It's due May 9, at the last class. If you provide an envelope addressed to yourself I will return your work with my comments.
I don't know quite how many "a few" means. Perhaps half a dozen - but not all alike. If you redo the one in which you show 0 is unique in a ring then don't also redo the one in which you show 1 is unique. If you do one computation showing how to use the Euclidean algorithm to solve ax+by=n (assuming you missed it the first time around) then don't do a second.
You should only spend time on problems worth spending time on. Some of the ones I asked turned out to be tedious and uninformative. Don't redo one of them, even if you got it wrong the first time - since you still won't learn much by doing it.
What did you learn? What was interesting (or boring)? How (if at all) has your attitude toward (some part of) mathematics changed? What do you think you might remember from this course N years from now? What do you think will be useful (in life, thought or your classroom)? How hard did you work? If I teach this course again (or when I discuss it with whoever does teach it next) what should I keep? What should I change (add or subtract)? How might I use the class time better?
The nominal goal was to do enough abstract algebra to be able to prove the three classic nonconstructability theorems - cube duplication, angle trisection and circle squaring (modulo the irrationality of pi). That matched the goal of the Sethuraman text, which we started out following pretty closely. But shortly after we'd dealt with the definitions of ring and field the book got too dense and (from the students point of view) technical. We pretty much abandoned the book. But we did get to the nonconstructability, more or less following the much more direct argument in Courant and Robbins.
The primary virtue of the way the course started was the way it led us to focus on the "abstract" part of "algebra" (and that is after all what the course should be about). The idea that "the usual rules of arithmetic" might (or might not) apply to objects other than numbers was striking and central. We worked on this by doing lots of computations in various rings (Z mod n, polynomials over an arbitrary ring, Q[sqrt(2)] and Q(sqrt(2)) rather than by proving theorems about rings. (We did do some of that and I would do more next time, but not at the expense of the calculations.)
We studied lots of important topics that I think belong in any high school math teachers repertoire (whether or not they show up in the high school classroom). Many of the students had never seen many of them, or had seen them and forgotten them, so these digressions were very worthwhile. Among the topics:
A few of the problems asked for proofs (which the students had trouble with throughout and which I did not teach well). But most asked for exploration - guessing theorems by looking for patterns. This worked well - we ended with quadratic reciprocity!
Among the choices:
Next time I would require Courant and Robbins (this time most of the students bought one at my recommendation). It's back in print in paperback, and good used inexpensive hardbound copies are available on the web.
I think I would also use Hugo Steinhaus' Mathematical Snapshots, just because it the book that first kindled my love of mathematics.