Over the past years of teaching, I noticed myself drifting more and more to the “flipped” side of things. I never made a conscious decision to do so, but it made more sense to me to work through the hard parts in the class while offloading easier things to pre-class work.
What I struggled with (among other things) is the structure for class preparation and class activities. Since I never took a flipped class myself, I was lacking a mental model for how to plan day-to-day activities. Thankfully, Robert Talbert published a manual for how to do just that (among other things), called Flipped Learning: A Guide for Higher Education Faculty. Stylus Publishing, LLC, 2017. [link]
While I still haven’t read the entire book, I did focus on the part where Talbert discusses day-to-day class prep. He gives a wonderful structure to one’s activities around planning the class. While none of the steps are surprising, having a step-by-step checklist takes care of the mental load of “what’s next, what did I miss” that comes with doing things haphazardly. I typed up a three-sheet summary of his prescriptions to put on my desk so I don’t have to leaf through the book. I figured someone else could benefit from it as well, so here I share it.
Google Docs link
Feel free to leave comments/suggestions on it for a few weeks.
Lesson planning overview
What if students are underprepared?
We know the big differences between trying out a calculation on a back of an envelope and writing a rigorous proof. Likewise, there are differences between prototyping in a Matlab script and writing a reliable pre that supports a reproducible research project. In a 15-minute presentation for a introductory workshop on scientific software at UW Madison math department, I showcased my own workflow on a simple example of plotting several solutions to an ODE in Matlab.
Repository for the workshop can be obtained by
git clone https://bitbucket.org/mbudisic/workshopworkflow.git
Today I gave a short introduction to compressive sensing, following the article:
Bryan, K., and T. Leise. “Making Do with Less: An Introduction to Compressed Sensing.” SIAM Review 55, no. 3 (January 1, 2013): 547–66. doi:10.1137/110837681.
The examples I’ve shown can be found below:
This is a short overview of the Proper Orthogonal and Dynamic/Koopman Mode Decompositions, which are commonly used in analysis of velocity fields of fluid flows. While I worked with the theoretical side of Koopman modes, I never implemented the numerical code myself; I wrote these notes up a I was teaching myself the basics of numerics of these decompositions, and consequently used the notes for two lectures. The notes are based References at the end of the post. Caveat lector: Notes may contain gross oversimplifications — the emphasis was on understanding and not on precision. I welcome your corrections and comments below. (You can always stop by my Van Vleck office if you’re in Madison to discuss any part of this).
UPDATE: I have now posted my own implementation of several algorithms for Koopman mode decompositions. [GitHub]
Last night I had an amazing time at Madison Math Circle, hanging out with a bunch of bright school kids, who were undaunted by either diseases or mathematics. Since I had quite a few questions after the lecture, I decided to post an overview so anyone interested can go over it themselves. For those of you who attended and have further questions, or even wish to explore mathematical dynamics on your own, feel free to leave a comment below or e-mail me at firstname.lastname@example.org and I’ll try to answer all your questions and provide some guidance for future.
I’ve given a short lecture on spectral graph theory in the Physical Applied Math group meeting. My notes are available as PDF.
The annotated reading list is below. I have copies of all the books listed so come and talk to me if you’re interested.
- An example of a common use of graph Laplacians as a stand-in for combinatorial optimization:
Shi, J., & Malik, J. (2000). Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 888–905.
- On structure of eigenvectors:
Biyikouglu, T., Leydold, J., & Stadler, P. F. (2007). Laplacian eigenvectors of graphs (Vol. 1915). Berlin: Springer.
- THE monograph on spectral graph theory, a lot of material, but very readable.
Chung, F. R. K. (1997). Spectral graph theory (Vol. 92). Published for the Conference Board of the Mathematical Sciences, Washington, DC. Sample chapters on Fan Chung’s page.
- The random walk picture:
Lovász, L. (1996). Random walks on graphs: a survey. In Combinatorics, Paul Erdős is eighty, Vol.\ 2 (Keszthely, 1993) (Vol. 2, pp. 353–397). Budapest: János Bolyai Math. Soc.
- A good cross-section through applications of spectral graph theory:
Mohar, B. (1997). Some applications of Laplace eigenvalues of graphs. In Graph symmetry (Montreal, PQ, 1996) (Vol. 497, pp. 225–275). Dordrecht: Kluwer Acad. Publ.
For those of you who would like to read more about the basics of applied ergodic theory that I talked about in 703 today, there are a few accessible papers and books below the fold. You are always very welcome to send me an e-mail or drop by my office (VV517) if you want to talk more about any of the papers or the topic in general.
Please e-mail me if any of the links below the fold don’t work, or if you have trouble locating the pdfs for the papers.
Here’s a simple demonstration of Arnold’s Cat Map. V.I. Arnold, a cool cat himself, figured out, decades before the age of the internet, that putting an image of a kitteh in your research vastly increases its appeal.