pi-Base: A usable map of the forest

Talk notes for South's ACM & Math Clubs

Posted by Steven Clontz on September 12, 2017

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.
• 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.

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!