Course title

Mathematical foundations of game development

Lecture type

Obligatory

Course code

23-11-500

Semester

1

ECTS

5

Lecturers and associates

• PhD Aleksandar Hatzivelkos, Senior Lecturer

Course overview

Within this module, students acquire knowledge of mathematical concepts and techniques used in the development of computer games: first of all, linear algebra, vector spaces and their use in the visualization (geometry) of planes and spaces. Emphasis is placed on application in the context of computer games, in contrast to the usual theoretical approach that does not target any particular field of application. The module acquires basic mathematical skills in the mentioned areas, up to the level necessary for use in creating computer games - in the part related to visualization, and the application of linear algebra and plane and space geometry.
The evaluation of acquired skills and knowledge is carried out through short knowledge tests during the year, and through a written exam.

Content

Students will learn:
• use trigonometric functions and polynomials in modeling and problem solving
• use different coordinate systems in the plane (Cartesian coordinate system, polar coordinate system)
• use different coordinate systems in space (Cartesian coordinate system, cylindrical coordinate system, spherical coordinate system)
• use matrices in modeling and problem solving
• use vectors in modeling and problem solving
• use determinants in modeling and problem solving
• use the Gauss-Jordan method to solve systems of linear equations
• manipulate vectors in different vector spaces
• algebraic properties of vector spaces
• use algebraic techniques in modeling plane geometry
• calculate with basic objects in space (direction, plane)
• use algebraic techniques in modeling the geometry of space.

Literature

1. Hatzivelkos, A., Kovač, H., Milun T. (2022) Matematika za IT. Zagreb: Algebra.
2. Axler, S. (2015) Linear Algebra Done Right (Undergraduate Texts in Mathematics). 3rd edn. Heidelberg: Springer.