Student Colloquium talk by Professor Chris Johnson, Bucknell University

**Abstract: ** The Prussian city of Königsberg once contained four land masses connected by a series of bridges, and citizens of the city would sometimes ponder the following simple puzzle: is it possible to walk through the city crossing each bridge exactly once? In analyzing this question, Leonhard Euler noted that the most important feature was how the bridges connected the land masses to one another. Understanding “connectedness” is one part of a branch of mathematics called topology, and in this talk I will give an overview of a few particular topological ideas. Beginning with Euler’s nearly 300 year old analysis of the bridges of Königsberg puzzle and ending with some recent developments concerning the shape of a data set, we will see that topological tools can have surprising applications.

**Speakers**:

Hannah Bokma ’20 – teaching intern, Breakthrough Houston

Elise Covert ’20 – data analytics, American Institute for Research

Mady Lawrence ’21 – data analytics, Highmark Health

Phil Thompson ’20 – financial sales and business development intern, IHS Market

**Abstract**: There are many exciting summer opportunities for students in the mathematical sciences! These range from internships in financial companies to research experiences at other universities to leadership development programs. In this week’s colloquium, a panel of your peers will tell you their experiences. What did they enjoy about their experiences? When did they apply? There will also be ample time for questions and answers. These varied opportunities, as well as being terrific fun, are also immensely valuable as you begin to think about your careers after Bucknell.

Student Colloquium talk by Professor Krishnan (Ravi) Shankar, University of Oklahoma

**Title: ** Archimedes’ Cattle Problem

**Abstract: ** Back in antiquity Archimedes devised a mathematical problem in the form of 22 elegiac couplets and delivered them to Eratosthenes of Cyrene (as a challenge of sorts). The problem is in three parts of increasing difficulty and the solution is rather astonishing, both for its complexity and for the problem’s ability to anticipate mathematics that didn’t come about for 2000 years (Pell’s equation). We will explore the problem and its solution (which was only completely solved in 1889 by Amthor) and ask ourselves the age old question: “What did Archimedes know?”

*Panelists:*

- Allison Gibson ‘13, Consultant, Boston Consulting Group; MBA Graduate 2019, Kellogg School of Management, Northwestern University
- Rachel Guen ‘19, Associate Analyst, Moody’s Investors Service
- Zach Moon, ASA ‘16, Actuarial Advisor, Cigna
- Jin On ’12, Manager, Data Science & Provider Analytics, Evariant
- Laura Papili ‘17, Forecast Analyst, Nielsen BASES

Moderated by Professor Linda Smolka, Mathematics

]]>Student Colloquium talk by Professor Kari Lock Morgan, Penn State University

**Title: **Understanding Statistical Significance

**Abstract: ** You may or may not have heard of results being “statistically significant,” and you may or may not know that results qualify as statistically significant if the p-value falls below a given threshold. Regardless of whether these phrases currently hold any meaning for you, the goal of this talk will be to shed light on the actual meaning of a p-value and statistical significance (beyond just “p < 0.05”). This will be accomplished by covering a modern and computationally intensive way of computing a p-value that will be illustrated both by hands-on and online activities (so bring a laptop or tablet if you want to play along!). This simulation-based approach will be both accessible to those who have never taken any statistics, and valuable to those who have taken statistics but want a deeper understanding or a more modern approach.

**Title: **Interacting with the Shadow of Data

**Abstract: ** In our first statistics class, we learn how to build a scatterplot to visualize two variables at once. But what happens when we have *many* variables? Projection methods such as Principal Component Analysis (PCA) can create 2D pictures of higher-dimensional data, much like how the sun projects our 3D body into a 2D shadow. However, exploring these high-dimensional datasets can be complicated. In this talk, we present a visual analytics model that allows the user to combine their personal knowledge with a projection method to find novel ways of exploring the data.

Yili Wang ’21, an applied mathematical sciences and computer science major from Sichuan, China, sees connections between the passions for music and mathematics that she’s pursuing at Bucknell.

]]>Student Colloquium talk by Professor Patrick McDonald, New College of Florida

**Title: **Problems and Pipelines: A story from the frontline of data science

**Abstract: **Suppose you were to suddenly obtain access to a remarkably rich data source, say, a trove of health records. What would you do? In this talk I will sketch how a group at New College handled such a situation. In so doing I will provide you with a glimpse of what it is like to work on a large-scale data science project, paying special attention to the vast array of required skill sets, social constraints and behavior patterns.

**Title: **The Dynamics of Continued Fractions

**Abstract: **While only rational numbers have a fraction representation, all real numbers have a *continued *fraction representation. Continued fractions illuminate interesting structure in real numbers, for example, by giving a way to express how close a real number is to being rational. In this talk, we investigate continued fractions from the point of view of a dynamicist, framing the topic in terms of iterating a function and asking questions about how orbits distribute. Multiple flavors of π will be present, and the golden ratio will make approximately 1.618 appearances.