Here are my notes for today’s talk on pi-Base for the University of South Alabama’s ACM and Math Clubs.
Clontz.org
- Notes/links from this talk are available on my website.
Relationship of Math and Comp Sci
- Math folks: knowing computer science/engineering can help you get a job.
- Don’t have to take classes; just pick up a fun sideproject!
- CS folks: knowing math can help you get a job.
- Having a math background makes people think you’re (a) smart, (b) a problem-solver (in general).
- I hope to see future collaborations between ACM and Math Club, and I encourage members of both groups to be involved with the other and leadership to work together to support their memberships.
What is Topology?
- Topology is the a of mathematical structure that generalizes geometry
and calculus.
- Classic example: donut and coffee cup
- My favorite example: topology of fonts
- Big data application: persistent homology
- One goal of topology is to identify the properties of topological spaces
that characterize them.
- Compactness: \([0,1]\) is compact, but \(\mathbb{R}\) is not.
- Hausdorff: \([0,1]\) is Hausdorff, but an indiscrete space is not.
- Normal: \([0,1]\) must be normal, because it is compact & Hausdorff.
What is pi-Base?
- Topologists have studied thousands of topological spaces and thousands of
topological properties over the past century.
- Counterexamples in Topology surveyed about 160 of these spaces and about 60 of these properties in 1970.
- Paraphrasing the famous topologist Mary Ellen Rudin in her review of Counterexamples, topology is a dense forest of counterexamples, and a usable map of the forest is a fine thing.
- pi-Base began as a sideproject of my colleague James Dabbs to digitize this information into a user-friendly web app.
- Later pi-Base was opened up to community contributions.
- Features:
- Properties
- Spaces
- Theorems
- Canonical naming as in OEIS.
Where is pi-Base going?
- Currently I have a small grant to convert pi-Base into a modern tool for
mathematical researchers.
- Major flaw in current version: lack of citations and peer-review.
- ACM officer Cody Martin worked for me last summer to add citations from pi-Base to Counterexamples.
- Once this audit is complete, all contributions will require references to a peer-reviewed manuscript to be marked as verified.
- pi-Base will become a treasure trove for undergraduate research.
- There are still many unknowns in topology.
- pi-Base can automatically catalog space/property pairs that are missing.
- Three possibilities:
- The question has been answered in literature not in pi-Base.
- The question hasn’t been answered because it’s hard.
- The question hasn’t been answered because no one’s tried: perfect for undergrads!