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. FAMUS is hosted by Jeff Rushall.

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

Note that talks are listed in reverse chronological order.

**Date:** Friday, May 3

**Speakers:** Jeff Rushall (NAU)

**Abstract:** I will be talking about this weird equation:
\[
1 + 2 + 3 + 4 + \cdots= -1/12
\]
This looks impossible - but is it? I’ll show why it might be true, and then open the floor for arguments.

The faculty guest is John Hagood. [PDF of Flyer]

**Date:** Friday, April 19

**Speakers:** Sudipta Mallik (NAU)

**Abstract:** I attended ICM 2018 (International Congress of Mathematicians) in Rio de Janeiro, Brazil. ICM happens every four years; among other things, it is where Fields medals are awarded. There were also interesting talks and events. I will share my experiences, stories, pictures, videos of ICM and Rio.

The faculty guest is Matt Fahy. [PDF of Flyer]

**Date:** Friday, April 12

**Speakers:** Luis Diaz and Jake Heneman (undergraduates at NAU)

**Abstract:** The Othello Bonus Game is played on a $6\times 6$ board consisting of a square of black disks, surrounded by a ring of white disks, surrounded by an outer ring of playable (blank) spaces. The game is played by randomly placing a black disk in a playable space and flipping white disks ‘sandwiched’ between black disks (as in Othello). The game terminates when placement of a black disk does not flip any white disks. The score is the total number of black disks on the board. In this project, we generalize the game to an $n\times n$ board. We determine properties of this game including: classification of initial playable spaces, all achievable scores, and the probability distribution of scores by enumeration and simulation.

The faculty guest is Roy St. Laurent. [PDF of Flyer]

**Date:** Friday, April 5

**Speakers:** Kaitlyn Lee and Mason Sargent (undergraduates at NAU)

**Abstract:** The speakers this week are Kaitlyn Lee and Mason Sargent, fellow undergrads here at NAU. They have been working on an undergraduate research project that has shown how to modify an existing algorithm for building classic Hadamard matrices to instead create complex Hadamard matrices. That might not sound sexy, but complex Hadamard matrices are used to build quantum computers. Is that awesome or what?

The “faculty guests” will be 2-4 current graduate students here at NAU who will regale those present with tales of how amazing it is be a graduate student in our department. [PDF of Flyer]

**Date:** Friday, March 29

**Speaker:** Robert Buscaglia (NAU)

**Abstract:** The study of stochastic processes allows one to describe random events through mathematical objects. Stochastic processes can be used to study systems that change randomly over time, and have become common place in the investigation of biology, chemistry, and engineering. The board game Chutes and Ladders will be explored as a random processes on a closed system. By considering the movement along the board as a finite discrete-time Markov chain, stochastic models are prepared to evaluate the expectation of winning from every spot. Several sub-games will be explored: games that contain only Chutes, which push a player back down the board. Games including only Ladders, which allow for one to move forward. A third sub-game combining Chutes and Ladders is explored to evaluate how expectation changes with board size, placement of chutes, placement of ladders, the size of the dice, and the position on the board. Simulations for the different sub-games will be run during the presentation to demonstrate how stochastic processes can be studied through the use of computational methods. Finally, a logistic growth model will be used to compose a mathematical expressions for the expected numbers of turns needed to win a game from any spot. These concepts will then be extended to describe the original game of Chutes and Ladders. The agreement between simulations and the theoretical composition will be discussed. Additional open problems involving the design of specific games will be provided.

The faculty guest is Amy Rangel. [PDF of Flyer]

**Date:** Friday, March 8

**Speaker:** Kurt Herzinger (US Air Force Academy)

**Abstract:** We will have 30-minute talk by Dr. Kurt Herzinger, who will discuss a fun problem called “Sylver Coinage.” Sylver Coinage is a game played with whole numbers; it is simple to explain, but devilishly difficult to analyze. It will also be fun to see how Dr. Herzinger gives his talk, since he will not be in Flagstaff tomorrow. But technology is magical!

