Vanderbilt University Undergraduate Seminar in Mathematics
The Vanderbilt University Undergraduate Seminar in Mathematics is designed to show some fascinating and exciting sides of mathematics to the undergraduate community at Vanderbilt . During the course of each semester, we'll feature talks by graduate students and professors on a variety of topics in mathematics, from set theory and abstract algebra to analysis and applied mathematics. Each talk will be interesting and accessible to undergraduates, whether they're math majors or not... yet ;).
Our goal is to show students the beauty and power of mathematical ideas they might not see in their regular coursework. We hope those same students will develop a better idea of, and a keener interest in, what mathematics is and what mathematics can do.
Abstract:Self-reference can lead to some fascinating but logic defying examples, such as the well-known Epimenides paradox ("This sentence is false"). Despite this, or perhaps because of it, self-reference has been put to good use in several important results in mathematics, including the Halting Problem and Gödel's Incompleteness Theorem. We will examine these results and on the way, explore mathematical thinking and it's limits.
Abstract: In this talk, I will give a gentle introduction to Ramsey theory, a beautiful area in extremal combinatorics. The crux of Ramsey theory is that in every large structure we can find some very ordered substructures. In other words utter chaos does no exist, no matter what your experiences at university may have taught you.
Abstract: Software tools such as Garage Band and Audacity, allow musicians to analyze and create music, but how do these tools work? In this talk, I will introduce a branch of mathematics called harmonic analysis and its most important tool, the Fourier Transform. I’ll show how this can be used to break down a short piece of music into its frequency components, and (hopefully) show how some techniques from machine learning can be used to allow a computer to identify what chords/notes are being played based on these frequencies.
Abstract:Two bank robbers are arrested and taken to separate interrogations rooms. The police know that they only have proper evidence for a traffic violation, which carries a hefty fine but no jail time. Somehow, though, they offer each prisoner a deal that persuades them to turn on their partner, and both end up serving time. This simple example highlights a perhaps counterintuitive idea in game theory, which pops up in various forms throughout our daily lives. We will discuss some of the theory behind it, see a few ways in which it comes up, and figure out ways we can change the game to get a more satisfying outcome.
Abstract: In this talk, I will give a brief overview of mathematical modeling approaches with their applications in various medical case studies. Different types of data have different features which can be visualized and analyzed by certain types of mathematical techniques such as histograms, scatter plots, and mean/median, variance. We can select appropriate modeling techniques for certain types of data to analyze the results and predict future trends.