Undergraduate Mathematics Symposium
Saturday, October 13, 2012
University of Illinois at Chicago
Organized by David Dumas
and Steven Hurder
About the symposium
The Undergraduate Mathematics Symposium at UIC is an annual one-day meeting focusing on undergraduate mathematical research and education. The meeting features invited lectures by mathematical researchers and contributed lectures by undergraduates on their own research projects.
The next UMS will be held at UIC on Saturday, October 13, 2012.
Download the poster (PDF)
Nathan Dunfield (UIUC)
Mathematical truths: experiment, proof, and understanding
Experimentation has played an important role in mathematical discovery for centuries. With the rise of powerful computers, more complex mathematical objects can be studied in this way. After explaining why "a topologist is someone who can't tell a coffee cup from a doughnut", I will give a concrete example of how experimentation lead (eventually!) to a new result in the mathematical area of topology. Along the way I will discus different forms of mathematical knowledge, contrasting the results from experiment with logical proofs on the one hand and intuitive understanding on the other.
Ramin Takloo-Bighash (UIC)
Distribution of orders in number fields
An order, or a number ring, is a subring with identity of the ring of integers of a number field which is a module of maximal rank over the ordinary ring of ingeres. In this talk I will discuss some old problems and recent theorems on how orders are distributed.
Andrea Young (Ripon College)
Discrete Differential Geometry
Abstract: Discrete differential geometry is a growing field of mathematics that has a wide variety of applications including computer graphics, medical imaging, geometric modeling, and discrete exterior calculus. In this talk, I will discuss discrete approximations of smooth 2- and 3-dimensional manifolds and describe how one can interpret the curvature of such objects. I will also discuss some problems that can (and have!) been studied and solved by undergraduates.
Attending the symposium
Online registration for this year's symposium has closed. If you have not yet registered but want to attend the symposium, please come to SEO 300 between 8:15am and 8:50am on Saturday morning to register in person. (See detailed location information and map links below.)
Schedule of events
Plenary lectures are 50 minutes and student lectures 20 minutes;
breaks of 10 minutes between talks allow for questions and discussion.
A catered lunch of sandwiches and salads is provided for all symposium
|8:15 - 8:50am
||Sign-in and coffee in SEO 300
|Morning session — Plenary Lectures — Lecture Center F1
||Andrea Young (Ripon) — Discrete Differential Geometry
||Ramin Takloo-Bighash (UIC) — Distribution of orders in number fields
||Nathan Dunfield (UIUC) — Mathematical truths: experiment, proof, and understanding
||Lunch in SEO 300
|Afternoon Session 1 — Student lectures — Lecture Center F1
||Charles Alley (UIC) — Continued Fractions as Linear Fractional Transformations and Related Results
||Jake Marcinek (Caltech) — Subrings of Z6
||Nathaniel Bude (Ripon) — Hill-Climbing Search for Metrics on Triangulations of S3
||Fiacha Heneghan and Ashley Sliva (DePaul) — Min-max Up-down Permutations
||Coffee break in SEO 300
|Afternoon session 2 — Student lectures — Lecture Center F1
||Sangwon Hyun (Michigan) — Examining the Sample Complexity of the Maximum Likelihood Estimator in Phylogenetic Tree Reconstruction
||Brian Freidan and Robert Halliday (UIUC) — The Sphere in Spacetime
||Milica Vesovic (UIC) — Mathematical Modeling of Biological Systems
All symposium events will take place on the UIC campus. Registration, lunch and coffee will be provided in room 300 of the Science and Engineering Offices building (SEO), while the lectures will take place in room 1 of Lecture Center F (LCF).
SEO and LCF are adjacent buildings on UIC's east side campus, near the Daley Library; refer to the campus map for details: