»Æ¹ÏÊÓƵ

MA117 Elementary Probability and Statistics

Professor Minho Kim

Stewart House

6:00 - 8:30pm

Tutt Science 1st and 2nd floor atriums

2:00 - 4:00 pm 

The Method of Archimedes: An Infinitesimal Balancing Act

Archimedes is one of the greatest mathematicians to ever live. Not only was he prolific, having written twenty-six known works, but he spanned a wide breadth of mathematics with amazing results in every area he touched. If one were to ask Archimedes his greatest result, he'd likely say finding the volume of a sphere enclosed within a cylinder, with this shape purportedly having been inscribed on his gravestone. In this paper, we'll explore some Greek mathematicians preceding Archimedes, as well as Archimedes himself, setting the stage for the state of Greek mathematics at the time he was active. Along the way, we'll dispel some common myths about the history of Greek mathematics. Then, we'll examine the winding journey Greek mathematical texts took to end up in the English speaking world. We'll also see how Archimedes' work, \textit{The Method of Mechanical Theorems}, was found hidden beneath prayers in a Palestinian monastery over 2,000 years later and the undertaking of translating and preserving them. These mechanical theorems introduced a style of proof invented by Archimedes, that while revolutionary, wasn't rigorous enough for him to consider a complete proof. However, he used these results to help him develop rigorous, geometric proofs. We'll end the paper by looking at several of these mechanical theorems, as well as their geometric counterparts.

Computing the Shape of X-ray Flux Data of Solar Flares

Motivated by a strong connection between pure and applied mathematics, this project focuses on the mechanics and applications of Topological Data Analysis (TDA) to time series data of solar flares. Using publicly available data from NOAA and NASA satellites, this analysis examines the shape of X-ray flux versus time plots that exhibit spike-like behavior through a topological lens. By employing tools from TDA, most significantly persistent homology, we compute simplicial complexes and persistence diagrams of time intervals before, during, and after solar flares. After analyzing four space weather events in total, a pattern emerges: in both periods pre- and post-flare there is a lack of persisting components and notable 1-dimensional holes, while during the event there is a dramatic increase in the number of connected components that persist suggesting a very different shape for the data during the actual flare.

FeatherWeight

 The eBird Hotspot Ranker is a data-driven web application designed to help birdwatchers identify the best times and locations to observe different species by leveraging real-time citizen science data from the Cornell Lab of Ornithology’s eBird platform. The eBird website and mobile app allow users to submit and view bird observation data from designated hotspots- locations that have a high number of submitted checklists. These checklists, completed by users, document the species they observed at a specific hotspot.

The Hotspot Ranker allows users to enter a hotspot name, specify a time window, and receive ranked likelihood scores for species occurrence. These rankings are generated by calculating the weighted average of each species’ observation frequency in the total checklists submitted per week. The tool also displays pictures of the top three species and provides hyperlinks to each high-ranking bird. Finally, users can add custom species to compare the likelihood of observing those birds against any number of the top-ranked species from that hotspot. 

Modeling Quorum Sensing Dynamics Using Stochastic Differential Equations

Quorum sensing is a process of intercellular communication that enables bacteria to ascertain population density and coordinate group behaviors through the release and detection of signaling molecules, often in response to environmental stimuli. This project investigates the stochastic dynamics of quorum sensing using two non-linear models of cellular activation, each differing in the mechanism of deactivation: one assumes linear deactivation while the other incorporates non-linear dependence on signal molecule concentration. To analyze these models, I apply a Fokker-Planck framework to approximate the long-term probability distributions of the number of actively quorum sensing cells. I further estimate mean first passage times to characterize the likelihood of spontaneous switching between steady-state population sizes of quorum sensing cells. Additionally, I
calculate splitting probabilities to determine the favored steady state once the population reaches the system’s unstable equilibrium. By examining system behavior across different population scales, this research highlights how noise influences bistable quorum sensing dynamics and provides insight into the stability and robustness of collective bacterial decision-making. I conclude that noise-driven switching is unobservable in simulation in large-scale populations and the lower steady state is heavily biased by the system.

Lucky Shot? Building Models to Predict Soccer Goals

Expected Goals (xG) is a statistic that quantifies the likelihood of a shot resulting in a goal. The goal of this study is to build statistical models that have the potential to replicate professional xG models in order to better understand the models themselves and their applications. Four different methods were used to develop these models: logistic regression, Ridge regression, LASSO, and Extreme Gradient Boosting (XGBoost). Each of these methods utilizes a different approach to fitting the model. Consequently, the xG values that these methods and models generate will be slightly different, leading to a series of comparative evaluations assessing the models' performance. By comparing the developed models' xG values to professional xG values from Hudl Statsbomb, we can determine which model most closely mimics a professional model. A second comparison against the outcome of each shot leads to determinations about which model has the best predictive performance. After completing both of these evaluations, there are interesting but seemingly contradictory results. The logistic model most closely resembles the professional model, but the XGBoost model has the best predictive performance. A further analysis of the models themselves gives us some insight into what constitutes a shot with a high chance of conversion.

