When writing out solutions to exercises, please take these directions into account. Be aware that at some point I might take these rules into account when marking solutions.
- If one has a compelling reason not to follow some rule or other, then one shouldn't follow it, but generally only in that case.
- Be nice to your reader.
- Read what you've written. If you don't want to, why should I? I don't mind the occasional mistake in grammar, spelling or typesetting, but I don't want to be left with the impression that a writer just doesn't care for their work.
- Find the right balance between the level of details you give and the level of the maths you're doing. For example, in a course on commutative algebra is not necessary to continuously write out all the details of why every map between \(R\)-modules that you give is \(R\)-linear. Similarly, near the end of a course on topology, one doesn't need to give reference when claiming that the intersection between two open sets is again open. On the other hand, writing "it follows from the definitions of [the thing that we do in this course] that [the thing we needed to prove] is true" is rarely sufficient.
- Recall the four reasons for why trying to avoid proofs by contradiction is a good thing:
- Such proofs have a higher chance of being confusing (for both the reader and the writer).
- When not working towards a contradiction, along the way one may prove statements that are interesting in their own right.
- There exist people who dislike proofs by contradiction for philosophical reasons.
- Such proofs (when incorrect) are harder to mark.
- Please take note of your margins. Formulas spilling over the margins are extremely aesthetically unpleasing.