MCS-313, Abstract Algebra
Fall 2002
MCS-313 homepage
Assignments and class schedule
Homework guidelines
Prof.
Moira McDermott
Additional practice problems
Proof checklist
Feedback
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.
*from Barbara Kaiser
Last modified: 9/3/02