###
Dr. Sarah's Proof-Writing Checklist for MATH 4710

### Proof Introduction

Are the hypotheses
clearly stated?
Is the goal of the proof clearly
stated?
Is the goal of the proof clearly reworded using definitions?

### Understanding the Problem and Planning a Solution

Turn in projects or prepare to present problems even if it
they are not complete, even if only to say, "I do not understand such and
such" or "I am stuck here." Be as specific as possible. Conjecture.
Is there evidence of partial understanding of the problem?
Is there evidence of complete and deep understanding of the problem?
Is there evidence of a partially correct plan based on correct
interpretation of the problem?
Is there evidence that the plan could lead to a correct solution if
implemented properly?
### Body of the Proof

Are all of the hypotheses clearly reworded using definitions?
Does the proof use the hypotheses correctly?
Does the proof give evidence
of deep mathematical understanding of the problem
and its solution?
Is the proof as brief and elegant as possible?
Does the proof make logical sense?
Is the proof correct?
Is the proof complete?
Does this proof prove the general case?
In a "Proof by Contradiction", is the contradiction hypothesis correct?
In a "Proof by Contradiction", is the contradiction clearly explained?
In a "Proof by Examining all Cases", have you explained why the
list of cases you have is complete and correct?
In a "Proof by Examining all Cases", have all the
necessary cases been checked?
### From One Step to the Next

Does each step follow logically
from the previous step?
Is the connection between steps
clearly explained?
### Terminology

Are all variables, terminology,
and notation that are used in the proof clearly defined?
Do all variables, terminology,
and notation represent the general case
(avoid hidden assumptions)?
### When Using Ideas from Elsewhere...

Are any theorems mentioned clearly stated and given acknowledgement?
Are all of the hypotheses of theorems used satisfied?
Is proper reference to books, classmates or other sources
given? It is fine to
talk to other people, but you must give proper reference and write it up
**in your own words**. Examples of proper references:
"p. 271 from...", "this website...",
"this was Henry's idea", or "Jill and I worked on this together",...
### Conclusion

Does the proof have the correct conclusion?
Is the conclusion clearly restated at the end?