IR102105 Discrete Mathematics and Linear Algebra

Minimum college entrance reqirements with additional 3MX/3MN (three years Mathematics in upper secondary school)

After completion of the course the students should:
- be able to calculate with complex numbers
- be able to do set algebra
- be able to do mathematical proofs realted to logical statements.
- be able to solve linear recurrence relations of first and second order
- be able to solve systems of linear equations using matrices
- know and be able to use the basic rules in the algebra of matices
- know how to diagonalize matrices using eigenvalues and eigenvectors
- know about vector spaces, basis, coordinates and linear transformations
- be able to do coordinate transformations and linear transformations
- be able to solve systems of linear differential equations of two variables.
- manage how to use CAS (computer algebra system) solving problems in linear algebra

Complex number: Complex numbers on Cartesian, polar and exponential form; deMoivres formula.
Set theory: Sets, subsets, difference, intersection and union of sets, complement of a set.
Logic: Statements, negation, conjunction, disjunction, implication and equivalence. Direct proof, proof by contradiction and proof by contraposition.
Recurrence relations of first and second order.
Matrix: Matrix operations, determinants, inverse of a matrix. Eigenvalues and eigenvectors. System of linear equations.
Vector space and linear transformation: Vector spaces, subspaces, linear independence, basis, linear transformations

Lectures and problem solvings.

At the beginning of the course the professor can decide if the students have to do some obligatory problems.

3-hour written exams