Proof Portfolio

The proof portfolio is intended to be a way to get practice writing lucid proofs without time pressure and with lots of feedback. You may like watching Serre’s talk, “How to Write Mathematics Badly.”

Choose problems. Pick out two problems from the relevant chapter(s) that you want to include in your proof portfolio. You can also choose chapter 0 exercises that were relevant for the chapter in question. They should be exercises that were not assigned for any reading assignment, and that we did not discuss as a class.

I encourage you to challenge yourself by choosing problems that look like they’ll push your mathematical abilities forward. If you look at a problem and immediately know how you’d write down a formal proof, that’s probably not a good one to choose for this; you won’t get anything out of the process.

First draft. You should neatly write (or TeX) up the statement of the exercises you’ve chosen and your solutions to the exercises. Do your best to explain everything clearly. Use complete sentences and avoid long strings of symbols whenever possible. If you can think of a useful picture to include, do it!

It might help you achieve the right level of clarity if you keep in mind that your intended audience is one of your peers (not me, and certainly not a computer). In other words, your goal is to have a proof written up sufficiently clearly that any one of your classmates could read through it and understand your argument.

Bring hard copies of your proofs to class on the days when we’ll be doing peer review (see the calendar for the dates).

Peer review. We’ll have some time for peer review in class, when one of your peers will look over your proofs, and you’ll look over your peers’.

As a reviewer, your job is to leave feedback about the proof you’re reading. That includes pointing mathematical or logical errors, of course, but it also includes pointing out things that are just confusing, or have too many symbols, or whatever. Remember that you are the intended audience for the proof you are reading, so if anything doesn’t make sense to you or is hard for you to read, you should point it out!

Revise. After you’ve gotten some feedback from your peers, you’ll have a chance to revise your proofs. You can ask your peers to look over your revision outside of class if you like, or you can ask me during office hours.

Submit. A couple of days after the peer review, the final drafts will be due. I’ll grade the final drafts for both mathematical correctness and proof writing style. (Mathematical correctness alone is not enough!)