# Mathematics

From 2001 to 2007 I studied Mathematics at the Free University in Amsterdam. I graduated with honors on August 22, 2007.

Below are some pages discussing topics from Mathematics. Only in Dutch yet, sorry...

In addition, I uploaded a few assays that I wrote during my study (partly together with a fellow student). Also this material is still available in Dutch only.

Why am I fascinated from mathematics? In the first place because I like to puzzle, but certainly I find the applications very interesting as well. In many cases it is possible to solve multiple - at first instance different - problems by one and the same mathematical model. To illustrate this I'll discuss a few examples below.

1. To determine the heat flow in a thin metal bar is essentially the same problem as to determine a fair price for an European option (traded at the Exchange). This problem is actually a partial differential equation, known as the heat equation or Black-Scholes equation.

2. A traveling salesman has to visit a number of cities in a sequence, and finally return to his starting position. Which order of visiting the cities is optimal for him, given the distances between the cities? This problem, known as the Traveling Salesman Problem (TSP), arises in the chip industry as well: A robot arm has to drill a number of holes in a printed circuit board, in such a way that to total time to move the drill machine is as short as possible. In which order should the holes be drilled?

Left side: the shortest route passed 120 German cities; right side: the shortest route passed 2392 holes in a printed circuit board. (source: kennislink.nl)

3. In an opinion poll for the next political election, 525 people out of a sample of 1000 say to be going to vote at a certain party. How confident is it to state that this party will make for a majority? A similar problem is: A examination candidate achieves a score of 43 out of 80 open questions. May we conclude that the candidate's level of knowledge is at least half of the curriculum? Both problems can be analyzed by means of a statistical test, the binomial test.