## Friday, September 20, 2013

### ANH: from end to start, for now.

so it feels like ages since i last thought about a blog post of any kind. it seems like there's so much to saybut at the same time, none of it is really worth mentioning. that's always the difficulty of beginning a story at the beginning ..

.. so, being lazy at the moment, i'll not. i'll begin at the ending instead, which is today.

so today i gave a lecture about metric spaces to my students. it's a first course in analysis and the textbook [1] happens to cover the topic, which to me sounds like a license to expound on it for 75 minutes.

so i showed them the discrete metric on any set, and how the unit circle would look if the set were the euclidean plane. i showed them the L-infinity norm, how the unit circle looks like the usual unit square, and how short the proof is for its triangle inequality. this is in contrast to how the proof of the triangle inequality goes for the usual L-2 distance, which uses Cauchy-Schwarz and in turn, a nod to Pythagoreas's theorem.

i thought it was cool. it would be the kind of lecture that would have inspired me as a student .. but i don't know. i'm getting to know the students in my class, but i'm still learning all the time.

[1] we're using baby Rudin.