# Algebra and Vector Geometry

5 credits

Syllabus, Bachelor's level, 1MA008

Code
1MA008
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1N
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 4 March 2021
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 simple algebraic equations and use power and logarithm laws;
• 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.

## Content

Elementary functions: polynomials, rational functions, power, exponential, logarithmic, and trigonometric functions. Rules for powers and logarithms, trigonometric formulas. The solving of simple algebraic equations.

Complex numbers, real and imaginary part, polar form, geometric interpretation. Second degree equations and binomial equations with complex coefficients.

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

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.

## Instruction

Lectures and problem solving sessions.

## Assessment

Written examination at the end of the course (4 credits) and assignments during the course (1 credit).

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.