Only if no partial credit is offered, which is not how his exam[0] reads to me:
As usual, answering any (sub)problem with “I don’t
know” (and nothing else) is worth 25% partial credit.
Yes, even for problem 1. Correct, complete, but
suboptimal solutions are always worth more than 25%.
A blank answer is not the same as “I don’t know”
I had a math prof who would give negative marks on proofs, preferring you say “I don’t know how to do this step” and finishing the proof over trying to BS the step.
A math prof of mine would label insufficient initialization in recursive proofs with i.i. (it also stood for a few other common mistakes, such as “incorrect integration” or whatever). And he would invariably add “i.i = -1”, which was the penalty for such mistakes (exams being graded out of 20). A deliciously nerdy joke, unless you’re on the receiving end.
How do you skip a step in a proof? You just say "assuming I can prove this assertion, this other stuff follows"? That seems to risk accidentally skipping way more steps than you thought you were skipping and quite probably the meat of the proof.
Well, from the math profs I've seen, the usual method is to interpose “it is intuitively obvious” in place of the skipped step(s).
The tricky part is having a correct intuition as to what you should be skipping to, sure, but that's the same problem as you have doing a proof (minus actually figuring out the justification) since humans don't generally do proofs by exhaustively listing every possible next step from what is already proven in a BFS until getting the desired result and then pruning all the other paths.
Essentially that. There is a risk a skipping a majority of the proof and hence a majority of the points, but point-wise it would work out better than handwaving the step and getting negative points.
It's been about 25 years, so my memory is a bit fuzzy, but it was an analysis class. I don't remember if I ever availed myself of this. I did have a classmate who completed, but didn't turn in his homework a couple of times. (I don't recall if it was the entire problem set or just a couple of problems that he omitted, but he got the paper out to consult while the prof was going over the answers.)
The teacher was competent but quirky - he also required the students to purchase a stapler (to staple their homework) and locked the door after class started (if you were late, tough luck).
