Comps, honors papers, and prize-winning works of the Mathematics and Statistics Department are featured here. All works have been self-submitted by the student authors. Descriptive information about each work is available to search or browse. Access to the full text of the works is limited to current Carleton affiliates with faculty permission. Learn more about how to submit your work and how to request access to the full text of works.


Submissions from 2024

Spencer Alvey, Mathematics (MATH) 2024, The Mathematics of Compressed Sensing

Aryan Arora, Mathematics (MATH) 2024, Beyond Arrow: Revealing True Preferences

Mem Awad, Mathematics (MATH) 2024, Crafting Engaging Lessons: Integrating Manipulatives and Demonstrations in High School Algebra

Thien Bui, Annelise Sokolow, and Erin Watson, Mathematics (MATH) 2024, Avoiding Atlantis's Fate

John Carragher, Statistics (STAT) 2024, An Introduction to Spatial Statistics Clustering Methods

Elena D'Avanzo, Evan Lauer, and Kenton Young, Mathematics (MATH) 2024, MCM Searching for Submersibles

Liam Etelson, Ed Dowling, and Xingyi Zhang, Mathematics (MATH) 2024, Fractals: The Attractors of Iterated Function Systems

Alejandro Gonzalez, Sophie Boileau, Hugh Shanno, Grace Hanson, and Ammy Lin, Mathematics (MATH) 2024, Binary Quadratic Forms: Properties, Groups, and Ideals

Alistair Pattison, Mathematics (MATH) 2024, An Introduction to Algebraic Number Theory

Varun Saini, Mathematics (MATH) 2024, An Introduction to the Hyperreals

Sammi Sheridan, Helen Moses, Miles Frisch, and Evan Christensen, Statistics (STAT) 2024, Incorporating Nonspatial Policing Information into Spatial Models

Submissions from 2023

Sam Hiken, Osip Surdutovich, Lee Camp, and Jimmy Lin, Mathematics (MATH) 2023, From Data to Donuts: Efficient Computation of Persistent Homology

Teagan Johnson, Elijah Jones, Samuel Koehnline Rosenberg, and Ton Meesena, Statistics (STAT) 2023, Classification Models for Statistical Graphics

Samuel Kim, Statistics (STAT) 2023, Using Statistical Classification Methods to Predict Hits Using Statcast

Bowen Li, Mathematics (MATH) 2023, Magnus's Freiheitssatz: A lively introduction to Combinatorial Group Theory

Lane Maitland, Mathematics (MATH) 2023, Error Processing for Linear Block Codes

Lane Maitland, Statistics (STAT) 2023, The Effect of Elevated Carbon Dioxide Levels on Plant Mass: A Meta-Analysis

Michaela Polley, Rachel Ziems, Riley Madsen, Isaac Fried, Tia Ahmed, Michael Dreger, Andrea Ramos, and Raine Bernhard, Mathematics (MATH) 2023, Unpacking Algebra: 98 Lessons with Applications

Sebastian Vander Ploeg Fallon, Aaron Schondorf, Thomas Zeng, and Nick Fitzhugh, Mathematics (MATH) 2023, A New Model for Random Square-Tiled Surfaces

Zhihan Yang, Mathematics (MATH) 2023, An Introduction to Markov and Hidden Markov Models with Applications

Xingyi Zhang, MurphyKate Montee, Erik Carlson, Willem Fletcher, and Chi Nguyen, Mathematics (MATH) 2024, Graphs with Many Hamiltonian Paths

Submissions from 2022

Eva C. Airoldi, Oliver A. Calder, Tom S. Patterson, Antonia L. Ritter, and Rebekah I. Stein, Mathematics (MATH) 2022, Applications of Ensemble Analysis to Gerrymandering in Minnesota and Texas

Henry Chapman, Soren DeHaan, Iain McCay, and Carl Tankersley, Mathematics (MATH) 2022, A Long and Winding Road: A Foray into Planar Metric Graphs

