Spring 2023
Office Hours
By appointment. You can contact me by email or calling (907) 474-2756 to set up a meeting.
Contact Me
The best way to get in touch is drop by my office or email me at giwilliams@alaska.edu.
Courses
Courses listed below without links are/were available through canvas.alaska.edu.
Current Semester
Spring 2024: Introduction to Proof.
Archived Courses
Fall 2023: Linear Algebra, Real Analysis, and the Graduate Teaching Seminar.
Spring 2023: Linear Algebra and Abstract Algebra
Fall 2022: Number Theory and Algebra I.
Spring 2021: Introduction to Proofs and Senior Seminar.
Fall 2020: Patterns and Society, Linear Algebra.
Spring 2020: Calculus II and Geometry.
Fall 2019: Patterns and Society, Linear Algebra and the Graduate Teaching Seminar.
Spring 2019: Patterns and Society and Abstract Algebra
Fall 2018: Calculus III and Introduction to Real Analysis
Spring 2018: Calculus III and Linear Algebra.
Fall 2017: Calculus I and Calculus III.
Spring 2017: Introduction to Mathematical Proofs and Introduction to Complex Analysis.
Fall 2016: Number Theory and the Graduate Teaching Seminar.
Spring 2015: Algebra course and Calculus II.
Fall 2014: Algebra I and Numerical Analysis.
Spring 2014: Geometry and Senior Seminar.
Fall 2013: Linear Algebra, Numerical Analysis.
Spring 2013: Calculus II, Complex Analysis.
Fall 2012: Algebra I, Polyhedra and Polytopes.
Spring 2012: Calculus I, Differential Equations.
Fall 2011: Calculus II, Linear Algebra.
Spring 2011: Calculus II, Linear Algebra.
Fall 2010: Linear Algebra, Algebra I.
Spring 2010: Polygons, Polyhedra and Polytopes
Fall 2009: Calculus II, Differential Equations
UAF Math Club
You can subscribe to the calendar.
I'm keeping a list of the talks and links to recordings where possible.
You can do math
I've long maintained, contrary to many people's expectations, that mathematics is not something that only smart people do, but that math is something that people can do to get smarter. Apparently, there is some research that backs this idea up! Check out this great article in The Atlantic for more information.
Research
As time permits in coming weeks and months I will post information here about my research program. Most of my current work is in the area of abstract polytopes.
A list of my published works that may or may not be up to date.
An appendix to a paper Daniel Pellicer and I wrote on the minimal coverings of the Archimedean tilings by regular abstract polytopes discussing why the core for the tiling (3.6.3.6) is the normal closure of two generators is provided as an attachment below.
Mathematics Magazine
Currently I am the editor-elect for Mathematics Magazine, and I'll be taking over as editor in January of 2025. It is a great honor to be serving in this role for a journal that has meant a lot to me over the years. Mathematics Magazine publishes high-quality, lively, readable, and appealing exposition on a wide range of mathematical topics for a broad mathematical audience that includes strong undergraduate students. A lot of fun, interesting, and novel material has appeared in those pages over its nearly 100 years in print, and I'm excited to see what the next few years bring!
Personal Information
You can follow me on Mastodon, or Tumblr, though unless you are related to me, I can't imagine why you would do any of those things.
Other Projects and Interests
I'm very interested in the intersection between mathematics and art, and I maintained a site debunking mathematics myths, but I need to find a new hosting mechanism for both of those things since they don't play nice with Google Sites. I'm also interested in projects dedicated to using mathematics to advance social justice. I'm not involved, but this one sure looks cool!
Posted as a Service to the Community
Here is Michael Hartley's thesis.
Here is Ian Douglas' data set of small chiral and reflexible maniplexes.
Stephen Wilson's data set of regular maps is available below.
Caveat Emptor
I apologize that the look of the linked sites I maintain is so incoherent, someday when I have time I'll come up with a master plan and implement it everywhere, but in the meantime, hodge-podge is the order of the day. This site is definitely a work in progress, and always will be.