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, December 2
Speaker: Jeff Rushall (NAU)
Abstract: Here’s the situation: when you flip a fair coin, most people think the probability of getting heads is 1/2. But a very strong argument has been made by some very smart people that the probability is actually 1/3. The Sleeping Beauty Problem is a puzzle that might lead some of you to conclude that the probability really IS 1/3. Wanna learn what the controversy is all about? Come to FAMUS and see!
The “faculty guest” will be a small subset of department faculty who will argue the merits of both sides of this Sleeping Beauty Problem paradox. I will umpire the debate: verbal punches may be thrown but no fisticuffs will be allowed. [PDF of Flyer]
Date: Friday, November 19
Speaker: Levi Heath (University of Nebraska-Lincoln)
Abstract: In his PhD thesis, Maxim Kontsevich used geometry to prove a conjecture in theoretical physics. His work also answered another outstanding question that eluded mathematicians for centuries. We will introduce this question, which involves counting geometric objects, and present Kontsevich’s solution.
Levi will also be the “faculty guest,” for which he has prepared a slide presentation. Here are his title and abstract for this second portion of FAMUS:
Title: NAU to PhD
Abstract: In the second part of the seminar, I will talk about my journey to become a PhD in Mathematics. My story is not a guidebook by any means; however, I will offer some advice and discuss some of things you do and don’t need to go to graduate school. I will also share plenty of photos…one of which may depict an injury I sustained while attending an undergraduate math conference. [PDF of Flyer]
Date: Friday, November 4
Speaker: Jeff Rushall (NAU)
Abstract: The Monty Hall Problem is a classic probability controversy associated with the TV game show “Let’s Make a Deal” and its host Monty Hall. Monty would let a contestant choose one of 3 doors; behind one of the doors was a great prize (big trip, new car, etc.) and behind the other 2 doors were not so great prizes. After the contestant chose a door, Monty would open one door, which would always reveal one of the lesser prizes, and then give the contestant the option of keeping their original choice or switching choices. Some say the probability of winning is the same regardless of keeping or switching; others say otherwise. I’ll talk about the problem, explain how to analyze it, and show some foolish comments about the Monty Hall Problem made by several smart people, many of whom regretted their actions.
The faculty guest interviewee is Roy St. Laurent. [PDF of Flyer]
Date: Friday, October 28
Speaker: Jeff Rushall (NAU)
Abstract: The “paradox” is a gambling puzzle: it involves a relatively simple game that you’ll never see in Las Vegas because no one knows a fair way to create a wagering system for it. Sound intriguing? Bring some students to FAMUS and let them find out what all the fuss is about.
The guest interviewees are two undergraduate students, Maddy Cox and Kaylee Freudenthal, who will talk about, and answer questions about, their summer REU programs. [PDF of Flyer]
Date: Friday, October 21
Speaker: Jeff Rushall (NAU)
Abstract: This problem is a graph theory puzzle: suppose every point in the plane is given a color, subject to the simple rule that any two points in the plane that are exactly one unit apart MUST have different colors. How many colors do you need? No one knows! But there are crude upper and lower bounds on the number of colors needed. It’s a neat problem that is easy to understand and fun to think about.
The faculty guest interviewee is Ben Lucas. [PDF of Flyer]
Date: Friday, October 14
Speaker: Jeff Rushall (NAU)
Abstract: A perfect number is a positive integer equal to the sum of it’s proper positive integer divisors. Only a few are known to exist, and all of these are even. In this talk, I’ll present a short history of the search for perfect numbers, and I might even show the audience an odd perfect number. Or will I? Come and see for yourself!
The faculty guest interviewee is Ian Williams. [PDF of Flyer]
Date: Friday, October 7
Speaker: Jeff Rushall (NAU)
Abstract: The title sounds scary, but the topic boils down to this: what integer values does the expression $x^2 + y^2 + 10z^2$ take on (or NOT take on) if the variables can be any integers? Despite being a computational genius, Ramanujan wasn’t sure about the answer to that question, which remains open to this day. In addition to presenting this fun puzzle, I get to discuss the life of Ramanujan, which never ceases to be entertaining.
The faculty guest interviewee is Dana Ernst. [PDF of Flyer]
Date: Friday, September 30
Speaker: Jeff Rushall (NAU)
Abstract: Graph labeling is a fun game played on graphs: given a specific kind of graph, and given a set of labeling rules, find a way to label the vertices and/or the edges of the graph that obeys the given rules. Some known theorems and known open problems will be presented.
The faculty guest interviewee is new faculty member Hannah Prawzinsky. [PDF of Flyer]
Date: Friday, September 23
Speaker: Jeff Rushall (NAU)
Abstract: The 10958 Problem involves the following puzzle: using the digits $1, 2, 3, 4, 5, 6, 7, 8$ and $9$, in that order, and using any of the standard arithmetic operations (addition, subtraction, multiplication, division, exponentiation, factorials and concatenation), what natural numbers can you build? Some answers are easy: you can build $45$ ($45 = 1+2+3+4+5+6+7+8+9$), you can build $43$ ($43 = 1^2 + 3+4+5+6+7+8+9$), and so on. Some are not so obvious, like: $10957 = (1 + 2)^(3+4) × 5 - 67 + 89$. It turns out you can build every natural number up through about $11,000$ according to these rules - except for one special integer (look closely at the talk title for a hint).
The faculty guest interviewee is Robert Buscaglia, who in addition to being interviewed will HAVE HIS HEAD SHAVEN DURING FAMUS FOR CHARITY. Others are welcome to also have their heads shaven. [PDF of Flyer]
Date: Friday, September 16
Speaker: Jeff Rushall (NAU)
Abstract: The talk topic this week is “The Happy Ending Problem,” so coined by Paul Erdos. This topic is a mix of math, tragedy, and a love story. The math revolves around a problem in planar geometry that involves convex polygons.
The faculty guest interviewee is Tyler Brock, who will answer a prearranged set of humorous questions and show humorous pictures from his past. In addition to being the first FAMUS of AY 2022-2023, both Math Club and the Putnam Exam will recruit from the students in attendance. [PDF of Flyer]