MCS  233: Discrete Math for Elementary Education
January 2009

 MCS-233 homepage Reading and homework assignments Proof checklist Prof. Barbara Kaiser Homework guidelines

Checklist for finding and writing proofs

• Be sure you have a clear statement to prove
• Understand what you're proving
• Figure out the logical structure.
• Rephrase the statement in several logically equivalent ways.
• Make sure you know the definitions of the mathematical terms.
• Think about what theorems, concepts, etc. that involve those terms.
• Decide how you might prove it
• Which proof techniques seem likely?  Best?
• What can you assume?  What is your goal?
• Find the proof
• Compare what you can assume with the theorems and definitions you know.
• Figure out what theorems would get you to your goal.
• Stuck?  Try an alternative proof technique.
• Still stuck?  See if you can prove the theorem is false.
• Write rough draft, check for logical errors
• Did you use all of the hypotheses?
• Did you assume the conclusion?  (This is bad.)
• Are there clear steps in your proof that lead directly to the conclusion?
• Does each step follow logically from the previous one?
• Are the steps consistently sized?
• Write first draft
• Check that you just prove one thing. If necessary, prove some propositions or lemmas first.
• Check for content.
• Check spelling, punctuation, grammar,  & writing style.
• Check for readability - format, spacing, visual appeal.
• Write the final draft
• Be sure to state the theorem you're proving.
• Be sure to leave room in the margins and between proofs for comments.