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

I am the Editor-in-Chief for Maple Transactions , a new open-access scholarly journal. The purpose of Maple Transactions is to disseminate excellent expositions on topics of interest to the Maple community. There are no page charges, and you need not use Maple to be published in this journal.

A draft paper on special functions in symbolic computation systems, for comment.

A draft paper on a Chebfun-like environment in Maple using blends, for comment.

A draft paper applying that environment and collocation to solve the Mathieu equation, for comment.

The Wikipedia entry on Bohemian Matrices

Computational Discovery on Jupyter Chapter 4 (or is it Unit 4? With a Jupyter Book the old words for divisions of a book are a bit obsolete) covers Bohemian matrices at an entry level.

Possible cover images from Doubly Companion Matrices:

Zoomed in near the left edge:

The cover shows a density plot in the complex plane of the eigenvalues of all 3¹⁶ = 43,046,721 "doubly companion" matrices of dimension $m=8$ with population {-1,0,1}. Because we were unsure of rounding error effects on the delicate structures at the left and right edges, we first computed all 2,184,139 distinct degree 8 characteristic polynomials and solved those accurately in Maple. In fact we need not have worried, and eigenvalue computation, which is faster, resolves the delicate structures quite well. We do

A version using the Maple kernel for Jupyter notebooks is under construction. Here is one such notebook, which validates a hand computation of approximate zeros of the Fibonacci function.

An example Jupyter notebook linking to a Maple kernel.- Letter paper, week starts Sunday
- Letter paper, week starts Monday
- A4 paper, week starts Sunday
- A4 paper, week starts Monday

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 academic CV
- 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 Mastodon profile
- 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 </ul>
- Maple in Mathematics Education and Research an edited 2021 volume containing selected papers from the Maple Conference 2020 . Videos of talks still available at that link.
- Algorithms and Complexity in Mathematics, Epistemology and Science (ACMES) An edited 2019 volume containing papers from the Computational Discovery/Computational Epistemology conferences
- 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
- Essential Maple 2nd edition, 2002, foolishly entitled "Essential Maple 7".
- The Lambert W Function Poster
- About the 1998 UWO Applied Math Coffee Mug Design (These mugs are collector's items, now)
- Perturbation Methods in Maple from the ACMES book listed above
- Nic Fillion's code repository for "A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis"
- Mathieu Functions in Maple for the Maple Conference 2022
- Algebraic Companions (for ILAS 2022, Galway)
- Computational Discovery with Newton Fractals, Bohemian Matrices, & Mandelbrot Polynomials (for ATCM)
- Hybrid symbolic-numeric methods for Bohemian matrices
- Mathieu Functions: A Historical Perspective
- Blends in Maple from the Maple Conference 2020
- The Functional Inverse of Gamma from a number of places