MCS 236: Graph Theory (Fall 2013)

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. 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.
Last modified:  8/7/13