## General directions

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.