Problem Set Rules (Constantly in progress)
A constantly evolving list of things I have to tell myself while working problem sets that are usually proof based. A few mechanical bits included from applied/ more mechanical classes. Rule 4 has no work arounds to situations listed yet I will add some in later but feel free to suggest some. Disclaimer: No set of rules is one size fits all for proofy problem sets. Sometimes it just takes that long. If it does you just gotta bite the bullet and redo them until they are concise or efficient (usually both).
Rule 1: If Stuck (ordered)
Solution or concept contained in question not immediately clear.
- Attempt a new solution using given materials only and or in class notes.
- Find definition, theorem, or other object containing unclear term(s).
- Find example of use or proof containing term and see how it was applied.
- If still unclear how you should proceed:
- Write down what you know/ think you know about the problem or its objects.
- Read findings from part 1 and 2 out loud.
- If still unclear how to proceed:
- Write conditions, givens in problem.
- Write down what result you are to show given these conditions.
- Create an outline of all parts you have leaving blank spots for the parts you don’t.
- Write in margins of the blank spots what type of methods might be used to get from one step you do know to the blank spot you don’t.
- If still unclear or completely lost:
- Look up a similar example, or proof.
Rule 2: Timing & Length Issues
30-45 minutes has passed but problem is not finished.
- Put the problem down. On a post it briefly write:
- Not Finished!
- Why are you stuck?
- What do you need to get unstuck?
Problem is finished but unreasonably or unnecessarily lengthy (more than one page usually).
- Put the problem down. Write on post it:
- Why is this longer than it needs to be?
- Too much exposition?
- Too much detail?
- Did you start from a definition or theorem too far removed from your problem?
- How could this be written to be more concise?
Rule 3: RTFMs
RTFM! (Read the F*%#ing Manual)
- In this case read the definition or theorem.
RTDQ! (Read the Damn Question)
- Read it again, what did you misread/ misunderstand/ assume.
Don’t hallucinate or invent problems that are not there or were not assigned.
Rule 4: Impossibles & Improbable’s
Conclusion you’ve reached states premise is impossible and you know it isn’t.
Conversely, your conclusion says the statement is true/ possible and you know it isn’t.
Result represents an unfathomably small/large number and it’s not likely the right one.
Conclusion reached is not accessible from the premises given.
Your result is more specific or general than the problem is clearly asking.
You’ve created a non-existent special case. Stop it.