Here are some useful supplementary tools for the course. I will add to this list as the course goes on.
Euclid: The Game — this is a great game for practicing your straight edge and compass constructions
Straightedge and compass tool This is an online tool that lets you do straightedge and compass constructions starting from a blank page
Hilbert’s axioms — a note on Hilbert’s axioms, with commentary
Euclid --- "The Elements", one of the most influential texts of all time
The construction of the heptadecagon
Here are potential suggestions for the final project:
Here are some guidelines for preparing a strong final project:
I would say a good way to think about the final project is: pick a topic you are interested in, and think about how you would explain it to someone else in the class. Then, try to present your explanation as a clear, compelling report. Then, be prepared to present your project to me.
You should likely start your paper with an abstract, where you say what you will do in the paper. Then, you should have a brief introduction, where you give for example very brief background and/or motivation for why the topic you are writing about should interest your audience. Then, you will have the body of your paper where you explain things clearly, giving good examples or relevant proofs. And then, probably, you will have a very brief conclusion. I think a really good test is — say one of your classmates gave you a 5-10 page paper to read about some topic they were interested in…what would that look like, so that you would enjoy reading it, and feel like you learned something interesting? If you write your paper with that in mind, I think you are likely to do a great job.
You might include references as well. This is not required; however, it is extremely important that the paper is in your own words, unless you are quoting someone else, for which proper citation is required.
If you would like to look at some strong sample papers, I would suggest:
https://ocw.mit.edu/courses/mathematics/18-034-honors-differential-equations-spring-2009/projects/. (The topic for that course was different than the topic for our course, but hopefully the samples are still useful.)