Project Based Differential Geometry

Next semester I am assigned to teach some of my favorite material: differential geometry. This is only the second time I have this assignment, so I still have a lot to do to think through the issues and plan a course of study.

I expect to have a class full of well-motivated and interested students. so this gives me the opportunity to do something fun: a project based class! What does that mean? I think it means the following things: I will give the students a clear list of goals to meet, and negotiate with them over projects they can work on to display their mastery of the material. There will have to be some structure to ensure that all of the students meet goals on core material. There will have to be some idea of “timed check-ups” to make sure that students are on a reasonable pace. (No course can be mastered all in the last two weeks.)

I will assign a textbook to make sure that the students all have one decent reference (and have it in common). Last time I used a “not exactly published’’ book by Ted Shifrin from the University of Georgia. I liked the text, so I will recommend it again. I won’t use it, though. I don’t intend to lecture unless students ask for it. I have a long list of other books to give them, and I think I will put a host of them on course reserve at the UNI library, too. (This will be the first time I have done that.) My list of suggested reading will need a bit of an update, too, as there have been a few new books at the undergraduate level in the last few years. I might have to write to some publishers to build a new list.

Another thing I would like to do is to give “an example a day.” I love the subject for all of its generality, but it is full of beautiful examples. I want the students to see lots of them. I am not sure if I will give all of these, or if I will assign them to students. Maybe I will start and then pass them off.

What I need to prepare:

  1. an updated copy of Shiffrin’s text to sell as a course pack
  2. an updated reference list
  3. a list of content outcomes for the students to demonstrate.
  4. Some real ideas for structure. You know, something I can explain to my students and defend at a disciplinary hearing.
  5. BIG DEAL: a sense of what the course is really about.

I’m not sure about that last one. I need it bad. I know what the material is about, of course, but I need to figure out what skills I am trying to teach. I am starting to think I am trying to teach the process of structuring your own learning.

Items 3 and 4 are intertwined. I know that I can split the semester into roughly two parts: curves and surfaces. And in each part I must develop a list of content objectives that I consider necessary, and longer list of “optional’’ projects where students can demonstrate deeper understanding of more challenging material.

Well, more when I figure it out.

2 thoughts on “Project Based Differential Geometry

  1. You have have “come up with some projects for students to do” in your to-do list. Is this hidden inside of another thing, or are you just going to wing it?

  2. Ha! I am prone to winging it.

    But that is hidden inside the list under all those bullets of content standards. Well, it was that way in my head when I wrote this piece. I think you are right that I should be more explicit about it. It certainly is at the front of my mind.

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