Linear Algebra, Trigonometry and Geometry

7.5 credits

Syllabus, Bachelor's level, 5SD901

A revised version of the syllabus is available.

Code: 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, 3 February 2016
Responsible department: Department of Game Design

General provisions

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

Entry requirements

Algebra and Discrete Mathematics, 7.5 credits

Learning outcomes

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

solve linear equation systems with Gausse limitation and say how the solution depends upon coefficient and total matrix ranks.
count with matrices, calculate the inverse and determinant of a matrix and interpret an m^n-matrix as a linear map from R^x to R^x.
define the trigonometric functions and use trigonometric identities to, for example, solve simple trigonometric equations.
use the concept of co-ordinates in geometric problem solving, for example, using line and circle equations.
give an account of the vector concept and the base and co-ordinate 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.

Content

Linear equation systems:

Gausse limitation, rank, solubility

Matrices:

Matrix calculation, inverse of a matrix, determinants

Trigonometry:

Trigonometrical identities, trigonometrical equations

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

Description of rotation, reflection and orthogonal projection in R^x and R^x, linear space in R^x and interpretation of an m^n-matrix as a linear map from R^x to R^x.

Instruction

Lectures, lessons, calculation exercises and group work.

Assessment

The possible grades for the course are Pass with Distinction, Pass or Fail.

Plagiarism and cheating

Uppsala University has a strict attitude towards cheating and plagiarism and disciplinary measures will be taken against students who are suspected of involvement in any kind of cheating/plagiarism. The disciplinary measures take the form of a warning and suspension for a limited period.

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