Algebra and Vector Geometry

5 credits

Syllabus, Bachelor's level, 1MA008

Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1N
Grading system
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 9 February 2024
Responsible department
Department of Mathematics

Entry requirements

General entry requirements and Physics 2, Chemistry 1, Mathematics 3c/Mathematics D

Learning outcomes

On completion of the course, the student should be able to:

  • solve trigonometric equations;
  • count with complex numbers;
  • define and count with the elementary functions;
  • use vectors and vector calculations;
  • solve systems of linear equations and count with matrices;
  • calculate inverses of matrices;
  • calculate determinants;
  • calculate eigenvalues ​​and eigenvectors.



Elementary functions: polynomials, rational functions, power, exponential, logarithmic, and trigonometric functions and equations. Rules for powers and logarithms, trigonometric formulas.

Complex numbers, real and imaginary part, polar form, geometric interpretation.

Vectors in the plane and in the space, vector algebra, scalar product and vector product. Lines and planes. Distance computations in space and time.

Systems of linear equation: Gaussian elimination, the coefficient matrix and the total matrix.

Matrices: matrix algebra, the inverse. Determinants of order two and three. Eigenvalues and eigenvectors.


Lectures and lessons. Volontary practice exam which may give bonus credits for the regular exam.


Written examination at the end of the course (5 credits)  

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 disability coordinator of the university.

Other directives

The course has a lower mathematical level than the courses Basic course in mathematics, Algebra and geometry and Linear algebra and geometry I and cannot be credited as any of them.

The course cannot be credited in the degree together with any of the courses Basic course in mathematics, Algebra and geometry and Linear algebra and geometry I.