Section A.1 Logic
Authors should adhere to the rules of logic in such a way that their readers understand what logical techniques they are employing.
In other words, the authors...
- state claims (propositions, theorems, lemmas, etc.) as logical statements;
- state claims appropriate to the assigned problem;
- write proofs with first and last sentences that indicate the proof technique they are using;*
- define notation and symbols before using them;
- employ a valid proof technique for the statement as written;
- employ a valid proof technique for the statement appropriate to the problem;
- include all necessary cases in the proof;
- write examples with a clear topic sentence;
- write prose using evidence to support claims;
- employ sound logic even in mathematical prose.
*this criterion relaxes a bit after the first proofs course; if you’re proving a theorem directly, you can just get to the proof without repeating the hypotheses at the beginning of the proof. But if you’re in your first proofs course, please include the first and last sentences that lay out your hypotheses and conclusions!
