# Fundamental concepts and proofs in mathematics

7.5 ECTS credits

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

Number theory: divisibility, prime numbers, Euclidean algorithm, 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.

Combinatorics: permutations, combinations, pigeonhole and multiplication principles, binomial theorem.

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

Number system: construction of the natural numbers, integers, rational numbers, real numbers and complex numbers.

Limits and continuity: formal definitions of limit and continuity, continuous functions and their properties, supremum axiom, 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, Euclidean algorithm, 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.

Combinatorics: permutations, combinations, pigeonhole and multiplication principles, binomial theorem.

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

Number system: construction of the natural numbers, integers, rational numbers, real numbers and complex numbers.

Limits and continuity: formal definitions of limit and continuity, continuous functions and their properties, supremum axiom, 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.

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Course code:
MAGA06

**The course is not included in the course offerings for the next period.**