The “Friday Afternoon Mathematics Undergraduate Seminar” (FAMUS) is a weekly event consisting of announcements, talks, and faculty interviews. FAMUS takes place most Fridays at 3:00-4:00pm in Room 164 of the Adel Mathematics Building. Typically the first half of FAMUS consists of a talk on a mathematical topic while an interview of a faculty member takes place in the second half. While Jeff Rushall is on sabbatical in Portugal, FAMUS is hosted by Dana C. Ernst.

Come join us for some entertaining talks! Refreshments always served.

Note that talks are listed in reverse chronological order.

**Date:** December 4, 2015

**Speaker:** Dana C. Ernst (NAU)

**Abstract:** In the episode “The Prisoner of Benda” of the television show Futurama, Professor Farnsworth and Amy create a mind-switching machine, only to afterwards realize that when two people have switched minds, they can never switch back with each other. Throughout the episode, the Professor, with the help of the Globetrotters, try to find a way to solve the problem using two or more additional bodies. The solution to this problem is now called the Futurama Theorem, and is a real-life mathematical theorem, invented by Futurama writer Ken Keeler, who holds a PhD in applied mathematics. In this talk, we will introduce the mathematics behind the Futurama Theorem and present its proof. [PDF of Flyer] [Slides]

**Date:** November 20, 2015

**Speaker and Guest:** Dr. Todd Wolford (NAU)

**Abstract:** We will look at the effect of applying an Iterated function system to geometric figures in $\mathbb{R}^n$. We will begin by looking at the results that can be achieved by applying a couple of linear functions repeatedly to a line segment in $\mathbb{R}$. We will see that a line segment, [0,1], can be turned into the famous Cantor Set. Does the result we get depend on our choice of line segment? What happens if we apply linear functions repeatedly to 2-dimensional or 3-dimensional objects? Attend this talk if you want to see the exciting and beautiful answers. [PDF of Flyer]

**Date:** November 13, 2015

**Speaker:** Dana C. Ernst (NAU)

**Abstract:** First, the most important part: there will be pizza! In 1850, the Reverend Thomas Kirkman, posed an innocent-looking puzzle in the *Lady’s and Gentleman’s Diary*, a recreational mathematics journal:

“Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.”

Here “abreast” means “in a group,” so the girls are walking out in groups of three, and each pair of girls should only be in the same group once. It turns out that this problem is harder than it looks. Is it even possible? We will begin by tinkering with a simpler problem and then spend some time playing with Kirkman’s original problem. Time permitting, we will also discuss generalizations of the problem that form the backbone of a branch of mathematics called combinatorial design theory. [PDF of Flyer] [Slides] [Blog Post]

**Guests:** Following the talk, Dr. Derek Sonderegger will discuss the merits of pursuing a graduate degree in mathematics, statistics, or mathematics education. In addition, Dr. Sonderegger will provide some details about our graduate program. We will also have a panel of our graduate students share a little bit about their current experiences as grad students.

**Date:** November 6, 2015

**Speaker:** Dr. Bruce Bayly (University of Arizona)

**Abstract:** The power of math to solve real-world problems derives from our ability to identify basic attributes and then think rigorously about them. Practical problems of ranking sports teams or creating balloon sculpture are very different in reality, but share the property that objects and their connections are the essential concepts. We’ll look at each of these problems separately and work inward, eventually converging on the Fundamental Theorem of Linear Algebra. [PDF of Flyer]

**Date:** October 30, 2015

**Speaker:** Andrew Lebovitz (NAU)

**Abstract:** A cube starts in the following configuration. A “move” consists of picking an edge and adding 1 to each of its vertices. The goal is to make all vertices be multiples of three. Can we win this game? If we can win, what is a winning sequence of moves? If we can’t win, how can we prove that? We’ll analyze the game on Friday, and (hopefully) solve it. [PDF of Flyer]

In lieu of interviewing Andrew after his talk, we will have a Halloween costume contest. So, come wearing your best costume. (And please come even if you don’t plan on wearing a costume.)

