Number Theory (level 1)
Verifying theoretical hypotheses by hand often is a very time consuming job and a computer lends itself quite well to this purpose. Mathematical intuition required!
But why programming? Check out this video. Mirjam Leunissen creates data visualizations for the Volkskrant among others. She shares her experiences with programming and creating visualizations.
Day 1: Getting started

Practice thoroughly with the basic elements of Python

Assignment Program the computer to be a number whiz
Day 2: Prime numbers

Learn more about algorithms

Learn about loops

Assignment Look for prime numbers
Day 3: Number theory

Store data in a list

Assignment Look for the longest sequence of nonprimes

Understand how to write “good code” — and from now on we expect you to implement these guidelines!

Assignment Try to (dis)prove Goldbach’s conjecture
Day 4: Plotting graphs

Learn how to use modules in Python

Find out how to plot

Assignment Make data intelligible by plotting graphs
Optional: Coprimes
We expect you to fully implement and submit the assignments above. But there’s also an optional assignment, intended to be done by anyone who feels ready to do more! In this module, you’ll test theorems from number theory about the frequency of coprime pairs.
Submitting
When you’re ready to submit, head to the submit page for this module.
Evaluation
Have you submitted each problem from this module? Then you’re done! Let us know by email if you have any remarks on the quality of this module. It’s important for us to get feedback on the course’s content, and we actually use it to improve!