Game Mathematics and Algorithms (5 cr)

Evaluation scale

H-5

Content scheduling

September – December 2024.
9/24 - 11/24: theory, homework
10/24 - 11/24: project work +reports
12/24: final exam Or Report
• Cartesian Coordinate Systems
• Vectors
• Multiple Coordinate Spaces
• Matrices
• Matrices & Linear Transforms
• More on Matrices
• Polar Coordinate Systems
• Rotation
• Geometric Primitives

Objective

After completing the module, the student will be able to:
- Describe a 2D Cartesian coordinate space and how to locate points using that space and extend these ideas into 3D
- Calculate vectors and use them in games
- Describe some basic concepts of image and video processing and compression
- Calculate matrices and use them in games
- Learn about linear transformations (such as translations, scaling, skewing, and rotations) and multilinear transformations (including rotations about an arbitrary axis)
- Calculate algorithmic (Kolmogorov) complexity and understand how this is related to game performance

Content

- Cartesian Coordinate Systems
- Vectors
- Multiple Coordinate Spaces
- Matrices & Linear Transforms
- Polar Coordinate Systems
- Rotation
- Geometric Primitives
- Algorithmic complexity

Materials

1. Mathematics For Game Developers, Christopher Tremblay
2. Essential Mathematics for Games & Interactive Applications, James M.Van Verth and Lars M. Bishop

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding of the basic gaming and graphical tools, and attempt to provide students with a conceptual understanding of the mathematics needed to create games, as well as an understanding of how these mathematical bases actually apply to games and graphics that are essential in the operating environment of an ICT engineer, such as game development and graphical designing.
The students will team up for a project work and writing reports on some current and relevant aspect of game math. The teams then present their work to the whole group, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency. In this way, all students will have the opportunity to view themselves as powerful learners of game mathematics.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration

Student workload

Classroom activities: Classroom activities participation 50 h
Homework: Working on homework sets 1-6 25 h
Project work: Research, writing report + presentation material, presentation 30 h
Final exam: Preparing for the final exam 25 h

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima.