Mathematics

• Mathematical proofs
• Platonic solids
• Complex numbers, part 1
• Complex numbers, part 2

• Portfolio Opportunity Distributions (pdf, May 2007)
  My master thesis. For more info (also in English) look at this page.

• Renewal sequences (pdf, August 2004)
  My bachelor thesis.

• Stochastic walks and electrical networks (pdf, March 2004)
  Written for a presentation course.

• Software reliability (pdf, July 2003)
  Written during a project "Mathematics Works 2".

• Poisson Processes (pdf, January 2003)
  Final essay for a course "Poisson Processes".

• Sounds in closed rooms (pdf, June 2002)
  Written during a project "Mathematics Works".

• Conjecture about limits (pdf, May 2002)
  Written for a project "Essay with presentation".

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.