Project Euler is a very popular self-challenge website where users complete various projects designed to test their number-theory intuition and programming skills.
I've been considering various ideas for a first year introduction to proofs course. One idea I've had is to choose project ideas from project Euler and run the class using the Moore method. Thus, students would work through the first large chunk of projects together, handing in proofs that their answer works and presenting their solutions periodically on the board.
- Introduces mathematical programming and number theory
- Students can check their answers through the website
- The internet resists people cheating on Project Euler (mostly, there are exceptions).
- Students may be mad if the website says they are right and the teacher says their proof is incorrect.
- Students may have already seen most of the material if they previously worked through the project.
Building off the previous item, how could standard material like proof techniques and basic logic be incorporated into such a course? Does project Euler have a wide-enough selection of topics to be an effective introduction to rigorous thinking?
A familiarity with a programming language would be a prerequisite. This class would give students more experiences programming math, which would be helpful in preparing them for a variety of future jobs.