Math problem pitfalls: Oxford guide
Hi, back with stuff from this guide, summarized and my own thoughts added. This is PART IV.
PART I: How to do math PART II: How to understand theorems PART III: When you’re stuck on a proof
Avoiding pitfalls
Be sure that you’re not skimping on rigour when finding the answer to a math problem. Recall the statement of the theorem that should be used to find the answer, to make sure that the answer is indeed correct.
Stupid mistakes -- you save a lot of time when you do things slowly and get it right, instead of hastily looking for the mistake after you’ve made it. Otherwise, look for checks that what you’re doing is correct. If your answer contains parameters, substitute in a parameter or two in order to either perform an obvious sanity check (probability between 0 and 1), or in order to simplify the solution (so that you can plug it in somewhere).
They say that you should first do some rough work. Then, rewrite the good copy without looking at the original rough work. Also, they say that it’s worth your time to make the working more concise as you write your good copy (I am personally not sure why, since I’ve never done it, but maybe it’s worth a shot?).
Part V will be about proofs and logic probably and other stuff like that.
