Date: Thursday May 4, 2023
Location: Math West WMC 2800-2830
Webpage: https://www.cecm.sfu.ca/~nbruin/compday/
Organizer/contact: Nils Bruin, nbruin@sfu.ca
Description: This event consists of several presentations and tutorials that will help you to be more efficient and productive in your mathematical research.
Modern mathematical research uses computational tools in many ways: You use computers to typeset your results in the form of an article, report, poster, or presentation slides. You will also use computers to archive and keep track of your work and to share it with your collaborators and supervisor. Furthermore, there are various advanced (and some experimental!) software packages that can do advanced and complicated computations for you, in a way similar to how you used a graphing calculator for basic problems in high school. This event consists of several presentations and tutorials that show you some of these tools and how to use them. You will also have opportunities to try them yourself.
This event has concluded and the page here is for archival purposes. Some materials used for the presentations are posted below, with the abstracts.
Git/Jupyter by Cedric Chauve and Mahsa Faizrahnemoon
Computational mathematics and data science projects can sometimes be difficult to manage, or even overwhelming, over the duration of a USRA project. This demo aims to introduce useful tools and best practices that are helpful to organize and manage the various elements of such projects:
See https://github.com/cchauve/CompMath-Day-2023 for the repository used during the presentation.
Lean theorem proving assistant by Jake Levinson
Formalising math means writing proofs precisely enough to allow a computer to check if the argument is sound. Until recently, such efforts were primarily of interest to computer scientists, because verifying anything but very simple statements (e.g. the square root of 2 is irrational) was extremely laborious.
This is beginning to change: modern proof assistants are user-friendly enough to make it tractable to formalize university-level and (to a lesser extent) research-level mathematics. For example, in 2021 a team of mathematicians and computer scientists using the Lean Proof Assistant made waves when, in under six months, they successfully verified a tricky technical lemma proposed by Fields medalist Peter Scholze. Scholze had posed it as a challenge because it was so technical (!) that he wasn't sure if it contained an error.
You can read Peter Scholze's blog post about the experience.
If you're curious what formalised mathematics is like, try out the Natural Number Game, a tutorial on proving the basic properties of the natural numbers:
https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/
In this workshop, I'll give a demo of how to prove some basic and some less-basic theorems in Lean, then attendees will try out Lean themselves.
Files from presentation: slides, exercises, solutions.
Macaulay2 Demo Session by Nathan Ilten
Macaulay2 is a computer algebra system that is designed for use in algebraic geometry. I'll demonstrate a number of computations in algebraic geometry including cohomology of line bundles on projective space, counting the 27 lines on a cubic surface and the 2875 lines on a quintic threefold, computing the Hodge numbers of a quintic threefold, describing the local structure of the Hilbert scheme of twisted cubic curves, and more!
The file used during the demonstation cecm2023.m2 is available.
Maple Demo by Michael Monagan
Maple is a computer algebra system. Information about Maple is available on the Wikipedia page. I will show Maple tools for studying
Maple Tutorial by Michael Monagan
An introduction to how to use Maple to do algebra and calculus
We will cover solving equations and ODEs, differentiation integration,
plotting functions of one and two variables, plotting curves, surfaces,
and drawing vertex-edge graphs. Also how to create a document in Maple
with mathematical text, create a .pdf of the document, and export
formulas and plots to $\mathrm{\LaTeX}$.
SFU has a site license for Maple. Faculty, students and staff can download and install Maple from SFU IT Services.
Magma by Nils Bruin
An introduction to the Magma computer algebra system. Magma is a computer algebra system that specializes in computations with various advanced algebraic objects, such as groups, number fields, quotients of polynomial rings, algebraic curves, and schemes. Particularly for arithmetic geometry, it provides various capabilities that are simply not available in other packages.
I will demonstrate some of these capabilities, emphasizing the underlying design principles and language used by the system. The aim is to provide you with the tools that allow you to look up and learn more about the system yourself.
While Magma is not a comercial system, it does employ license fees to fund its development and maintenance. Within the Department of Mathematics, access to Magma can be obtained through the CECM computer network.
The notebook used during the presentation is available as PDF file and as a Jupyter Notebook. Note that for the latter you would need access to a machine that has Magma installed and has Jupyter as well as the Jupyter Magma Kernel installed.
Some dos and don'ts in scientific visualization by Nilima Nigam
An important aspect of mathematical communication consists of presenting quantitative information in a visually informative manner. In this tutorial you'll learn some basic strategies for generating plots of scalar as well as vectorial objects, with an emphasis on readability and clarity.
| Time | WMC 2810 | WMC 2820 | WMC 2830 |
|---|---|---|---|
| 9:30-10:30 | Scientific Visualization | Macaulay 2 | |
| 10:30-11:00 | Coffee | ||
| 11:00-12:00 | Jupyter and git | Magma | |
| 12:00-12:45 | Lunch | ||
| 12:45-13:30 | Install Fest | ||
| 13:30-14:30 | Maple | Lean | |
| 14:30-15:30 | Maple | ||
Install Fest: Bring your own laptop and get help from other participants to get mathematical software installed on your own computer. Results not guaranteed, but we'll try and help you.