Most single-part problems will be scored on a scale of 0 to 5, using the following guidelines. For proof-problems that require more steps than I feel can be accommodated by the above 5-point scale, I increase the number of points, but the criteria for earning the top two possible scores are the same as for 5-point problems.
- The score 5 (or \(N\), if the point-value of the problem is \(N>5\)) is reserved for complete solutions that are both correct mathematically and (essentially) perfect stylistically.
- The score 4 (or \(N-1\), if the point-value of the problem is \(N>5\)) is given for solutions that are mathematically correct and have only minor flaws in the exposition.
- The score 3 is given for solutions that contain all the correct steps, but contain a minor mathematical mistake or are poorly written.
- The score 2 is usually given for solutions that contain some significant correct steps but also contain one (but no more than one) serious mathematical mistake or are missing an important step, or contain all the correct steps and no serious mathematical mistakes but are very poorly written.
After the first assignment, an incorrectly or ambiguously quantified statement will usually count as either a serious mathematical mistake or a very poorly written solution. Other writing that was considered merely "poor" early in the semester may be considered "very poor" later.
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 score lower than 2 may be given.
- A maximum score 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 are missing more than one important step, represent a serious misunderstanding of the problem posed, or are written so poorly that it is impossible to judge correctness without an extraordinary effort on the part of the reader.
- The score 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 score 0 may also given in all other cases not covered above.
For problems with multiple parts, the different parts may have different point-values (typically from 2 to 5) depending on the amount of work needed for a correct answer. For problems (or problem-parts) that are not purely proofs (e.g. figuring out a formula and justifying it), the exposition is not always scored as strictly as it would be otherwise. In some circumstances, extra-credit points may be earned by going beyond what the problem required.