# 2014-2015 Mathematics Colloquia

## Winter 2015

### Symmetric Groups and the Rubiks Cube

• Speaker: Jim Coykendall (Clemson University)
• March 30, 2015 at 4:40 pm in Robinson 105
• Refreshments at 4:20 pm in Robinson foyer
• Abstract: This talk will be a very hands on look at the mathematics of the Rubik's cube. We will briefly explore some of the mathematics that goes on (starting with counting the number of possible combinations possible) and explore the question: "OK how do we approach trying to solve this thing?"

In this talk, we will introduce some basic group theory (and the basics of computing in symmetric groups) to get down to the brass tacks of how one would go about figuring out how to solve the cube (without reading the solutions book). This talk will be about solving problems and how to use your mathematical skills to figure out something new. A little bit of "practical math" will be introduced, but it will be pretty elementary. I cannot promise that you will walk out of the talk with the ability to solve the cube, but I can promise that you will walk out with the tools to solve it. This talk should be interesting and accessible to all.

### Quadratic Forms - from Fermat to the present day

• Speaker: Michael Bush (Washington and Lee University) — Pi Mu Epsilon Initiation
• March 24, 2015 at 4:40 pm in Robinson 105
• Refreshments at 4:20 pm in Robinson foyer
• Abstract: Quadratic forms are polynomials in some number of variables in which the total degree of each term is 2. For example, $f(x,y,z) = 3 x^2 + 5 x y - y^2 + z^2$ is a quadratic form in three variables over the integers. Such forms arise throughout mathematics and have been studied for hundreds of years. I will give a survey of some of the highlights in the theory of such forms including results on the representation of primes and criteria for universal forms.

### Partitions and Compositions: A Tale of Two Symmetries

• Speaker: Sara Mason (Wake Forest University)
• February 19, 2015 at 4:40 pm in Robinson 105
• Refreshments at 4:20 pm in Robinson foyer
• Abstract: This talk explores the role of partitions in symmetric function theory and their counterpart, compositions, in quasisymmetric function theory. We look at properties that are common to both settings, ways in which they differ, and interactions between the two. Along the way we develop several new bases and explain how these can be used to prove results in both settings.

### Math for Drones: Miniature Aerial Vehicles Under the Hood.

• Speaker: Simon Levy (Washington and Lee University, Department of Computer Science)
• January 29, 2015 at 4:40 pm in Robinson 105
• Refreshments at 4:20 pm in Robinson foyer
• Abstract: Miniature Aerial Vehicles (MAVs), or "drones", are everywhere these days. With little training, an ordinary person can now fly one of these vehicles safely. This rapid progress in MAVs has been enabled by three factors: (1) the availability of powerful, lightweight motors, batteries, and other electronic components; (2) rapid increases (Moore's Law) in the power of the onboard computers that run the vehicles "firmware"; (3) adoption of mathematical methods that have been around for decades. In this talk I will focus on (3), describing the Extended Kalman Filter (EKF), which dates back to the space program, as well as the concept of quaternions, which dates back to the work of William Rowan Hamilton in the nineteenth century. Despite being literal "rocket science", these methods are understandable to anyone with curiosity and a little math background (calculus, linear algebra). I will describe how they are combined to provide the extraordinary capabilities and rapid progress that we see in MAVs today. I will conclude with a live demonstration of an MAV built at W&L.

## Fall 2014

### How to Win at Beanbag Toss (if you're a robot), or why you already know calculus, and how a little more could change your life

• Speaker: Jason Cantarella (University of Georgia)
• November 10, 2014 at 4:40 pm in Robinson 105
• Refreshments at 4:20 in Robinson foyer
• Abstract: Suppose you have to make a free throw in basketball, toss a coin into a wishing well, or throw a horseshoe onto a peg. All of these tasks require you to swing your arms to accelerate the ball to the right speed, and then let go at just the right moment. You can do this, but how do you do it? How do you know what the right speed or the right time are?

### On Becoming a Mathematician

• Speaker: Barbara MacCluer (University of Virginia)
• November 7, 2014 at 4:40 pm in Robinson 105
• Refreshments at 4:20 in Robinson foyer
• Dr. MacCluer will share her experiences and the advice that helped her succeed through graduate school and academia. A Q&A session will follow the talk.

### What I Did Last Summer (Parent and Family Weekend Event)

• Speakers: W&L Math students Candace Bethea, Mary Kamp, Xichen Zhu, Danjoseph Quijada, Noah Duncan and James Quigley.
• October 10, 2014 at 3:45 pm in Robinson 107
• Refreshments at 3:15 in Robinson foyer
• The students will talk about their summer research on graph theory, folded ribbon knots, deBruijin sequences and Tsirelon space.

### I'm a Math Major---Now What?

• Speaker: Liz Townsend Beazley '03 (Haverford College)
• October 3, 2014 at 3:45 pm in Robinson 107
• Refreshments at 3:15 in Robinson foyer

### The Quest to Tabulate Composite Links

• Speaker: Matt Mastin (Wake Forest University)
• September 25, 2014 at 4:40 pm in Robinson 105
• Refreshments at 4:20 in Robinson foyer.
• Abstract: A mathematical link is a particular embedding of a collection of circles into 3-space. Just like the integers, there are prime links and composite links and the composite links can be (uniquely) decomposed into prime links. However, there is as of yet no precise classification of the composite links which can be built out of a given collection of prime links. For knots (an embedding of only a single circle) there is a nice algebraic construction which classifies the composites. This construction will be discussed as well as the difficulties that arise in generalizing to links. We will end with an ongoing computational project that utilizes cloud computing and techniques from the data science world to perform a classification of all knot diagrams (a particular picture of a link) through a certain complexity.