**Date:** October 23, 2015

**Speaker and Guest:** Dr. Roy St. Laurent (NAU)

**Abstract:** Gambling is one of the earliest forms of human entertainment, going back over 4000 years. Interest in gambling is what prompted mathematicians in the 1600’s to develop probability as the mathematics of chance. I will talk about gambling problems, old and new, and how probability can be used to analyze chances of winning, optimal strategies to win, and other considerations. [PDF of Flyer]

**Date:** October 16, 2015

**Speaker and Guest:** Dr. Brian Beaudrie (NAU)

**Abstract:** The essence of Quantitative Literacy is to use mathematical and logical thinking in context. But sometimes that context might be difficult to grasp. We’ll spend some time discussing what Quantitative Literacy (a.k.a. Quantitative Reasoning or Numeracy) is, and its importance in today’s world; then, we’ll try a few fun problems and examples that illustrate and develop quantitative literacy. [PDF of Flyer]

**Date:** October 9, 2015

**Speaker:** Dr. Martin Flashman (Humboldt State University)

**Abstract:** Solving simple linear equations is something taught in beginning algebra, but without connection to functions or a visualization that makes sense of the process. Professor Flashman will demonstrate how mapping diagrams can be used in the study of functions, inverses, and compositions to understand symbolic manipulations visually. [PDF of Flyer]

**Host:** Ellie Kennedy (NAU)

**Guest:** Sal Vera (NAU)

**Date:** October 2, 2015

**Speaker:** Dr. Terry Blows (NAU)

**Abstract:** Research in applied mathematics often connects to differential equations, but this is not a good topic for undergraduate research as a graduate course in this topic is often a prerequisite. But differential equations has a close relation in discrete dynamical systems, which in one-dimension has the form $x(n+1)=f(x(n))$. Start at $x(0)$, apply a rule to get $x(1)$, apply the same rule to get $x(2)$, etc. What happens in the limit as $n$ tends to infinity? Bring your calculator. [PDF of Flyer]

**Guest:** Ellie Kennedy (NAU)

**Date:** September 25, 2015

**Speaker:** Dustin Story (NAU)

**Abstract:** In this episode of FAMUS, Dustin Story will discuss the work he did during his summer REU (Research Experience for Undergraduates). Here are the details. Capturing the effects of absorption and scattering on light passing through a medium has various applications in areas such as biomedical optics, atmospheric sciences, and several other areas of physics. We study these effects, first using the Kubelka-Munk equations, and later using the radiative transfer equation. To find solutions to these equations, we study the associated generalized eigenvalue problems by taking advantage of several inherent symmetries. The symmetries are first established by analyzing the Kubelka-Munk system. Later, we establish these symmetries and apply them to find numerical solutions to the radiative transfer equation using the discrete ordinate method. The solutions to these models lay the ground work for posing and solving related inverse problems. Optimization and root finding techniques are applied to approximate solutions for most inverse problems except in special cases where analytical approximations are available. These solutions are extended to solve similar inverse problems in the field of medical imaging. [PDF of Flyer]

**Date:** September 18, 2015

**Speaker:** Dana C. Ernst (NAU)

**Abstract:** In this FAMUS talk, we’ll explore several cool mathematical theorems from a visual perspective. [PDF of Flyer] [Slides]

**Guest:** Dr. John Hagood (NAU)

**Date:** September 11, 2015

**Speaker:** Dana C. Ernst (NAU)

**Abstract:** The Friendship Paradox is the observation that your friends, on average, have more friends than you do. This phenomenon, which was first observed by the sociologist Scott L. Feld in 1991, is mathematically provable. In this episode of FAMUS, we will discuss the “paradox”, sketch its proof, and explore some applications. The idea for the talk was inspired by a post by Richard Green on Google+. [PDF of Flyer] [Slides]

**Guest:** Dr. John Neuberger (NAU)