Today's Math Lesson - One Sided Paper

Today's math lesson is about Mobius Strips. Watch the movie below first. 

       

One of the last courses that I took at NIU before getting a masters degree in mathematics was

Topology, the branch of mathematics that the study of Mobius strips falls under. The professor, Robert Wheeler, was the first professor I had in grad school that I felt was a teacher. I had a number of good professors at NIU; college professors are usually just different from teachers. My former boss Bill (who I played golf with today) had a system for hiring new math teachers that involved asking a number of strange questions. One of them was to ask the prospective teacher, "Do you teach math or students?" If he was lucky, the question elicited a long discussion. I don't think your answer mattered as much to Bill as the discussion did. For most young teachers who have not reached a point where reflection about their teaching is the norm, the discussion tended to be fairly short, maybe a quick answer that the jobseeker hoped would match what Bill wanted. Unfortunately that was true for some more veteran teachers as well. If Bill was lucky, the discussion lasted a lot longer, with forays into questions like "Is teaching an art or a science?" Now they mostly ask, "Have you used a smart board before?"     

Well, Dr. Wheeler taught both math and students at NIU.  His topology class was very difficult; I remember trying to get to DeKalb plenty early after work (4 nights a week) so I could run through my homework and notes one more time before class and maybe talk to some of the other high school math teachers (there were three of us amidst all the grad students) who were taking the class. Homework was turned in and graded. The tests were a challenge. I found some of them tucked in the textbook when we were cleaning the basement last spring. I actually did pretty well, from 85% to 95% on the tests and usually 6 or 7 out of 8 on the homework, which shows how hard I worked. Most of the grad students who were in the class were better math students than I was.   I know that I couldn't answer too many of the questions now. It would take a lot of work to figure out what the Heine - Borel Theorem was all about, and I don't have the time now that I'm working on turning my truck into a robot car.