Monday, September 25, 2017

Week Unknown: "Open" Problems

The four problems on which I want to work when I have time:

On the circle, S1, with its standard Riemannian metric it inherits as a subspace of ℝ2, find a second-order ODE that is
  1. gradient but not Hamiltonian
  2. Hamiltonian but not gradient
  3. both gradient and Hamiltonian ("harmonic") (I think I have a heuristic proof there are no non-trivial ones)
  4. neither gradient nor Hamiltonian

Sunday, March 12, 2017

Week 62: Self-Realization

[This post doesn't really belong here, but I've been thinking about it for a while, and I want to preserve the post, not let it just get lost amongst my Twitter postings.]

So, I've done some thinking about my teaching/teaching style, and I guess what I really like and what "got me into teaching" is that I like teaching new concepts to students. This is probably a mistake to say, especially given the School at which I'm currently teaching, but I appear to dislike teaching skills: I like teaching new concepts and the new worlds of ideas to which they lead for students, but I dislike working with students to develop skills and real proficiencies with the new topics. I had professors in the past (well, at least one professor :/ ) who would give exams that emphasized knowledge over skill - he would design his exams so if you had a good theoretical knowledge of the course, you would do well, but didn't need a good skill set to be able to perform well on the exam in the time allotted - and I kind-of thought that was math. But developing skills - both for myself and in my students - is a very important part of the game, I'm beginning to realize, even if you're not teaching them any new ideas.

[On an unrelated note, I (finally!) began Tony Robbins's Ultimate Edge program today; I intended to start it 10/09/2016, evidently, but never "felt I had the resources", I correct myself, until today. I'm very excited about it and can't wait to finish it; I hope it will bring a lasting improvement in me.]