so today was my final lecture;

tomorrow will be my last day in spain .. for a while, anyway.

part of me wonders whether it was really wise to agree to a lecture series. i don't know if the students who attended got much out of my ramblings about metric spaces, geometry, and differentiability.

originally i thought that it would be best to focus on the ideas and how the proofs are structured [1], so a lot of what i presented consisted of special cases of theorems and sketches of proofs. looking back at it now, i don't think i left enough of a trail to follow what was going on .. and i admit that i went rather fast [2].

the course shouldn't be about the educator who gives the lectures, and it shouldn't be about impressing colleagues either. it should be about the students who are to learn from the lectures.

that's the whole point of a lecture, after all.

[1]

[2]

[3]

tomorrow will be my last day in spain .. for a while, anyway.

part of me wonders whether it was really wise to agree to a lecture series. i don't know if the students who attended got much out of my ramblings about metric spaces, geometry, and differentiability.

originally i thought that it would be best to focus on the ideas and how the proofs are structured [1], so a lot of what i presented consisted of special cases of theorems and sketches of proofs. looking back at it now, i don't think i left enough of a trail to follow what was going on .. and i admit that i went rather fast [2].

i skipped a lot, yet still didn't get very far;my colleagues tell me that they really enjoyed the course .. but from experience, if an expert thinks your course is interesting, then you have to ask: is this really good for the students, to whom the course was directed? [3]

in the end, maybe the compromise was for nothing.

i don't know.

they're over now; that's all i really know.

the course shouldn't be about the educator who gives the lectures, and it shouldn't be about impressing colleagues either. it should be about the students who are to learn from the lectures.

that's the whole point of a lecture, after all.

[1]

*put another way, details are easily accessible, by way of the full proofs in the referenced articles. ideas and intuition --- the kinds of things that only an expert can convey quickly and efficiently --- are harder to come by*.[2]

*that's my fault, really. i promised more topics than i could really discuss in depth, despite the fact that there were four lectures. i underestimated how long it takes to motivate the topic (1 hr) and what is really required to prove standard lemmas that i use every day (1 hr). in the remaining time i discussed two topics, each of which would be a full finnish seminar's treatment (2 x 2 = 4 hrs)*.[3]

*i think it would be fun, one day, to teach a semester-long advanced topics course, but i realise now that it comes with a personal price. if you teach nothing but advanced topics, then it disconnects you from the day-to-day reality of students, their experience, and their expectations.*

*there's a school of thought that says that "if the student is strong, then (s)he will rise to the challenge" .. but that's like saying that mathematics is only for the masochists .. which some would believe to be true, too. i believe otherwise, that***if the student is inspired and if (s)he is shown that (s)he can succeed, then (s)he will succeed**.