**February 20**: Alex Popkin

**Title**: The Four Color Problem

**Abstract**: Have you ever looked at a painted map and wondered whether it could be colored with fewer colors? This may seem like an unusual problem, but in fact many mathematicians have worked on the four color problem: can any map be painted with four colors such that no two adjacent regions have the same color? Several different solutions were offered before the final proof was found using computers in the 1970’s.

**February 27**: Tara Davis

**Title**: A Construction of the Real Numbers

**Abstract**: Did you ever wonder exactly what the real numbers are? Where do they come from and what interesting properties do they have? We will show how the real numbers are built up from the rationals, and explain that this was necessary because the rationals are “incomplete.” We will also speak about other ways to “complete” them, leading to a different version of the real numbers.

**March 20**: Justin Fitzpatrick

**Title**: Combinatorics: I choose YOU!

**Abstract**: The question of how many ways there are to form a group of k things from a group of n things is a very natural question that arises frequently in various real-life situations. In this talk, I’ll define permutations and combinations, show how they are calculated and related to one another, and demonstrate several interesting applications.

**March 27**: Adam Dailey-McIlrath

**Title**: ONE FISH TWO FISH RED FISH BLUE FISH

**Abstract**: This talk will present some fundamental examples from mathematical biology. We will explore some simple biological systems by constructing and analyzing differential equations.

**April 3**: Hannah Callender

**Title**: Using Mathematical Models to Predict the Future

**Abstract**: The field of mathematical biology is a relatively new yet rapidly growing area of research. Opportunities are endless, and employers across the board (from industry to academia) are looking to hire people in such interdisciplinary fields. This talk will be somewhat of a review and a continuation of last week’s seminar in mathematical modeling. I will discuss several different applications (including population dynamics, spread of infectious diseases, and complex cellular signaling networks) as well as introduce the power of computer simulations in helping us understand the complex interactions within the system we have set out to model.

**April 10**: Casey Leonetti

**Title**: What Mathematicians Do: Mathematics Beyond Calculus

**Abstract**: Contrary to popular belief, most mathematicians don’t spend their days using calculators and computers to compute answers to really hard word problems. In fact, most mathematicians rarely deal with numbers other than 0, 1, e, i, and pi. Unfortunately, students usually don’t get a glimpse of real mathematics until late in their college careers – long past the point at which most students stop taking math courses. In this talk, we’ll attempt to uncover what it is that mathematicians really do.