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, 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.