## MATHEMATICS FOR COMPUTER GAMES

 SHE Level 1 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M1I623007 Module Leader Leonard Scott School School of Computing, Engineering and Built Environment Subject Computing Trimester A (September start)-B (January start)

### Summary of Content

This module provides an introduction to the mathematics underpinning the computing engines and graphics libraries used in games technology. Students will be able to formulate and solve simple one and two dimensional problems of the type arising in games programming environments.

### Syllabus

Solving equations: linear systems, quadratics. Sets: definition, operations, representations of objects Vectors: definition, operations, mechanics, dynamics Basic geometry: angle, trigonometry, Pythagoras, distance, symmetry 2D coordinate systems: Polar and Euclidean, Galilean transformations. Matrices: definition, operations, inversion of a 2x2; representing transformations, investigation of the isometries of the plane (translation, rotations and reflections). Composing transformations. Wire frame models: point matrix, adjacency matrix; applying transformations. Differential equations: differentiation and partial differentiation; Newton's second law, Solving first and second order constant coefficient differential equations. Modelling applications Integration: definition, simple examples, numerical approximation methods. The Euler method and Backwards Euler Methods, comparison. Time evolution in a games environment.

### Learning Outcomes

On completion of this module, students should be able to:- formulate and solve linear and quadratic equations- formulate and solve mechanics problems in 2D- construct and manipulate 2D planar wire frame models- construct algorithms incorporating time stepping procedures- perform transformations between 2D co-ordinate systems

### Teaching / Learning Strategy

This module will be based on lectures, self learning and tutorials. Lectures will place the mathematics in the context of games development; demonstrate techniques and indicate analytic and numerical problem solving approaches. Techniques will be practised under directed learning and tutorials, and problem solving will be tutorial based.

Berry, C et al (2004) MEI AS Further Pure Mathematics, 3ed, Hodder and Stoughton. Bryden, P. (2004) MEI Mechanics 1, 3ed, Hodder and Stoughton. Holland, D. and Bryden, P. (2004) MEI Mechanics 2,3ed, Hodder and Stoughton. Mitchell,P. et al. (2004) MEI Differential Equations, Hodder and Stoughton

### Transferrable Skills

D2 Independent working and self-reliance D3 Reviewing and evaluating own learning, strengths and weaknesses

### Module Structure

Activity Total Hours
Independent Learning (FT) 120.00
Lectures (FT) 36.00
Tutorials (FT) 24.00
Assessment (FT) 20.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 2.00 60.00 35% Written Exam
Exam (School) 0.75 20.00 35% Class Based Test (45 minutes)
Exam (School) 0.75 20.00 35% Class Based Test (45 minutes)