Things I Need to Run Differential Geometry

Time to get down to brass tacks. What things do I want to have in hand at the first meeting of my differential geometry course this semester? What things must I create before I meet the students so that everything can run in an orderly fashion? (Given the course structure, I am using the word “orderly” in a rather loose sense, here.)

  • An Official Syllabus: this is the document required by state law. It has to have certain things on it.

  • An IT structure for dealing with recording student achievement and demonstrations of competence. (Somewhere between “scattered pieces of paper” and “My own web-app grade book database with customized reporting options.”)

  • The first assignment: this is the one that gets students rolling towards making an overview and choosing their learning goals.

  • My own outline of how to handle phase one of the course: the theory of curves in the plane and in space.

  • A set of ideas for projects (Josh Bowman helps me here)

  • A list of examples to fill out my “example a day” plan.

  • A tightly controlled structure for a warm-up project to help students get over the disorienting freedom I will give them. (With great freedom comes great responsibility, or something like that.) (Patrick Honner helps me here.)

  • An annotated bibliography to share as a guide to the available literature students might use to get started. This will lean on my book review project, which is languishing right now. I will do a few more in the next week.

  • Something to guide my students through the “advanced calculus gap.” I don’t need real analysis, I don’t need full-blown differential topology, but I do need more than the standard multivariable calculus and linear algebra courses require. Spivak’s Calculus on Manifolds is probably aiming too high. I have a copy of Shifrin’s Multivariable Mathematics, so I will look through that. I might have to make my own thing here. I hope not.

  • Speaking of Shifrin, I need to arrange the latest of edition of his undergraduate diff geom book as a course pack for the students.

  • Some way of carting my stack of books to class each day. Seriously. I need to figure out a mechanism for getting my undergraduate level differential geometry library from my office down to the classroom. I need a cart, or a bunch of sturdy square bags or boxes with handles.

  • A killer opening. I want to grab attention with the first twenty minutes. This stuff is seriously cool, and I want to build a little excitement for the material.

  • Some serious spine-stiffening. I have to present this craziness, and I have to do it in a self-assured and encouraging manner.

Have I missed anything? I think I can have half of these squared away by the end of the day on Friday, with good progress on the others.


6 thoughts on “Things I Need to Run Differential Geometry

  1. I was doing talks about kids’ books for a while. A rolling suitcase I bought at a thrift store worked great for carting those books back and forth. Would that work for you?

    I’ve always made Excel work for my grading, but there’s an inexpensive grading system called ActiveGrade (, created by a teacher who’s into SBG (standards-based grading). A lot of the high school teachers who blog use this term to mean that they assess each standard they care about with each student until the student achieves mastery. I don’t like the term, perhaps because it reminds me of standardized and the common core standards, but I’m moving in that direction. What you’re doing sounds similar; maybe ActiveGrade would work for you.

  2. I hope I don’t have to go so far as to buy anything, but a rolling suitcase might be the answer.

    I have heard of ActiveGrade, I will give it another look.

    Thanks, Sue!

  3. Ooh, I had seen that Hopf fibration animation before, but I hadn’t thought about it in this context. Thanks!

    And quadric surfaces will be a major class of examples. If we can’t understand those clearly, we haven’t achieved anything.

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