Tips on writing proofs
If you haven't had much experience writing proofs before, here are some tips to keep in mind. I will revise this list according to feedback from the homework grader, and address common issues, so please check back from time to time.
(Updated February: The level of the homeworks has been quite high,
so I haven't added anything here. However, if you are concerned
with how to write proofs, please email me or come to see me to discuss it.)
- Write complete sentences. Don't use too many mathematical symbols.
A good check is to read your proof out aloud and make sure it sounds like English!
- To set the "level" of your writing, aim at an audience of your peers (i.e., others in the math 109 class).
In other words, one of your fellow students should be able to follow every step of your proof without difficulty.
- Do not try to "fudge" things if you don't know them.
If you are in a situation where you have a proof with a missing step, simply state clearly what
is needed to fill that step, and explain that you don't know how to justify it.
- Give references where appropriate: "By a theorem from class," or
"By Theorem XYZ from the textbook," etc.