Theorem: Dining hall tables have no finite bound on the number of people sitting at them.It turns out that apparently the same thing applies to teaching. There is no upper bound on the amount of material I can "cover" in a fixed class period. In the job I've worked for years, we have rigid schedules for most lower level courses: if it's Wednesday, it must be the chain rule. In most cases, even the homework problems are specified by the department in advance. The first time I taught (ever), I did not reach the end of the syllabus at the end of the semester. (No one else I talked to did either; the course was ridiculously overfull, in a topic-a-day, cobbled-together kind of way.)

Proof: Suppose that n were a bound on the number of people sitting at a table, and suppose that we have n people sitting at that table. If an n+1st friend comes along, everyone will rearrange their stuff so as to make room for this person. Thus there can be no such upper bound.

My problem? I was worried about whether students understood what I was teaching. Silly me. After enough departmental pressure, I learned to correct the problem. Instead of teaching, I had learned to, like a cat in a little box, "cover material." After I few semesters I could be right on time with the schedule. If needed, cut down on examples, cut out theory, stick to material that was bound to be on the final exam (if there was a common exam), and forge ahead at all costs. (Of course, was still trying to do this with a minimum of critically lost students. I can't completely change my spots.)

Admittedly, I never quite achieved the mastery of a graduate professor of mine, who covered some sections in the book "by fiat." In other words, he covered it because he said he covered it, and it was up to us to fill in what we needed to know from the text. Someday I plan to use this.

Nonetheless, I've certainly learned from my teaching job how to stick to a schedule no matter what, and finish in one day whatever appears on the schedule for that day. Which brings me to tonight. I was working off another schedule someone else designed, and found that what used to be two relatively full days had become one class period. And yet, I finished essentially on time, and with a minimum of lost students. Somehow I've covered the twice the material in the same time. Which make me wonder if there is an upper bound to the amount of material that can be covered in one class period.

Of course, all this means that I've also learned two other things:

- I like much better classes in which I set my own schedule and don't work off someone else's; and
- I really want a new job.

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