Fundamental concepts and proofs in mathematics
6.0 ECTS creditsLogic 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)