February 6: Hayden Jananthan
Title: The Limitations of Ruler-and-Compass Constructions
Abstract: Most people know that the ancient Greeks excelled at geometry, producing the foundations of the Euclidean plane and solid geometry we learn today in school. Those geometers focused on their constructions being physically possible, and their tools consisted of an unmarked ruler and a compass (to draw circles).
Some geometrical constructions plagued the ancient Greeks, seeming entirely out of reach. Among these:
– Squaring the circle: drawing a square of area pi (equivalently, construct a line segment of length square-root-of-pi)
– Doubling the cube: construct a line segment of length cube-root-of-2
– Angle Trisection: given an angle, trisect it
It wasn’t until the 1800s that these constructions were shown to be impossible using algebraic techniques.
February 13: Ryan Solava
Title: How Many Crayons? (Graph) Coloring Problems
Abstract: A question that you might (or might not) ask is how many different colors of crayons do you need so that for any page of a coloring book, you can color each region, so that no two adjacent regions have the same color. This question is more commonly phrased in terms of maps, and the answer is given by an important theorem, which I won’t name here because the name gives away the answer. In this talk, we will explore this problem and the more general topic of graph coloring. Together we will get a glimpse of discrete mathematics and combinatorics, a side of math that you don’t often get to see in required math courses.
February 20: Andrew Moorhead
Title: Fourier Series and Representations of Sound
Abstract: If you have messed around on a guitar a little bit you know that if you lightly place your finger on the midpoint of the string and pluck, a bell-like sound will result. This is because the guitar string has many basic ways in which it can oscillate and a finger in the middle of the string is preventing some of those oscillations from happening. In mathematical language, you are deleting some of the summands from the Fourier series that represents the waveform produced by the guitar string.
I’ll review the basics of a Fourier series for continuous functions defined on a finite closed interval and we will listen to a few demonstrations of a series converging to a piece of music. For the remainder of the talk we will discuss how these ideas can be applied to discrete time signals, and how these applications have changed music from a fully analog endeavor to a digital one.
February 27: Zack Tripp
Title: Points of Curves
Abstract: There are problems in geometry and number theory that are easy to state but extremely difficult to prove (some of which are still unsolved!), especially focusing on problems that relate to concepts that students are familiar with from high school algebra and geometry. As a part of our discussion, we will see the basic ideas behind one of the biggest solutions in mathematics in recent years, namely Andrew Wiles’s solution to Fermat’s Last Theorem. Moreover, we will see the deep interaction between geometry and number theory and how techniques in each of these fields can help us solve problems in the other.
March 13: Glenn Webb
Title: Unseen Enemies: Surveilling, Predicting, and Controlling Epidemic Outbreaks Using Mathematical Models
Abstract: Pandemic influenza, endemic Zika, emergent Ebola, and many other infectious diseases exist inevitably in human society. The pathogens that cause these diseases threaten all humans, independent of social, economic, and geographical context. Mathematical models, formulated in terms of time and space, and individuals and communities, track the dynamics of infectious pathogens, with regard to the effectiveness of vaccination, quarantine, medical treatment, and other interventions. New developments in mathematical epidemiology, with greatly advanced theoretical and computational technology, provide new hope to combat these unseen enemies.
March 27: Zach Gaslowitz
Title: Paradoxes in Politics
Abstract: Don’t worry, this talk isn’t actually about politics. Instead, we’ll be talking about some logical and mathematical challenges that one would run into when designing a government. There is surprising subtlety in even seemingly easy questions. “How many representatives should each state get?” “Will people actually vote for their favorite candidate?” “After they vote, how do we decide who wins?” We’ll take a look at some different ways of answering these questions, and discuss the real world implications and tradeoffs that come along with them.
April 3: Jon Ashbrock
Title: Finding Clarity in the Madness: An Introductory Look at Sports Analytics
Abstract: Each March, the top 68 college basketball teams compete in a single-elimination tournament to determine the year’s champion. The winners are notoriously hard to predict so the tournament has earned the nickname “March Madness”. In this talk, we will apply statistical techniques and algorithms to try to predict the winners and put an end to the madness.
April 10: The Undergraduate Seminar Planning Committee
Title: (Math) Jeopardy!
This! Is! (Math) Jeopardy! This semester we’re going to end the Undergraduate Seminar with a fun and competitive game of math-themed Jeopardy. Test your mathematical knowledge, from intriguing deaths of famous mathematicians to your ability to calculate derivatives or integrals on the spot. Sweet prizes are awarded to the winner of each round.