Rob Corless, Academic Vagabond

This page provides links to my papers & other expositions; connective tissue for an internet world

View My GitHub Profile

My current obsession: Bohemian Matrices

See bohemianmatrices.com for details. But here’s an image, just for a teaser.

A density plot in the complex plane of the Bohemian eigenvalues of a sample of 73 million 5x5 matrices where the entries are sampled from the set {-20, -1, 0, 1, 20}. Color represents the eigenvalue density. Viewed on -40 <= x,y <= 40. Image credit Steven E. Thornton.

Research Interests

I have three major overlapping research areas: computational dynamical systems, computational algebra, and computational special functions, each of which is used in scientific and engineering applications. My main overall concern is for the fidelity and reliability of these algorithms in actual applications. The main approach that I use is Computer-Mediated Thinking or Computational Discovery, or Computational Epistemology. That link goes to a paper describing that idea in a teaching context, but it is a much broader idea, namely that the combination of human plus computer, especially equipped with thin slices of Artificial Intelligence, can be better than the human alone.

My Google Scholar profile

My YouTube Channel

My channel includes some talks, and some course videos. I'm still learning, but making the videos is quite fun! There will be more.

My computational discovery and epistemology home: The Rotman Institute of Philosophy

My computer algebra research group: The Ontario Research Centre for Computer Algebra

My LinkedIn Profile

Books

  1. Algorithms and Complexity in Mathematics, Epistemology and Science (ACMES) An edited 2019 volume containing papers from the Computational Discovery/Computational Epistemology conferences
  2. Nic Fillion and I wrote “A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis” together for 2013. Here are some excerpts from reviews of the book
  3. Essential Maple 2nd edition, 2002, foolishly entitled "Essential Maple 7".

Code Repositories for Books and Papers

  1. Perturbation Methods in Maple from the ACMES book listed above
  2. Nic Fillion's code repository for "A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis"

Maple Documents and Workbooks and Worksheets from talks

A free Maple Player which can read these items is available at Mapleplayer .

  1. Mathieu Functions: A Historical Perspective
  2. Blends in Maple from the Maple Conference 2020
  3. The Functional Inverse of Gamma from a number of places