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# Mathematical foundations of game development

• Class 30
• Practice 30
• Independent work 90
Total 150

### Course title

Mathematical foundations of game development

Obligatory

23-11-500

1

5

### 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.

#### Minimal learning outcomes

• Solve simple problems with trigonometric functions and polynomials, using different plane and space coordinates.
• Solve problems using matrices and vectors.
• Represent a vector in a given basis in finite and infinite vector spaces and write linear operators using matrices.
• Carry out basic mapping in plane and space (translation, scaling, rotation, mirroring).

#### Preferred learning outcomes

• Model and solve more complex problems using trigonometric functions and polynomials.
• Use properties of matrix and vector calculus in problem modeling.
• Calculate the orthonormal basis of the vector space and complement the set of vectors to the basis of the vector space and determine the kernel and image of the linear operator.
• Carry out mapping compositions in plane and space.