments of inertia of simple bodies, parallel and perpendicular axis theorems. Rotation of a rigid body about an axis, energy, angular momentum. Rolling and sliding motion.

3 An Introduction to AI for Games:

The importance of good game AI. The differences between Game AI and so called ‘real’ Academic AI and their relative advantages and disadvantages.

4 ‘Traditional’ Game AI:

Pathfinding, including A* and its derivatives, Flocking and Steering, Rule Based Systems, Finite State Machines.

5 Academic AI Techniques:

Fuzzy Logic and Fuzzy State Machines, Genetic Algorithms, Artificial Neural Networks.

6 The use of AI in Games:

Combining AI techniques to produce A-life and Intelligent Agents. The future of AI in games.

7 Combining AI techniques


Statement on Teaching, Learning and Assessment

Contact time is split approximately 50/50 between lectures and tutorials plus time for supervised practical activity. The learning outcomes will be assessed by a coursework and an examination. The assessment will cover LO 4, whereas the exam will cover LOs 1 to 3. The tutorial sessions will allow the students time for active enquiry into the topics covered in the lectures. The supervised practical activity will give students a chance to investigate various Game AI techniques. Materials are available electronically via Blackboard, which is updated weekly with copies of the lectures, tutorial activities and also includes information on the assessments.

Teaching and Learning Work Loads

Total 200
Lecture 24
Tutorial/Seminar 24
Supervised Practical Activity 12
Unsupervised Practical Activity 0
Assessment 80
Independent 60

Guidance notes


