These questions require direct proofs. A full inductive proof will lose you
points for both the main outline and style/clarity.
Correct (2)
Buggy (1)
Missing or very wrong (0)
Main Outline
Variables and assumptions are declared at start.
A direct (or perhaps contrapositive)
proof outline is used to reach the conclusion.
One small issue, e.g. doesn't end with conclusion,
doesn't start with assumptions,
variable(s) not declared at start.
Missing, has multiple issues, or
uses an inappropriate proof outline such as induction or contradiction.
Correct (3)
Buggy (2)
Missing or very wrong (0)
Flow of equations
The sequence of steps between assumptions and conclusion is
mostly present and in logical order.
Clearly delimited lemmas are ok.
A couple steps are written backwards but the main flow is in logical order.
Proof assumes the claim, or runs backwards for a non-trivial number of steps,
or large amounts of the algebra are missing.
Correct (3)
Buggy (1)
Missing or very wrong (0)
Connects from assumptions to conclusion.
The sequence of steps connects completely, with no gaps
getting from assumptions to conclusion.
The proof seems to connect but small bugs mean that it doesn't actually do so.
There is a significant gap (e.g. in the middle) where
a step doesn't follow from the previous information.
Correct (2)
Buggy (1)
Missing or very wrong (0)
Details
Definitions are used correctly.
Except for a possible gap in the middle (see previous row),
algebra steps are correct and non-obvious ones justified,
Minor bugs in definitions or algebra.
A step that does too much at once or needs a brief explanation.
Multiple or large errors.
Large amounts of the proof are missing.
Correct (3)
Buggy (2)
Missing or very wrong (0)
Style and clarity
Easy to follow, with appropriate use of punctuation, notation, latex, and whitespace. Algebra
and use of definitions is correct or nearly so.
Slightly hard to follow. Small number of minor mistakes e.g. formatting bugs, algebra mistakes, too few steps or key steps not explained.
Small amounts of work or background information poorly delimited from the proof.
Hard to follow or looks unprofessional. Serious or multiple technical issues.
Large amounts of extra work are mixed into the proof,
e.g. writing the inductive proof that this claim might form part of.