Mika Cooney, Ben Hafner, Shelby Johnson, and Sean Lee, Mathematics (MATH) 2022, The Effect of Habitat Fragmentation on Plant Communities in a Spatially-Implicit Grassland Model

Risa M. Fines, Mathematics (MATH) 2022, Dirichlet’s Theorem on the infinitude of primes in arithmetic progressions and the Law of Quadratic Reciprocity

Paul Hinton, Mathematics (MATH) 2022, The Rationality of Economic Discounting

Jeremiah Mackin-Alonzi, Karryn Leake, Sagal Ahmed, and Henry Farnsworth, Statistics (STAT) 2022, Survival Analysis: An Application with Censored Head and Neck Cancer Data

Jacob Martens, David Krakaur, and Bryan Boehnke, Mathematics (MATH) 2022, Seeking Lines Using Resultants and More: Statistics on Cubic Surfaces Over Finite Fields

Chi Nguyen, David Chae, John Groos, Xander Roti, and Sabrine Shanaa, Mathematics (MATH) 2022, A Modern Take on the Proof of Jacobi's Four-Square Theorem

Noah Pinkney, Shira Julie, and Elliot Heyman, Mathematics (MATH) 2022, Algebraic Topology and Discrete Morse Theory for Finite Spaces

Colette Pollard, Nathan Hayes-Rich, Dominic Enriquez, and Emily Schulenberg, Statistics (STAT) 2022, COVID-19 Incidence Rate in Minnesota: A Bayesian Spatial Analysis

Yicheng Shen, Jacob Flignor, Karen Wang, and Libby Nachreiner, Statistics (STAT) 2022, Behind the Smoke: An Extreme Value Analysis of Air Pollution in Minnesota

Conner Taylor, Mathematics (MATH) 2022, Construction and Coefficients of a Cyclotomic Polynomial

Juanito Zhang Yang and Owen Barnett, Mathematics (MATH) 2022, Introduction to Lie Algebras

Submissions from 2021

Gianmarco Bommarito, Marcella Manivel, Bo Peng, and Marguerite Shaya, Mathematics (MATH) 2021, Bernoulli Numbers and the Class Groups of Cyclotomic Fields

Travis Brown, Marko Jurkovich, Vincent Gu, and Andrew Vance, Statistics (STAT) 2021, Predicting COVID-19 Using SIR Models

Daniel Clipper, Statistics (STAT) 2021, Lighting the Lamp: Calculating Individual Contribution in Hockey

Evan Michael David, Ian Klein, Benjamin Colby Richardson, and Sameer Swarup, Mathematics (MATH) 2021, Northcott’s Theorem: An Adventure in Preperiodic Points of Rational Functions

Charles R. Grogan-Kaylor, Mathematics (MATH) 2021, Tensors, differential forms, and computer graphics

Eugenia Korobova and Matthew Zacharski, Statistics (STAT) 2021, A Network Analysis of Twitter Discourse About the Death of George Floyd

Ruofei Li, Mathematics (MATH) 2021, Hilbert Space and the Riesz Representation Theorem

ZhaoBin Li, Mathematics (MATH) 2021, Brownian Motion and Its Applications

Jaylin Lowe, Statistics (STAT) 2021, Generalized Additive Models

Pierce Gissler McDonnell and Hiromichi Ueda, Mathematics (MATH) 2021, Topology of Partially Ordered Graph Configuration Spaces

Jack L. Moran, Mathematics (MATH), Statistics (STAT) 2021, Introduction to the Simple Branching Process

Molly Potter, Statistics (STAT) 2021, Spatial Data Analysis with Applications in Epidemiology

Lucy Reece, Sophie Schafer, Muyang Shi, and Qianzi Li, Mathematics (MATH) 2021, Transient Dynamics in Ecological ODE Models: Plant Population Under Habitat Destruction