CICC Portfolio Platform

The »Æ¹ÏÊÓƵInvestment Club (CCIC) previously relied on Excel-based portfolio tracking hosted on OneDrive, which lacked essential security features like role-based authorization and structured historical data storage. Excel's limitations meant the club’s financial records were vulnerable to unauthorized modification, lacked analytical clarity, and needed a large amount of manual effort. To resolve their issues, we engineered a custom, free, web-based portfolio tracking platform using a modern tech stack with React, Node.js, Vercel, Render, and Turso. The system provides a centralized environment for managing holdings, featuring Colorado College's OpenID Connect system, DUO Mobile, to distinguish between Admin and Member roles, ensuring that only authorized users can execute buy/sell transactions or modify data.

The platform also allowed the club to more easily stay up-to-date on holding news by integrating real-time and historical market data through the Finnhub and YahooFinance2 APIs, allowing for overall and stock-specific news feeds. Throughout the development process, we prioritized ease of use and data integrity, including by building custom debug tools for frontend simulation, stress-testing the database to prevent duplicate entries, and implementing an automated recovery system to backfill data gaps. Deployed via Vercel and Render, the platform is designed for sustainability, granting the CCIC full ownership of its infrastructure. Future development will focus on expanding analytical depth through time-weighted return (TWR) metrics, more granular user permissions, and a collaborative group calendar to further professionalize the club's operations.

Misinformation Spread Across Complex Networks: An Epidemiological Approach

This thesis takes a Mean Field Approach (MFA) to epidemiological modeling on complex networks, with the goal of understanding misinformation spread across complex networks. We, analytically, derive and analyze SI, SIR, and SIS compartmental models on homogeneous and heterogeneous network structures.

Our central finding demonstrates that for scale-free networks with degree exponent 2 < γ < 3 the epidemic threshold becomes null, implying that any nonzero transmission rate produces endemic spread, regardless of a recovery rate.

This result offers a mathematical explanation for the observed spread of misinformation across weakly scale-free networks. We extend the analysis to correlated networks by bounding dominant eigenvalues via the Gershgorin Circle and Perron-Frobenius theorems. Although the MFA neglects stochastic fluctuations and assumes static network structure, it provides an analytic angle that might complement simulation-based approaches.

Local Heterogeneity in the Police Elasticity of Crime: A Multilevel Predictive Framework

The economic literature regarding the police elasticity of crime is vast. While this
literature produces robust estimates of causal effects, traditional methodologies do not
evaluate the predictive performance of the underlying models. From a policy perspec-
tive, the reliability of these estimates is critical. The purpose of this work is to expand
upon the estimation techniques used in Chalfin et al., 2022 to improve the predictive
performance of estimates for the marginal effect of policing on crime. To improve
predictive performance, this research proposes a multilevel mixed-effects model that
captures local heterogeneity in the police-crime relationship. Using data from 242
policing jurisdictions over 21 years, this research finds that a random-slope mixed-
effects model produces estimates for the marginal effect of policing that are both
more accurate and more stable than those from a traditional Ordinary Least Squares
approach. This research also identifies significant heterogeneity in the police-crime
relationship across local contexts, which will help to inform future causal research.

Detecting Racially Polarized Voting

This project examines how mathematical methods for estimating minority voting preferences have evolved in Voting Rights Act litigation. Because individual ballots are secret, courts must rely on aggregate data to infer voter behavior. This problem is important because such estimates provide courts with evidence of vote dilution and inform proposed remedies through redistricting. Early cases used ecological regression and method of bounds, which provided simple estimates but limited measures of uncertainty or bounds so broad as to be difficult to interpret. More recent cases also employ ecological inference methods, which use likelihood-based modeling to produce bounded estimates and explicit uncertainty intervals. By comparing these approaches, this project explains how mathematical advances have shaped the evidentiary standards and practical use of quantitative analysis in VRA cases.

A Compartmental Model for Measles Transmission Dynamics with Vaccination

This project investigates measles transmission dynamics through mathematical modeling, using an SIR-type compartmental model with vaccination. Using real-world data to paramaterize the model, quantitative analyses are conducted to identify mitigation strategies and evaluate how model paramaters impact disease spread. The findings are then transformed into evidence-based recommendations for mitigation strategies, demonstrating how mathematical modeling can be beneficial in public health decision-making.

