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!
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
Day 3: Number theory
Store data in a list
Assignment Look for the longest sequence of non-primes
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
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 co-prime pairs.
When you’re ready to submit, head to the submit page for this module.
Have you submitted each problem from this module? Then you’re done! Let us know by e-mail 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!