Applied Mathematics and Artificial Intelligence


This module covers the basic mathematics necessary for graphics and introduces students to Artificial Intelligence, specifically in Computer Games.


The aim of this module is to provide the student with: the mathematical techniques involved in creating realistic computer graphics, and a critical understanding of the basic features and techniques used to implement AI, in a computer game or entertainment product.

Learning Outcomes

By the end of this module the student should be able to:

1.  Apply 2 and 3-dimensional vector/matrix/quaternion-transformation techniques to typical computer graphics problems in the area of computer games.

2.  Demonstrate the application of the principles of ray tracing and collision detection in 3D computer games.

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 Revision of Vectors and Matrices

Revision of Vectors and Matrices

2 3D Geometry:

Lines, planes, angles and intersections. Parametric curves, normal and tangent planes to Cartesian and parametric surfaces.

3 Matrix Transformations:

Homogeneous coordinates, 2D and 3D transformation, projection.

4 Quarternions:

Their algebra and representation of 3D rotations..

5 Ray Tracing and Collision Detection:

Intersection of rays and various 3D objects, modelling reflection and refraction using vectors. Bounding volumes, detecting collisions between various 3D objects.

6 An introduction to AI for Games:

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

7 ‘Traditional’ Game AI:

Rule Based Systems, Finite State Machines.

8 Academic AI Techniques:

Fuzzy Logic and Fuzzy State Machines, Case Based Reasoning, Genetic Algorithms, Reinforcement Learning, Probibalistic Methods, Artificial Neural Networks, Clustering Algorithms. 

9 The use of AI in games:

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

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 LOs 3 & 4, whereas the exam will cover LOs 1 & 2. 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 MyLearningSpace, 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

Credit Value – The total value of SCQF credits for the module. 20 credits are the equivalent of 10 ECTS credits. A full-time student should normally register for 60 SCQF credits per semester.


We make every effort to ensure that the information on our website is accurate but it is possible that some changes may occur prior to the academic year of entry. The modules listed in this catalogue are offered subject to availability during academic year 2019/20 , and may be subject to change for future years.