Reviews are at the discretion of the reviewer (although I reserve the right to implement software for reviewing reviews). Thoughtful reviews should be pinpoint accurate and not be offensive to the reader.

Common Mistakes

Here is an incomplete list of common mistakes. If you have more that you want me to add, let me know!
  1. Proofs by Example
  2. Proofs that don't use all of the hypotheses of the problem.
  3. Illegal assumptions. "Suppose... (thing you are definitely not allowed to do)".
  4. incorrect terminology: "expands to", "let" instead of "if",
  5. undefined terminology or notation: the letter "k" appears in the proof but k is defined nowhere.
  6. Arguing by assuming an equation is true. 1=-1, (1)^2 = (-1)^2, 1 = 1, so we conclude 1=-1.
  7. Unjustified steps.
  8. Missing parts: no base case of induction, not proving one direction in an "iff" statement, skipping a letter of a problem (if it asks to prove (a),(b),(c) but the author only proves (a) and (b).)
  9. Expressions that are floating on the page and appear to have nothing to do with what is going on.

Example Feedback

Below we give some examples of what appropriate scores and commentary could look like for some problems from Dummit and Foote. All feedback should technically be addressed to the editor (me).

1.1: 1(c,e), 2(c,e) 3(c,e,f)

Score Comments
8 For (1c), it is true that division is not associative, but this isn't what they are supposed to be considering.
Proof omits (6f).
10 Small mistake on division in associativity proof.
6 no proofs, the second part is a "proof by example".
7 In (1c) they are working with the wrong operation.
In (6) they don't check the closure operation.
10 We say "…is closed under addition" not "…is close under addition".

1.1: 31

Score Comments
8 Proof never draws the conclusion it needs to in order to complete the problem.
5 The proof repeats part of what is supposed to be proved but makes no reference to t(G) or its complement.
7 The language is imprecise. For example the word "pair" is not properly defined in the way that it is used.