For many diseases there are so-called screening programs where more or less big parts of the population are called to undergo certain tests with the goal to early discover these diseases. The probably best known example is the mammography screening. Especially there public critizism is frequently voiced because the number of misdiagnoses is high. In this article I want to use relatively simple mathematics to deduce an index that allows to judge the quality of such tests. As specific examples I present the already mentioned mammography as well as HIV tests.
Last summer, together with a colleague I held an introductory course in the programming language Python at the University of Münster where the participents were especially taught in the basics of numerical programming with this language. At that time I stumbled over a paper by J. E. Pearson (1993) in which a mathematical model for pattern formation in biological systems was presented that despite its relative simplicity is able to produce a variety of complex dynamics. Since the implementation is already possible with the means presented within the course I presented it as a motivating example in the end. Months had passed until this week I read an article at Spiegel online (a german newsportal) where a paper (Stoop et al., 2014) about a model for pattern formation on elastic surfaces was described. Because the images presented therein had strong similarities with my own simulations I decided to make an article about it.
For the last two weeks the chess world championships were held. I did not take a very great interest in it but in that context I stumbled over an old riddle, the so called eight queens puzzle. With this article I want to introduce that problem together with a solution stategy. The original idea behind the eight queens puzzle is to take a usual chess board of 8 x 8 fields and place eight queens on it in such a way that none of them can capture another one (as a reminder: a queen can move horizontally, vertically and diagonally). The question for the total number of such solutions was posed first in 1848 and answered in 1850: There are exactly 92.
Renouncing meat entirely or to least partly comes into fashion more and more lately. That this doesn't mean we have to quit eating classical recipes containing meat I want to show today using the example of the Ragu alle Bolognese. I own a vegetarian version of this for quite some time, but last weekend I asked myself why not to take the original one and vary it directly. Based on this the following recipe was developed.
Recently there was a little mathematical paper written by Cannarella and Spechler (2014) with the title "Epidemiological modelling of online social network dynamics". The basic message of their work is that Facebook will undergo a rapid decline and almost nobody will be interested in it anymore within the next few years. For this unusual statement I started to read the paper myself and implemented the software necessary to reconstruct their results. In the next paragraphs I will try to explain to you the paper with as less advances calculus as possible.