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.
My current obsession: Bohemian Matrices
The Wikipedia entry on Bohemian Matrices
My new book, with Neil Calkin and Eunice Chan! Open access, and in beta: comments welcome!
Computational Discovery on Jupyter
Chapter 5 (or is it Unit 5? With a Jupyter Book the old words for divisions of a book are a bit obsolete) covers Bohemian matrices at an entry level.
Proposed Cover Design
Have a look!
Jupyter and Maple
A version of the book 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.
The Bohemian Calendar 2023 is out! (Many images produced by the code from the book above) Licensed under CC-by-SA 4.0.
See bohemianmatrices.com for more information about Bohemian matrices.
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.
- 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".
Some Older Mathematical Visualizations
- The Lambert W Function Poster
- About the 1998 UWO Applied Math Coffee Mug Design (These mugs are collector's items, now)
Code Repositories for Books and Papers
- 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"
Maple Documents and Workbooks and Worksheets and PDFs from talks
A free Maple Player which can read these items is available at Mapleplayer .
- Talk slides for CICM (Cambridge) Sept 2023
- Talk slides for Blendstrings: An Environment for Computing with Smooth Functions, Numerical Analysis in the 21st century, Oxford, Aug 2023
- Talk slides for Teaching Mathematics in a Mechanized Environment (CUNEF 2023-06-28)
- Talk slides for ILAS July 2023
- My talk, Generalized Standard Triples, for FMD60 in Madrid July 2023
- My talk for ANODE, February 2023
- 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
My (boring) allergies, as of October 2021