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
  1. Practice thoroughly with the basic elements of Python

  2. Assignment Program the computer to be a number whiz

Day 2: Prime numbers
  1. Learn more about algorithms

  2. Learn about loops

  3. Assignment Look for prime numbers

Day 3: Number theory
  1. Store data in a list

  2. Assignment Look for the longest sequence of non-primes

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

  4. Assignment Try to (dis)prove Goldbach’s conjecture

Day 4: Plotting graphs
  1. Learn how to use modules in Python

  2. Find out how to plot

  3. Assignment Make data intelligible by plotting graphs

Optional: Co-primes

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.

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 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!