## Discrete Mathematics

### Full course description

The students will learn the what the following fundamental concepts involve:

- Numbers: We discuss a.o. integers, natural numbers, real numbers and prime numbers and properties that these classes of numbers have;
- Logic: This involves drawing (correct!) conclusions and how to use logic to prove mathematical statements.
- Sets: A set is nothing more than a collection of items. Often those items will be numbers, but this is not necessarily the case. We discuss properties of sets and concepts related to sets, like intersections, and unions;
- (Mathematical) relations: A relation is essentially a comparing mechanism for elements in a set. E.g. ‘smaller than’. We discuss several relations and their properties;
- Functions: A function is a mapping from one set to another. We discuss several properties that functions may have, like invertibility;
- Combinatorics, the science of ‘smart counting’: The question is ‘In how many ways…’, the answer will often be a big number and we discuss how to find them quickly. For this purpose we use concepts like permutations and combinations.

Almost every time mathematics is used, it concerns some of the above concepts. A good understanding of these topics is therefore very important and Discrete Mathematics is a perfect course to combine with other mathematics courses. Hence, students who are interested in (applied) mathematics, computer science and/or econometrics might find this course particularly useful.

### Course objectives

- To make students familiar with several fundamental concepts in mathematics, a.o.numbers, logic, proofs, sets, relations, functions and combinatorics (see description).
- To get the students to notice how beautiful the world of mathematics is.

### Prerequisites

Substantial high school experience in Mathematics (For an indication of the relevant topics, see SCI-M, p. vi-viii). Students who are unsure if this course is suitable for them can contact the coordinator to discuss their situation.

### Recommended reading

- Chetwynd, A., & Diggle, P. Discrete Mathematics.

SCI2002

Period 1

4 Sep 2023

27 Oct 2023

ECTS credits:

5.0Instruction language:

EnglishCoordinator:

Teaching methods:

PBL, Presentation(s), Lecture(s), Assignment(s), Paper(s)Assessment methods:

Final paper, Attendance, Participation, Written exam, Oral exam, Take home exam