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:** April 7, 2017

**Speakers:** Faculty who want to mentor undergraduate research

**Abstract:** The structure of this particular FAMUS is nonstandard: we will see 7-10 short (circa 5 minutes) math “infomercials,” one each from the following faculty (or surrogates):

- Nandor Sieben
- Shannon Guerrero
- Roy St. Laurent
- John Neuberger
- Jim Swift
- Dana Ernst
- Jeff Rushall
- and possibly more

The theme of these short presentations is simple: they will each be a version of “I want to do undergrad research next year, here are the problems I want to investigate, and here are the qualifications I seek in prospective students.” [PDF of Flyer]

**Date:** March 24, 2017

**Speaker:** Pauline Gonzalez (undergraduate at NAU)

**Abstract:** The talk, Pauline will be reporting on an undergraduate research project she has been working on with fellow undergraduate Ryan Wood. The project has involved building matrices using something like the Legendre symbol from MAT 318.

After the talk, instead of a faculty interview, we will continue enjoying our refreshments–namely, some hors d’oeuvres–namely, cheese and crackers–and talk about the upcoming SUnMaRC undergraduate mathematics conference, which happens here at NAU the weekend of March 31-April 2. There will be no faculty member interview this week. [PDF of Flyer]

**Date:** March 3, 2017

**Speaker:** Jeff Rushall (NAU)

**Abstract:** In this presentation I will do four things:

- Define a Hadamard matrix (they are special matrices featuring ONLY 1 or -1 for entries) and explain why are they interesting and important.
- Talk about generalizations of Hadamard matrices (nothing to be scared about).
- Discuss some undergrad research students who have worked with me in the past on some unsolved questions about Hadamard matrices, as well as where those students are now.
- Finally, I will show some new unsolved problems that I would like to work on with undergrads next year.

So this FAMUS is like an infomercial. Who is interested in doing undergrad research next year? Students who are interested in doing undergrad research should come to FAMUS. And those who aren’t should come to FAMUS anyway. [PDF of Flyer]

The faculty guest-to-be-interviewed is Ben Lantz.

**Date:** February 24, 2017

**Speaker:** Jeff Rushall (NAU)

**Abstract:** Last week at FAMUS we saw a presentation on non-Euclidean space-time modeling, and aside from all the neat and weird geometry and complex numbers and so forth, it occurred to me that the very basics associated with all that - the measurement of space and time - are things that by themselves are tricky to define. So this FAMUS will try to explain how we measure things. Minimal math, lots of history, good stories: it’s a great way to end the week. [PDF of Flyer]

The faculty guest-to-be-interviewed is Sal Vera.

**Date:** February 17, 2017

**Speaker:** Etude Oneel-Judy (undergraduate at NAU)

**Abstract:** Etude will be explaining the role that non-Euclidean geometry plays in helping to understand 21st century physics, most notably some of the work of Einstein. The talk assumes no prior knowledge of non-Euclidean geometry or modeling or even of physics. Etude has also promised to provide some 3D printing prizes to those lucky enough to attend! [PDF of Flyer]

**Date:** February 10, 2017

**Speaker:** Amy Rushall (NAU)

**Abstract:** This talk will be given by the faculty representative who attended the conference, along with lots of input from the 4 students who also attended the conference. What the conference is, why it is, who the 4 students were who attended the conference, and the impact it has on those who attend will be among the discussion topics. [PDF of Flyer]

The faculty guest-to-be-interviewed is also Amy Rushall.

**Date:** February 3, 2017

**Speaker:** Jeff Rushall (NAU)

**Abstract:** Some social scientists and mathematicians have investigated various kinds of privacy questions, such as:

- Where should I choose to sit in a movie theater to maximize the chance of not having someone sit in front of me?
- Where should I choose to sit in on an open-seat flight to maximize the chance of not having someone sit next to me?
- Where should I choose to sit at a multi-table banquet to minimize the chance of having strangers sit on both sides of me?

Well, as the talk title suggests, these privacy concerns have also been researched in the context of urinal privacy. Come to FAMUS to learn a bit about the history of this problem, the various ways it can be attacked, and to see LOTS of pictures and cartoons involving urinals. [PDF of Flyer]

The faculty guest-to-be-interviewed is Amy Rangel (NAU).

**Date:** January 27, 2017

**Talk 1:** Tree of Primitive Pythagorean Quadruples

**Speakers:** Marcela Gutierrez and Courtney Schmitt (undergraduates at NAU)

**Abstract:** A primitive Pythagorean triple is a 3-tuple of natural numbers sharing no nontrivial common factors that satisfies the Pythagorean Theorem. Hall (1970) and Price (2008) found distinct perfect infinite ternary trees whose vertex sets are precisely all primitive Pythagorean triples. This talk will present progress towards the construction of an infinite tree whose vertex set consist of all primitive Pythagorean quadruples, i.e., 4-tuples $(a, b, c, d)$ of natural numbers sharing no nontrivial common factors that satisfy $a^2 + b^2 + c^2 = d^2$.

**Talk 2:** A Game of Chance Inspired by Othello

**Speaker:** Alexandria Medeck (undergraduate at NAU)

**Abstract:** Inspired by the board game Othello, consider a one-player game of chance on a 4-by-8 board where the new twist on the game includes choosing your color disk, white or black, and the objective is to get four disks of the chosen color in a line. The more lines you complete, the more “money” you win. Consider a mathematical generalization, representing the game board by an r by c matrix, r< c. Each entry in the matrix is an independent Bernoulli random variable (i.e., either 1 or 0 with probability $p$ and $1−p$, respectively). The result is a random matrix. Associated with each possible matrix outcome is a score based on the number of completed vertical and diagonal lines of r ones in the matrix. My research is focused on determining the probability distribution of the score as a function of $r$ and $c$. I will present results concerning the probability structure of the game.

The faculty guest this week is Ellie Kennedy (NAU). [PDF of Flyer]