Linear Algebra, Trigonometry and Geometry

7.5 credits

Syllabus, Bachelor's level, 5SD901

Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Grading system
Fail (U), Pass (G), Pass with distinction (VG)
Finalised by
The Department Board, 31 March 2021
Responsible department
Department of Game Design

General provisions

The course is part of the Bachelor's programme Game Design and Programming, 180 Credits.

Entry requirements

General entry requirements and Mathematics 3c/Mathematics D

Learning outcomes

Upon completing the course, students with a Pass grade will be able to:

  • solve linear equation systems with Gaussian elimination and determine how the solution depends upon coefficient and total matrix ranks.
  • perform matrix operations, calculate the inverse and determinant of a matrix and interpret an m×n-matrix as a linear map from Rm to Rn.
  • define the trigonometric functions and use trigonometric identities to, for example, solve elementary trigonometric equations.
  • use the concept of coordinates to solve geometric problems, for example, using line and circle equations.
  • give an account of the vector concept and the base and coordinate concepts; apply arithmetical properties for vectors and determine whether vectors show linear independence.
  • give an account of the concepts scalar product and vector product, calculate such products and interpret them geometrically.
  • determine equations for lines and planes and use these to calculate intersection and distance.
  • define rotations, reflections and orthogonal projections on a plane in space.
  • calculate the matrices of such maps.


Linear equation systems:

Gaussian elimination, rank, solubility.


Matrix calculation, inverse of a matrix, determinants.


Trigonometrical identities, trigonometrical equations.

Vector calculation, linear dependence and independence, bases, coordinates, scalar product and vector product, straight line equation, distance, area and volume.

Description of rotation, reflection and orthogonal projection in R2 and R3, linear space in Rn and interpretation of an m×n-matrix at linear mapping.


Lectures, lessons, calculation exercises and group work.


Assessment is with written tests and hand-in assignments. The possible grades for the course are Pass with Distinction, Pass or Fail.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the University's disability coordinator.

Uppsala University does not accept cheating or plagiarism. Suspected incidents of cheating or plagiarism are reported to the Vice-Chancellor, which may issue a formal warning to the student or suspend the student from studies for a certain period.

NB: Only a completed course may be counted towards a degree.