# Fundamental concepts and proofs in mathematics

6 ECTS credits

Logic and set theory: propositions, logic operators, sets and set operations.

Number theory: divisibility, prime numbers, the Euclidean algorithm, the fundamental theorem of arithmetic, position system, linear Diophantine equations.

Functions and relations: surjections, injections, bijections, equivalence relations, congruence calculation.

Proof methods: direct proofs, proofs by contradiction, and mathematical induction.

Polynomials: divisibility, the factor theorem, the division algorithm, the Euclidean algorithm, polynomial equations.

Elementary linear algebra: linear equation systems, Gauss elimination, matrices, calculation rules for matrices, inverse matrices, determinants and calculation rules for determinants.

Limits and continuity: formal definitions of limit and continuity, continuous functions and their properties, least upper bound property, extreme value theorem and intermediate-value theorem.

Instruction is in the form of lectures and workshops. Students are required to perform a minor assignment in the form of a proof or calculation individually and present it orally.

Number theory: divisibility, prime numbers, the Euclidean algorithm, the fundamental theorem of arithmetic, position system, linear Diophantine equations.

Functions and relations: surjections, injections, bijections, equivalence relations, congruence calculation.

Proof methods: direct proofs, proofs by contradiction, and mathematical induction.

Polynomials: divisibility, the factor theorem, the division algorithm, the Euclidean algorithm, polynomial equations.

Elementary linear algebra: linear equation systems, Gauss elimination, matrices, calculation rules for matrices, inverse matrices, determinants and calculation rules for determinants.

Limits and continuity: formal definitions of limit and continuity, continuous functions and their properties, least upper bound property, extreme value theorem and intermediate-value theorem.

Instruction is in the form of lectures and workshops. Students are required to perform a minor assignment in the form of a proof or calculation individually and present it orally.

Progressive specialisation:
G1N (has only upper‐secondary level entry requirements)

Education level:
Undergraduate level

Admission requirements:
Upper secondary school level Mathematics E or Mathematics 4, or equivalent

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Mathematics Programme (studied during year 1)