Mathematics Comps (priority given to Mathematics majors)
Applications of persistent homology
Advisor: Claudio Gómez-Gonzáles
Terms: Winter/Spring
Prerequisite: Math 342; Math 352 and Math 354 would be nice but are definitely not required. Note that I will be teaching Math 352 in the Winter, so this could make a nice co-requisite. Coding experience is great!
Designing Lessons to Teach Algebra Though Applications
Middle and High School students have difficulty learning Algebra, in part because they don’t see the connections between algebra concepts and future careers. Without seeing why they should care, they lack the passion to persevere when the work gets challenging. We will look at the requisite skills for success in Algebra listed in something like Amanda Vanderheyden’s Spring Math skills progression. Then, with those in mind, we will devise lesson plans rooted in a variety of careers that highlight and practice one or more of the skills students need to learn. By the end of comps, we will have a large collection of such lesson plans, cross-listed by algebra skills used, and make them available to middle and high school teachers.
Advisor: Deanna Haunsperger
Terms: Fall/Winter
Prerequisite: None
A Guided Tour of Asymptotic Analysis and Perturbation Methods
A directed reading in asymptotic analysis and perturbation methods. Finding approximate solutions to algebraic equations via asymptotic series. Dealing with issues such as multiple time scales within differential equations and solutions rapidly changing qualitatively in between two regions (boundary layers). Applying perturbation methods to integrals and bifurcation analysis could be addressed if time allows.
Advisor: Joseph Johnson
Terms: Winter/Spring
Prerequisites: Math 241; Math 341 would be beneficial but completely optional.
Systoles in Square-tiled Surfaces
Advisor: Sunrose Shrestha
Terms: Winter/Spring
Prerequisites: Math 342. Knowledge of Math 354 is a bonus, but not required.
The Riemann zeta-function
Advisor: Caroline Turnage-Butterbaugh
Terms: Fall/Winter
Prerequisite: Math 361
Mathematics and Statistics Comps (Mathematics and Statistics majors accepted, but priority will be given to Mathematics majors.)
Mathematical modeling from bicycle races to brownie pans
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? In what ways will the prevalence of certain spoken languages shift over the next 50 years? 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 over 4 days in February 2023 (exact date not yet announced but likely Feb 17-20). This comps will focus on preparing for and participating in this contest. We’ll read outstanding solutions from previous years, acquire and employ various tools of applied mathematics, and run a mock contest or two before jumping into the real MCM 2023. 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 spend time expanding on and polishing our contest solutions.
Advisor: Rob Thompson
Terms: Fall/Winter
Prerequisite: None
Statistics Comps (priority given to Statistics majors)
Prediction in time series using machine learning techniques
Advisor: Deepak Bastola
Terms: Fall/Winter
Prerequisites: Stat 220, Stat 250, Stat 320 (would be nice but is not essential).
Spatial Open Policing Data Initiative
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 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 as calls for transparency and reproducibility increase and ideas about a national reporting system surface (Klinger 2016). Though scholars and the public are interested in answering questions related to police use of force, there is currently no clear, easily accessible, user-friendly collection of data on police use of force. Instead, these data sources exist in various formats in myriad locations.
Different data sources have 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 is also a lack of analysis of how findings from one data source compare with results from other data sources. Though there is currently a push for comprehensive reporting of police use of force against civilians [CampaignZero, 2020] that results in publicly available data, the cities that are undertaking this task are each collecting and publicizing data in a different way. As such, it is unclear what the standard is for these datasets, what the content and quality are of each of the datasets, and how results vary based on differences in data collection. Understanding the benefits and drawbacks of each dataset and triangulating results among different data sources is crucial to get a more accurate picture of police use of force dynamics. Researchers can only achieve this goal if they know what data are available and can evaluate the quality and contents of the data.
There are many goals of the proposed project, which will build off of preliminary data collections that has already been completed. The first is to gain data science skills through the processing of datasets from many jurisdictions. This will involve analysis of missingness patterns and processing of text fields related to the level of force used and the disposition of those involved in use of force incidents. Text matching will be helpful when comparing text fields across jurisdictions. The second is to provide comprehensive visualization of the police use of force datasets across numerous jurisdictions. Next, we will compare what information is available across cities. 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. Time permitting, we will fit nonhomogeneous Poisson process models and more complex Bayesian models, when applicable, to draw preliminary conclusions about the relationship between police use of force events and neighborhood/event-level information. We may explore methods to compare point processes across spatial windows, especially regression coefficients and covariance parameters when some information is missing. There is exciting potential for this project to contribute to policing and statistics, as these datasets have not been explored and synthesized simultaneously.
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: Winter/Spring
Prerequisites: Stat 230, Stat 250, Stat 220 preferred
Classification models for statistical graphics
Advisor: Adam Loy
Terms: Winter/Spring
Prerequisites: Stat 230 and Stat 250, Stat 220 preferred
Modeling animal abundance using removal models
Advisor: Katie St. Clair
Terms: Fall/Winter
Prerequisites: Stat 230 and Stat 250. Suggested but not essential: Stat 260 or Stat 340