The Undergraduate Seminar in Mathematics is a weekly, hour long talk. There you can hear about some of the many deep and interesting areas of mathematics beyond what you would see in the classroom of most math classes. The talks are designed to be accessible to any college student; little to no math background is required. The seminar occurs most weeks on Tuesday from 6-7pm, in Stevenson 1206. Come by and enjoy some pizza and soda before the talk, and hear about something new. We hope to see you there!

This semester’s talks: (This list will be updated as talks are scheduled.)

**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**: TBD

**Title**: TBD

**Abstract**: TBD

**March 13**: TBD

**Title**: TBD

**Abstract**: TBD

**March 20**: TBD

**Title**: TBD

**Abstract**: TBD

**March 27**: TBD

**Title**: TBD

**Abstract**: TBD

**April 3**: TBD

**Title**: TBD

**Abstract**: TBD

Check out all of the awesome talks we have had in the past!