Title: 1+2+3+4+… = -1/12
Abstract: Infinite series. Every Calculus II student hates them; every mathematician loves them. So, why do mathematicians love infinite series? Well, ask one, and you’ll never hear the end of it… (just sum math humor).
We’ll see how two standard examples of series, the geometric series and the zeta function (p-series), lead to beautiful applications, such as in economics and signal processing. We’ll also see how even divergent series are fascinating.
Title: Wavelet-based Probit Functional Models
Abstract: Recent advances in functional regression include the development of a wide range of function-on-scalar regression models where outcome is a function of time regressed onto a set of scalar covariates. Most of these methodologies require the outcome to be normally distributed. However, very little work has been done on the case where the outcome is categorical. In this talk, we will discuss a flexible Bayesian procedure for function-on-scalar regression for categorical functional outcomes of varying levels. Simulations and data examples will be presented to illustrate the methodology.
Title: Losing Altitude: A story of airplanes, heart rate, and one “controversial” dataset
Abstract: When you ride in an airplane, the lowered pressure in the cabin causes your blood oxygen levels to decrease. If oxygen saturation levels go low enough, you may experience some interesting side effects (like temporary color blindness, for example), that much we know. What we don’t know is if there is also an impact on the functioning of the heart. Partially motivated by a rash of flight related medical case studies, a study was conducted in 2007 to more formally assess the effects of exposure to altitude on heart health while in flight. We will explore this study, the complex dataset it generated, and the “controversy” of conducting research a certain airline manufacturer would rather we not.
Title: What Did You Do Last Summer?
Moderator: Alexander Murph ’18
Presenters:
Trevor Adriaanse ’17 – Cryptanalysis & Exploitation Services Summer Program, at the NSA.
Alexander Murph ’18 – Research Apprentice for the Bucknell Geisinger Research Initiative (BGRI)
Laura Papili ’17 – Actuarial Internship at Genworth in Richmond, VA. Genworth’s Actuarial development program.
Ryan Buzzell ’17 – AEW Capital Management, L.P. (Boston Office). Real Estate Investment Firm.
Katie Lunceford ’17 – Susquehanna International Group LLP (SIG)/Statistical Options Trading/Intern – Bala Cynwyd, PA
Tung Phan ’17 – Susquehanna International Group LLP (SIG)/Statistical Options Trading/Intern – Bala Cynwyd, PA
Naba Mukhtar ’18 – REU: Partial Differential Equations and Dynamical Systems – Florida Institute of Technology
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.
Title: Investigating students’ engagement and motivation in Mathematics Class
Abstract: The National Council of Teachers of Mathematics’ Principles to Actions: Ensuring Mathematical Success for All requires that students be able to understand the material, justify responses, and determine when, how, and why a mathematical statement or rule should be used. In order to accomplish this, students need to be meaningfully motivated and engaged in learning the mathematics. Often times we characterize engagement along a continuum ranging from disengaged to highly engage. However, such characterizations may be misleading, and in some cases, counterproductive. During this session, we will explore some of the different ways in which students engage in mathematics learning, and how to support them in the process.
Title: Electoral College Math: How to Become President with 20% of the Popular Vote
Abstract: The Electoral College makes it possible to become U. S. President with less than a majority of the popular vote. In a two-candidate election, what is the minimal percentage of the popular vote possible for a winning candidate? In this talk we’ll first mimic an approach suggested by George Pólya that to find a theoretical solution. We’ll then make use of of tools not readily available to Pólya – spreadsheets and binary linear integer problem software — to see if we can improve on his results using actual presidential election data. Anyone with a vague recollection of high school algebra has the mathematical background necessary to enjoy this talk.
Title: Sequential data mining
Abstract: Data representing DNA, proteins, literature, weather, and the stock market all share one common characteristic: their data are sequential. Sequence data present some of the most challenging problems for machine learning and data mining methods. In this talk, Professor Brian King will present a generalized, probabilistic framework for modeling sequential data. He will show how he and his students have adapted this model for classification and prediction tasks, reporting results from recent studies.
Title: Being fair in a world of limited resources
Abstract: Fair division is a problem that all of us encounter regularly. Every time you and another person or several people have to divide something – pizza, money, space, Neapolitan ice cream, band width, candy, etc. – you are working on a fair-division problem. How can several people share a limited resource and make sure that no person feels the resulting allocation is unfair? Before we can answer this question, we need to figure out what exactly is means to be ‘fair’. The mathematical development of this subject is fairly recent and the results touch issues in economics and game theory. We will do lots of examples.
Title: From airlines to healthcare: scheduling services with high variability
Abstract: What do the airline and healthcare industries have in common when it comes to managing their capacity? What makes scheduling surgeries so much more difficult than an airline’s management of its seat inventory? How can hospitals improve their surgical scheduling system? While most optimization models suffer from the curse of dimensionality, simulation-based optimization is often a better choice when dealing with demand that is highly variable. Drawing from revenue management techniques developed by the airline industry, I will show how simulation modeling can help hospitals to more efficiently schedule surgical procedures, in order to better address and balance over- and under-utilization of their resources.
Title: Mock and quantum modular forms
Abstract: Mock modular forms were first formally defined in the literature by Zagier in 2007, though their roots trace back to the mock theta functions, curious power series described by Ramanujan in his last letter to Hardy in 1920. As the overarching theory of harmonic Maass forms has progressed over the last 15 years, we have seen applications of mock modular forms in number theory, combinatorics, representation theory, and more. Zagier also defined quantum modular forms in 2010, which like mock modular forms feign modularity in some way, but unlike mock modular forms are only defined on sets of rational numbers. In this talk, we will give an introduction to and brief history of these subjects. We will also discuss an application in joint work with Ken Ono (Emory) and Rob Rhoades (CCR Princeton), in which we revisit Ramanujan’s last letter and prove one of his remaining claims as a special case of a more general result.