Some Math Notes

• Sometimes a comment in a comment thread for a post just needs to be given more attention than it will in a comment thread. Such is this comment by Mark Chu-Carroll at his "Good Math, Bad Math". An excerpt:
  
  

  It's infuriating to me that we continually expect students in math, in english, in compositional writing, to understand logic, but we never bother to actually teach it to them.
  
  Basic logic - just enough basic propositional and predicate logic to be able to understand proofs, and distinguish between valid arguments and invalid arguments - should be part of very basic math - no later than 7th or 8th grade. It's not that hard, and that's the age where we expect them to start using it - we just don't bother to teach it.

  
  
  Amen, amen. We need a lot more people to be infuriated by the same point, because it is right. A little bit of logic goes a long way, and, as he says, they are forced to use it anyway, so the choice is between forcing them to figure it out entirely on their own, or making a slight adjustment so that they have the means they need to advance in mathematics. This sort of thing is dear to my heart, because one thing that irritates me is how much my mathematical education was botched by things like this.



• If you haven't passed the word about the upcoming Flatland: The Movie yet, please do so. (And if you haven't read the classic book on which it is based, read it!)



• Jack Perry has a nice post at "Cantànima" on Modern Algebra as an instance in which what was basically a failure led to fruitful discoveries.



• An interesting paper by Imre Bokor on teaching mathematics (PDF).