DIY Math

cF. The Cult of Done Manifesto

What to do when stuck

• Try to formulate a question to ask someone.  Often the very act of phrasing the question will help you get un-stuck!  And if not, there's always the chance that the person you ask will know the answer :)
• Look for simpler examples that will help you understand the issue (see next item)

How to build our own examples (and counter-examples) for things that are given to us abstractly

• Probably we need an example of building an example.  Maybe we can take Jonsul's Hanoi Tower as a first example and work through that as a group?
• If you know what you're looking for, it certainly helps.  (Then you can do a search... or a grep if you're a programmer.)  But how do you figure out what to look for?  Interesting challenge.

How to find (or make up) examples of the practical application of what we are learning

• It's always helpful to have a long-term goal in mind and then "work backwards".  At this point in the course maybe we can assume long-term goals are set for now (but we can come back to the issue later).  In the mean time, finding the simplest step (that you can actually) do that gets you toward your goal is an interesting challenge.  Often textbooks will try to walk you through something step by step, but that may not always be what you want.  Further discussions of this point would be useful.

How to test ourselves for understanding (both on a line-by-line basis and cumulatively)

• It seems to me that this gets at the very important idea of "proof" -- but let's start with a simpler topic, "evidence".  Like other sciences, a lot of mathematics these days uses computation to come up with evidence that isn't proof, but can still give the idea for a proof.