Educational Forum on the Teaching of Computational Geometry and Topology: Some History, Current Practice, and Future Trends

The Educational Forum on the Teaching of Computational Geometry and Topology occupied one afternoon session on Wednesday, June 13, 15:30-18:30 (with break 16:45-17:15). This workshop accompanied Computational Geometry Week 2018 in Budapest, Hungary, 2018.

Thanks to all the participants of the workshop! Thanks especially to our speakers and our distinguished panelists, who provided a lively discussion on the topics of education in the CG/CT class. We will be providing a report based on minutes of the workshop discussion, and feedback and input we received.

Please see our blog/website, Teaching Computational Geometry and Topology, where data and follow-up resources are being posted.

The slides presented at the workshop (with slight corrections) are here.

Schedule:

  • 15:30-15:50 Sandor Fekete, "IDEA instructions: Visualizing algorithms without words "
  • 15:50-16:10 Brittany Fasy, "Teaching Computational (Geometry and) Topology"
  • 16:10-16:30 Jisu Kim, "R package TDA for Topological Data Analysis"
  • 16:30-16:50 Efi Fogel, "Teaching with CGAL Arrangements"

Break: 16:50-17:15

  • 17:15-17:30 Dave Millman and Joe Mitchell, "Overview of CG/CT courses taught worldwide"
  • 17:30-18:30 Panel discussion: Franz Aurenhammer, Erin Chambers, Dan Halperin, David Mount, Joe O'Rourke

Abstracts:

Title: IDEA instructions: Visualizing algorithms without words

Speaker: Sándor Fekete, TU Braunschweig, Germany

Abstract: The description of an algorithm can take on many different possible shapes. Many of these are tailored towards implementation in a computer; this is not a problem, as long as the objective is to simply have the recipient carry out a sequence of instructions without having to understand the underlying ideas.

When teaching humans, it is vital to appreciate the different objectives (learning design and concepts of algorithms) and the different platform: a human brain works best with connections and images. This difference is compounded when dealing with geometric algorithms, whose nature is visual rather than text-based.

In this talk, I will illustrate (!) a novel approach to dealing with some of these concepts by the ongoing IDEA project, in which we turn algorithms into visual instruction sets for „building“ the output of an instance. In addition to distilling the key steps into a sequence of images, each instruction supports an inductive approach to teaching, which lets students discover the key concepts of a problem solution by solving instances as puzzles of increasingly difficulty, with the IDEA instruction as a „cheat sheet“. First experiences with 6-9-year-olds in elementary school are encouraging.

The IDEA project is joint work with Sebastian Morr.

See https:/idea-instructions.com for more.

Title: R package TDA for Topological Data Analysis

Speaker: Jisu Kim, Carnegie-Mellon University

Authors: Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clément Maria, Vincent Rouvreau

Abstract:

This presentation gives an introduction to the R package TDA, which provides some tools for Topological Data Analysis. The salient topological features of data can be quantified with persistent homology. The R package TDA provide an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus, and PHAT. Specifically, The R package TDA includes functions for computing the persistent homology of the Rips complex, alpha complex, and alpha shape complex, and a function for the persistent homology of sublevel sets (or superlevel sets) of arbitrary functions evaluated over a grid of points. The R package TDA also provides a function for computing the confidence band that determines the significance of the features in the resulting persistence diagrams.