Mathematics

With Dr. Casey Schine, Postdoctoral Research Associate, Biology

Presented by Richard Single, University of Vermont

Women in Data Science (WiDS) Middlebury aims to celebrate the participation of women in data science and to feature outstanding women doing outstanding work in the field. Come listen to mini research talks by Middlebury professors, and be inspired by our keynote speaker Professor Kaitlyn Cook, a biostatistician from Smith College. All students, faculty, and staff are encouraged to attend! Lights snacks and refreshments will be provided.

Bell numbers count the number of ways that n objects can be sorted into any number of buckets. They were studied and named after Scottish-American mathematician E.T. Bell who wrote about them in the 1930’s, but their study actually dates back much further. We will introduce the topic from scratch, investigate some of its interesting properties, learn more about the intriguing character E.T. Bell, and delve deeper into the history of Bell numbers and their connection to Russian dolls and to an ancient Japanese incense game!

Interested in taking a Math or Stats course in Fall 2025? Join the Math & Stats faculty over dessert to learn about course offerings for the upcoming semester, receive information about the different majors we offer, or celebrate taking your last Math or Stats course at Middlebury. Anyone who is currently taking or wants to take a course in the department is welcome!

Are you interested in taking some Mathematics or Statistics courses next semester? Are you currently taking a Math or Stats class? Do you have a sweet tooth?

Join the Math & Stats faculty over dessert and learn about their Spring 2025 course offerings! This is a great opportunity to get more information about the different majors and minor, receive advice on planning a course of study that aligns with your dream Middlebury experience, and chat with students currently enrolled in Math and Stats courses.

We hope to see you there!

Are you interested in taking some Mathematics or Statistics courses next semester? Are you currently taking a Math or Stats class? Do you have a sweet tooth?

Join the Math & Stats faculty over dessert and learn about their Spring 2025 course offerings! This is a great opportunity to get more information about the different majors and minor, receive advice on planning a course of study that aligns with your dream Middlebury experience, and chat with students currently enrolled in Math and Stats courses.

We hope to see you there!

Along with geometry, number theory is one of the oldest and most revered areas of mathematics. Topics that are often studied in an elementary number theory course include triangular numbers, squares, and the Fibonacci sequence. Later topics include continued fractions and a class of equations called Pell’s equation.

The classical Möbius inversion formula was introduced to number theory in 1832 by August Ferdinand Möbius. It relates two arithmetic functions (e.g., Euler’s Phi function) in terms of sums over divisors of a given integer. In 1962, Gian-Carlo Rota introduced a vast generalization of this idea for functions defined over partially ordered sets (posets). Rota applied his generalized Möbius inversion formula to numerous problems in combinatorics.

In order to learn about broad scale ecological patterns, data from large-scale surveys must allow us to either estimate the correlations between the environment and an outcome and/or accurately predict ecological patterns. An important part of data collection is the sampling effort used to collect observations. Through simulations and an application using Forest Inventory Analysis data, we will see if and how sampling effort affects statistical inference and predictions under simple modeling assumptions.