MusicFinder Website

This project's goal was to create a proof of concept for a service that would help musicians find ensembles or bands at CC that are looking for someone of their skill set. The software achieves this through a recommendation algorithm styled loosely after the concept of a dating app.

Using Ring Theory to study Neuroscience

This talk presents an algebraic perspective on how groups of neurons represent features of a stimulus space. Starting from observed on and off firing patterns, the project asks a central question: what can we infer about receptive field organization directly from neural activity data?

Many standard topology based summaries are useful, but they can blur important details by allowing patterns that were never actually observed. This project addresses that limitation by using an algebraic framework designed to preserve the exact combinatorial structure of the neural code.

Ramsey Theory on the Integers

The basic philosophy of Ramsey theory is that ``complete disorder is impossible." This appears in sinℤ⁺  through 𝑟-colorings (partitions of ℤ⁺ into 𝑟 subsets). A set 𝙳 ⊆ ℤ⁺ is 𝑟-accessible if every such coloring contains arbitrarily long monochromatic sequences 𝑥₁,𝑥₂, ... where 𝑥ᵢ₊₁ - 𝑥ᵢ in 𝐷 for all 𝑖 ≥ 1. The degree of accessibility is the greatest 𝑟 for which this holds. Determining this value is challenging and requires constructing functions that exploit set-specific properties. Using a growth-rate-based coloring method introduced by Quester (2025), we investigate the accessibility of different sets, including powers of the integers and the Pell numbers.

Reframe Systems

Our Team partnered with Reframe Systems, a modular housing company based in Massachusetts, to develop a property visualizer designed to be used during sales pitches. The Reframe Site Configurator is a web-based visualization system that enables site-specific configuration of Reframe housing models on residential parcels. It supports Reframe’s sales and business development workflows by translating address-level location data into an interactive 3D scene that combines parcel geometry, surrounding context via Google Map-Tiles, and configurable housing layouts for a desired property in Massachusetts. Our team enjoyed exploring Three.JS, a 3D rendering framework, and all the fun vector math that comes with manipulating objects in 3D space.

Analyzing Champions League Based on Domestic League Performances

This project develops a statistical framework to analyze and predict match outcomes in the
2023/24 UEFA Champions League using team-level statistics from the previous domestic
season. By applying multinomial logistic regression and k-Nearest Neighbor (KNN), match
results are modeled as categorical outcomes using performance metrics such as shooting,
passing, defensive, possession, and league strength statistics. The regression coefficients provide
insights into how different aspects of team performance contribute to competitive advantage,
offering underlying interpretations about match dynamics. Building on individual match
outcome predictions, the framework extends to a group stage by aggregating predicted results
across all fixtures. Accumulating points based on predicted wins, draws, and losses then
determines each team’s predicted group stage standing. In addition to producing predictions, this
model highlights the uncertainty in categorical events by assigning probability distributions to
each possible result. This approach emphasizes how statistical modeling can bridge descriptive
performance data and predictive outcomes. More broadly, the framework demonstrates how
multinomial logistic regression and KNN across multiple performance metric categories can
inform outcome predictions in a structured tournament.

BellHops

The Bellhops project presents a transcript-based analytics system designed to evaluate a conversational voice AI agent used in hotel environments. The system transforms call transcripts into actionable insights by analyzing user intent, sentiment, engagement, common queries, and multilingual performance. Using transformer-based models, it enables accurate interpretation of diverse conversations. Results are displayed through an interactive dashboard built with Dash Plotly, allowing users to filter, visualize, and export data. Overall, the system provides a scalable solution for improving AI performance, enhancing customer experience, and supporting data-driven decision-making in real-world applications.

Tutt Science 122

12:15 pm

Tutt Science 215

12:15pm

Tutt Science

Pi-k, Tie-Dye with Ben Nye, Pie a Professor

1:30 - 3:30pm

The 23rd annual will take place on Saturday, February 21st at »Æ¹ÏÊÓƵin Colorado Springs, CO.

Deadline to submit an abstract: Tuesday, February 10th

Deadline to register: Wednesday, February 18th

Online mathematics exam open to all students.

1 - 5 pm

Rawles Exam history at CC

12/6 11am - 12/7 11am

Tutt Science

1:30 pm

Math&CS Lounge (2nd floor of Tutt Science) 

1:30 pm

Math&CS Lounge (2nd floor of Tutt Science) 

6:30 - 8:30 pm

2nd floor Tutt Science

1:30 - 3:00 pm, following the Homecoming Fearless Friday

1st and 2nd Floor Atriums, Tutt Science

4:00 pm

2nd floor Math & CS Lounge, Tutt Science