After the talk, all present are invited to stay and FINALLY/HOPEFULLY finish the gigantic “Menger Sponge” project from last year. To entice you to participate, all present will be fed pizza, courtesy of the math club and a few faculty members. [PDF of Flyer]

**Date:** Friday, March 1

**Abstract:** After brief announcements, we will have a few short presentations by faculty members on potential undergraduate research projects for the upcoming 2019-2020 academic year. The faculty who will present - or will have surrogates present for them - include:

- Dana Ernst
- Nandor Sieben
- Bahattin Yildiz
- Jeff Rushall
- Roy St. Laurent
- Michael Falk

Many of the faculty will stick around to discuss said projects, so there will be no faculty interview. [PDF of Flyer]

**Date:** Friday, February 15

**Speaker:** Jeff Rushall (NAU)

**Abstract:** The 10958 problem is simple to state: using each of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 in that order, can you “build” 10,958 using simple operations like addition, subtraction, multiplication, division, etc? You can insert parenthesis wherever you like. So some possibilities are $(1+2+3)^4 +(5\cdot 6)-7 +(8\cdot 9)$ or $(1+2+3+4)/5 + (6\cdot 7+8)^9$. Hint: neither of those simplify to 10,958. Can you solve this puzzle? Come to FAMUS and see if a solution exists.

The faculty guest is Tyler Brock. [PDF of Flyer]

**Date:** Friday, February 8

**Speaker:** Jeff Rushall (NAU)

**Abstract:** A magic square is an $n\times n$ grid filled with the integers $1, 2, 3,\ldots, n^2$ such that each row, column and diagonal sum is the same. How are they built? Do they exist for every possible size? How many distinct magic squares of a given size exist? Do 3D versions of magic squares exist? The list of questions about them goes on and on - but this talk will only last about 30 minutes.

At least 3 faculty in the math department have birthdays this week: Katie Louchart, Jeff Rushall, and Dana Ernst. In lieu of a faculty interview, we will sing happy birthday and serve birthday cake. [PDF of Flyer]

**Date:** Friday, February 1

**Speakers:** Stephanie McCoy, Adeline Moll, Rebecca Broschat, & Alyssa Stenberg

**Abstract:** We will have a single talk, featuring undergraduate math majors Stephanie McCoy, Adeline Moll, Rebecca Broschat and Alyssa Stenberg; the presentation is a description of their experiences attending last week’s Nebraska Conference for Undergraduate Women in Mathematics. There will a combination of pictures and stories from the conference. Two subthemes of this FAMUS are “How does a person get involved in undergraduate research? And how does one attend a math conference?” Throughout the presentation, questions and inquiries are welcome, especially from undergrads who might be curious about pursuing undergrad research in mathematics, and ESPECIALLY especially from female math majors who might be curious about pursuing undergrad research in mathematics. [PDF of Flyer]

**Date:** Friday, January 25

**Speakers:** Dana Ernst and some current NAU graduate students

We will have a single talk, given by Dana Ernst, that advertises our graduate programs in mathematics, mathematics education and statistics. We will hear testimonials, from a smattering of current and former NAU grad students, on how fun and challenging and rewarding (FREE PIZZA) our graduate programs are. We will EAT PIZZA. FREE PIZZA. Pizza paid for BY THE DEPARTMENT. Pizza paid for by faculty who REALLY WANT our students to think about pursuing graduate work in our department. [PDF of Flyer]

**Date:** Friday, January 18

The speakers are the undergraduate math majors who will be attending and presenting at the upcoming Nebraska Conference for Undergraduate Women in Mathematics. Below are the speakers/titles/abstracts.

**Speakers:** Alyssa Stenberg and Rebecca Broschat

**Abstract:** Given a set $S = {a_1, a_2, \ldots , a_n}$ of relatively prime positive integers, the $k$th Frobenius number, $g_k(S)$, is the largest natural number that can be expressed as a linear combination of ${a_1, a_2, \ldots , a_n}$ over the nonnegative integers in precisely $k$ distinct ways. We will present new results on computing $g_k(S)$ by computing integer lattice points inside an associated $n − 1$ dimensional polytope.

**Speaker:** Stephanie McCoy

**Abstract:** We study a game where two players take turns choosing elements from a fixed finite set of points in R^n until the convex hull of the jointly selected elements contains all the points of a given winning set. The winner of the game is the last player who was able to make a move. We determine the nim number of these games for several configurations of points, including one-dimensional games and all games with a winning set consisting of vertex points. This allows us to determine the outcome and the optimal strategy of these games.

**Speaker:** Adeline Moll

**Abstract:** In the game Misere Switch without Elimination, we start with a graph whose vertices are initially colored green. On each turn, the designated player selects a single vertex that is either green or yellow and colors it red. Additionally, if a green vertex is connected by an edge to at least two red vertices, it will then be colored yellow. A player loses if they make a move that results in the graph no longer having any green vertices. We will discuss this and other variations of Switch, and reveal winning secrets.