A student is trying to determine which modules to study in the next semester.

1.2) Write Python/SymPy code that implements a recursive function according to the following description:

The Kaprekar-number:

The Indian mathematician Kaprekar discovered that if you take a 4 digit number (for example 1746) and sort it a) so that the digits decrease (7641) and b) so that the digits increase (1467) and then subtract these two numbers (7641 - 1467) the result is often 6174. If the result is not 6174, one repeats the sorting and subtraction with the result. After at most 7 steps the result will be 6174. For example:

7652:

1. step: 7652-2567=5085

2. step: 8550-0558=7992

3. step: 9972-2799=7173

4. step: 7731-1377=6354

5. step: 6543-3456=3087

6. step: 8730-0378=8352

7. step: 8532-2358=6174

Implement this as a recursive function.

Hints:

(The module.csv file contains modules and their grouping into subject groups: CSN (computer systems and networks), SET (software engineering technology), INF (information systems), IMD (interactive media design) which all belong to SOC (school of computing). The prereq.csv file contains prerequisite information. The module on the left is a prerequisite for the module on the right.)

2.1.1) Using Excel, calculate measures of central tendency (mode, median, arithmetic mean, geometric mean) and of dispersion (variance, standard deviation) for the modules.csv data. The data may require some preprocessing, e.g. calculation of frequencies, first. Calculate only those measures that are appropriate and meaningful for the type of data. Also, produce a chart (diagram) of the data. For your answer, provide the values and print the chart. Write a couple of sentences explaining why certain measures are meaningful or not meaningful for this data.

2.1.2) Using NetworkX, calculate the PageRanks for both data sets and determine whether any of the two data sets is a small-world network. Your answer should include the code; the nodes with the highest PageRank and an answer to the question about small-world networks.

2.1.3) Produce a gif file for the non-bipartite graph using NetworkX and a concept lattice for the bipartite graph using ConExp. Choose a good layout for the gif file and make sure that there are not any overlapping nodes/labels in the concept lattice. Print the pictures and write a couple of sentences explaining/analysing the graphs.

Challenge: the average clustering coefficient used for determining small-world networks is not meaningful for bipartite graphs (why?). Write a Python script which calculates a clustering coefficient for bipartite networks that is at least somewhat meaningful. Test your script on the data from Part 2.

A basic solution for this problem can be developed with what you learned in this class and with looking for suitable functions in NetworkX. You should not need to use materials from the web for this, but you are allowed to use web materials if you want. If you are using web materials, you must include a list of URLs of the materials that you used.

- A printout of your answers is to be submitted to the School Office. Staple your printout in the upper left corner. Write your matric number on the printout, but not your name. Please, do NOT use plastic folders. Please remember to show your matriculation card when you are handing in your report at the School Office.

- Demonstration of Part 1: you need to demonstrate your work for Part 1 to the module leader by Wednesday March 2.
- Demonstration of Part 2: you need to demonstrate your work for Part 2 to the module leader by Wednesday March 23

You should change the permission of your files on the server (by using chmod 600 filename) so that others can't read them.

If you have mitigating circumstances, you should discuss this with your Programme Leader who might give you an extension. But extensions of more than 2 weeks are not accepted by the module leader, even if your Programme Leader signs this. If you have severe mitigating circumstances then you must go through the official mitigating circumstances process and submit your coursework at the resit diet.

You can reach a total of 50 points for the coursework. This is 100% of your final mark. The points will be distributed as follows:

1.1 logic | 10 points |

1.2 recursive function | 10 points |

2.1.1 statistical measures | 7 points |

2.1.2 PageRank/small-world | 7 points |

2.1.3 pictures | 6 points |

Challenge | 10 points |