Mathematics Comps (priority given to Mathematics majors)
Chebyshev charms: orthogonal polynomials, approximation theory, and beyond
Advisor: Rafe Jones
Terms: Winter/Spring
Prerequisites: Math 321 is recommended but not required.
Fractals: The Geometry of Nature
Advisor: Sunrose Shrestha
Terms: Winter/Spring
Prerequisite: Real Analysis (Math 321)
An adventure in mathematical modeling
How should a cyclist expend or reserve effort over the course of a race? How might fish populations migrate as water temperatures rise due to climate change, and how will that affect fisheries? In what ways will the prevalence of certain spoken languages shift over the next 50 years? How should the Kenyan government best manage the Maasai Mara preserve to protect both wildlife and economic interests of the people who live near it? What shape of brownie pan will cook brownies most evenly?
What do these questions have in common? They are all recent contest problems from the Mathematical Contest in Modeling (MCM). The MCM is an annual team-based competition full of open-ended, multifaceted, messy, and endlessly engaging questions and scenarios in applied mathematics. The next MCM will take place February 1-5, 2024. This comps will focus on preparing for and participating in this contest. We’ll study problems and solutions from previous years, acquire and employ various tools of applied mathematics, and run a mock contest before jumping into the real MCM 2024. Our goal here is to learn lots and enjoy our time training and competing with teammates, not to achieve a certain ranking or result. After the contest, we’ll reflect on the experience and polish our contest solutions as time allows.
Note: This is a Large Group Comps which will enroll 9-12 students and has a different structure from regular Group Comps. The main difference is that you will enroll in a 6-credit seminar course in the Fall that will meet on a regular course schedule with the full group of 9-12 students. In Winter you will enroll in the usual 3 credit comps, and we will form smaller groups that will meet with me individually while preparing for the MCM.
Advisor: Rob Thompson
Terms: Fall/Winter
Prerequisite: None
Primes and Quadratic Forms
Advisor: Caroline Turnage-Butterbaugh
Terms: Fall/Winter
Prerequisites: Math 342 (required), Math 282 (helpful but not required)
Statistics Comps (priority given to Statistics majors)
Incorporation of Nonspatial Policing Information into Spatial Models
Excessive use of force by police presents an urgent problem of concern to sociologists, statisticians, policymakers, and the general public. Transparency and accountability are being demanded of police departments on a national level. Specifically, there is a call to make detailed policing data publicly available and transparent. At the foundation of this call is an effort to provide oversight for police actions (Greene 2007) and generate data-driven ideas for police reform. There is currently a lack of transparency and reproducibility, even though these are demanded and we also see an increase in demands for a national reporting system surface (Klinger 2016).
Nonspatial information is an increasingly common and requested element of policing datasets. For this project, we will primarily focus on use of force incidents as policing “event” outcomes. Nonspatial variables with use of force data often include information about the people involved in a use of force incident (such as age, gender, race, or officer tenure) or the event itself (such as the type of force used by an officer or if there was an injury). Nonspatial variables vary widely across different data sources with key distinctions, such as reporting sources, available variables, geographic identifiers, and accessibility options. There is currently no repository that hosts a comprehensive list of these datasets, with descriptive information about each dataset’s contents and quality.
There are many goals of the proposed project. The first is to gain data science skills through the processing of datasets from many jurisdictions and comparison of nonspatial information available across those jurisdictions. The second is to provide comprehensive visualization and quality analysis of the police use of force datasets across numerous jurisdictions. Lastly, the project will focus on methods from spatial statistics when analyzing these datasets. We will conduct preliminary point process model checking and exploratory data analysis across selected jurisdictions. The core statistical component of the project will consist of a review of statistical methods to incorporate nonspatial information into spatial models. We will compare existing methods to draw preliminary conclusions about the relationship between police use of force events and neighborhood/nonspatial information. Time allowing, we may also work with a community partner in Minneapolis to understand questions they have about nonspatial information related to police use of force and how their community is being policed. There is exciting potential for this project to contribute to policing and statistics, as these datasets have not been explored and synthesized simultaneously.
References:
Jack R Greene. Make police oversight independent and transparent. Criminology & Pub. Pol’y, 6:747, 2007.
David Klinger, Richard Rosenfeld, Daniel Isom, and Michael Deckard. Race, crime, and the micro-ecology of deadly force. Criminology & Public Policy, 15(1):193-222, 2016.
CampaignZero. #8cantwait, October 2020. URL https://8cantwait.org.
Advisor: Claire Kelling
Terms: Fall/Winter
Prerequisite: Stat 230 and Stat 250 (required); Stat 220 (preferred but not required)
Statistical Methods for Tail Events
Advisor: Andy Poppick
Terms: Winter/Spring
Prerequisites: Stat 230 and 250