Most problems will be graded on a scale of 0 to 5, using the following guidelines. For problems that are not purely proofs (e.g. figuring out a formula and justifying it), the exposition is not graded as strictly as it would be otherwise. Extremely short or problems may be graded on a scale of 0 to 2. For the 5-point problems:In some circumstances, extra-credit points may be earned by going beyond the problem asked.
- The grade 5 is reserved for complete solutions that are both correct mathematically and (essentially) perfect stylistically.
- The grade 4 is given for solutions that are mathematically correct and have only minor flaws in the exposition.
- The grade 3 is given for solutions that contain all the correct steps, but contain a minor mathematical mistake or are poorly written (but are still written well enough that the reader can easily tell whether all the correct steps are there).
- The grade 2 is usually given for solutions that start correctly and contain some significant correct steps but also present one (but no more than one) serious mathematical mistake. If no significant progress is made towards a correct solution of the correctly interpreted problem, or if the writing is so poor that it is impossible to judge correctness without an extraordinary effort on the part of the reader, a grade lower than 2 may be given.
- A maximum grade of 1 is given for solutions that are understandable without an extraordinary effort on the part of the reader, and contain some significant correct ideas, but introduce a significant extra hypothesis, present more than one serious mathematical mistake, or represent a serious misunderstanding of the problem posed. The category "serious mathematical mistake" includes, but is not limited to, all of the wrong answers to questions 1 and 2 on the proof-writing_quiz (whose correct answers are here). In particular, if you start a proof with logic that is incorrect or is irrelevant to a correct proof, I may not read anything you write beyond that point, and will assign a maximum grade of 1.
- The grade 0 is given in all of the following circumstances, as well as in all other cases not covered above or below.
- The problem is so drastically misinterpreted as to make all work on it meaningless for the problem that was actually assigned.
- No (or too few) significant true facts are stated; the only true facts are stated are not facts that could lead to a correct solution of the problem.
- The solution presented contains numerous serious mathematical errors. Usually, "numerous" means more than two or three, unless a correct solution only requires a very small number of steps.
- The writing is incomprehensible without an extraordinary effort on the part of the reader.
The grade 0 may also given in all other cases not covered above.