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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.

Pros:

  • 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).

Cons:

  • 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.

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I personally think that most of the problems on the site require a more algorithmic perspective than a rigorous-proof one. –  Mon Kee Poo May 5 at 5:09
    
@MonKeePoo, I think for the earlier problems you are right, but math can be learned in several steps and I think a class using project Euler would be both fun and spark an interest in learning things carefully. You will have to explain some things anyways, and sometimes you simply have to learn new math in order to solve the problems (too hard to solve some of them on your own). –  nayrb May 13 at 16:30

3 Answers 3

I don't think it is a disadvantage if the students have seen the material before. What you are interested in at the end of the course is that the students are familiar with it; if it was before or during the course is not that relevant. Or ask them beforehand what problems they have seen/solved.

And presumably you are able to convince them of your assesment that their proof/development is wrong.

I'd be more worried that the problems turn out too hard for the class, you'd need to screen them beforehand. That means solving (at least most of) the ones suggested.

You could also give other problems, open ones, and encourage discussion e.g. on MSE.

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I am just now ending a semester in which I allowed students to do Project Euler problems for credit. There was a slush of math-y things to do that would garner credit, so the problems weren't required.

I had a persistent problem with cheating, which is unusual at my university. There are a number of people (jerks!) that have posted their solutions in any reasonable programming language. Google "euler python 38" and you find several solutions to Problem 38, with Python code. Some have a detailed discussion of the problem and methods, which has some value, but several just have code. I consider such activity to be overtly evil and directly counter-productive to our future as a species.

I love the problems, and wish you success. With guidance and discussion, perhaps you will have a better experience.

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+1 for "overtly evil" :) –  Kathy Jun 5 at 21:25

We're using Project Euler in a grad class for inservice teachers on Number Theory. I like the problems - intuitive and accessible. They'll allow us to develop some programming skills, which actually supports conceptual development in number theory. The forums which you can see after solving the problem allow them to see alternative approaches to the problem, some substantive discussion and programming tips in a variety of languages. Because of possibilities like what Kevin saw, I wouldn't want to grade on number of problems done. Instead, for us, it's one of the sources that students can use for mathematical writing. So I think that might fit into your proof writing course.

It seems like it would also dovetail with my colleague Ted Sundstrom's freely available text for intro to proof writing. https://sites.google.com/site/tedsundstrom/

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