This semester I am in charge of organizing our Friday Afternoon Mathematics Undergraduate Seminar (FAMUS). As the title suggests, the seminar is aimed at undergraduates and happens on Friday afternoons. You might be surprised to hear that we usually pack the room every week…on Friday afternoons!!! Typically the first half (30 minutes) of FAMUS consists of a talk on a mathematical topic while an interview of a faculty member takes place in the second half.

I usually give a couple talks in FAMUS each semester, but this year I’m also responsible for all the logistics while the usual host (Jeff Rushall) is on sabbatical in Portugal.

Yesterday kicked off the first FAMUS of the semester and we had close to 60 students and faculty in attendance. It was definitely the biggest turnout that I’ve seen at FAMUS. Hopefully, we keep them coming. The talk was given by me and the topic was the Friendship Paradox. The idea for the talk was inspired by a post by Richard Green on Google+. Richard has lots of great posts on Google+ on a variety of mathematical topics and I’ll definitely be mining his posts for more ideas for talks.

The official title of the talk was “The Friendship Paradox: Your friends, on average, have more friends than you do” and here is the 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.

Here are the slides for the talk:

A lot of the content of my slides came directly from the article Friends You Can Count On by Stephen Strogatz at NY Times Opinator. I also relied on the Wikipedia article on the Friendship Paradox, which contains a sketch of the proof of the paradox. I also took some ideas and used a figure from the article The Majority Illusion in Social Networks by Lerman, Yan, Wu.

The faculty guest this week was John Neuberger. I really enjoyed interviewing John and I think the audience found it pretty entertaining.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 226: Discrete Math
  MAT 690: CGT

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Land Acknowledgement

  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.