Discrete Mathematics (5cr)

Objectives

After this course the student understands the idea and necessity of mathematical proofs and can apply logical inference in reasoning. The student uses mathematical notations correctly and and knows the basic concepts in set theory as well as about functions and relations. The student can solve combinatorial problems using principles like the pigeonhole principle. The student is familiar with the properties of integer numbers and modular arithmetic and can solve congruence relations. The student can manipulate permutation groups. 

Content

Briefly: logic, set theory, functions, relations, induction and recursion, combinatorics, modular artihmetics, permutation groups and symmetric groups In more detail: Set theory and logic: basic concepts and operations in set theory and logic, proof techniques and logical inference, induction and recursionRelations and functions, equivalence relation, bijection, cardinalityCombinatorics: basic concepts, multiplication principle, inclusion-exclusion principle and pigeonhole principleNumber theory: congruences, modular arithmeticsPermutations and group theory: permutation as combination of transpositions, sign of a permutation, permutation groups and symmetry groups.

Prerequisites

Mandatory prerequisities: high school mathematics, long course. This course is not recommended to be taken as the first mathematics course at university level. The students are advised to study at least Introductory Calculus first. 

Further information

This course belongs to the SEFI 2 level of engineering mathematics.