Nicholas Rosen and Will Fletcher, Mathematics (MATH) 2021, Modular Forms and Number Theory

Muyang Shi, Waleed Iftikhar, Nate Isbell, and Sarah Grier, Statistics (STAT) 2021, Quantile Regression with Applications in Agriculture and Temperature Study

Changlan Wang, Statistics (STAT) 2021, Are Personality Traits Universal? Exploration of the Cross-culture Validity of Big Five Personality Traits Using Factor Analysis

Daniel Zin, Cindy Guo, and Erika Mino, Statistics (STAT) 2021, Twitter’s Reaction to Mask Mandates: A Network Analysis

Submissions from 2020

Tyler A. Chang, Mathematics (MATH) 2020, Topology of Second Order Tensor Fields

Katie Chavez, Bryan Kim, Jay Na, Aaron Prentice, Jin Ruan, and J. Liralyn Smith, Statistics (STAT) 2020, Respondent Driven Sampling

Sam Chen, Marietta Geist, Alex Kiral, and Brody Lynch, Mathematics (MATH) 2020, Fermat's Last Theorem: Kummer's Special Case

Todd Johnson, Adam Kral, Aaron Li, and Justin Soll, Mathematics (MATH) 2020, Pathologies of the Axiom of Choice

Fares Soufan, Tenzin Kunsang, Elisa Loy, Taylor Yeracaris, and Jackie Chan, Mathematics (MATH) 2020, Guiding Mathematical Discovery: How We Started a Math Circle

Siang Wongrattanapiboon and Oscar Smith, Mathematics (MATH) 2020, Homological Algebra

Submissions from 2019

Andrew Biehl, Brianna Fitzpatrick, Dallas Keate, and Janna Wennberg, Mathematics (MATH) 2019, Number Theory Without Numbers

Sara Canilang, Ian Seong, and Nicolas Graese, Mathematics (MATH) 2019, Kuratowski Closure-Complement-Frontier Operators on Sorgenfrey and Usual Topology on a Real Line

Noah Feldman, Dylan Rye, Christian Zaytoun, and Elliot Cahn, Statistics (STAT) 2019, Ranking Rankings: Alternate Ways to Evaluate NCAA Football Teams

Pedro Girardi, Trevor Freeland, and Joseph Nardi, Statistics (STAT) 2019, A Statistical Analysis of Changes in Extreme Precipitation in the Coastal Carolinas

Noah Goldman, Mathematics (MATH) 2019, Bézout’s Theorem and Algebraic Geometry

Marshall Ma, Psychology (PSYC), Statistics (STAT) 2019, Do App-Based Mindfulness Programs Reduce Stress and Increase Well-Being?

Alief Moulana, Nupur Bindal, Tim Schoch, and Ned Wang, Mathematics (MATH) 2019, Jackknifing Biodiversity

Submissions from 2018

Ben Nealon Clark, Mathematics (MATH) 2018, "From Euclid to Poncelet: The Rulers of Geometric Constructions"

Lynn Nicole Daniel, Angel Villa, Yuhao Wan, and Maya Davis Banks, Mathematics (MATH) 2018, Recovering Edge Conductivities in Electrical Networks

Clara Overbeck Livingston, Emily Corway Kaegi, Nicholas Daniel Fredrickson, and Alana Morgan Danieu, Statistics (STAT) 2018, Survey Designs for Distance Sampling: A Study of Zebra Mussels

Martha Torstenson, Rebecca Deland, Jon Gillespie, and Killian Roberts, Mathematics (MATH) 2018, Shadows of the Cantor Set (II)

Tegan Ellen Wilson, Mathematics (MATH) 2018, Electrical Networks and Applications in Mathematical Theory

Submissions from 2017

Margaret Crenshaw, Zoe Peterson, Charlotte Mann, and Alli Domingues, Mathematics (MATH) 2017, Bar Modeling: Adventures in Algebra

Benjamin Azaria Matson, Mathematics (MATH) 2017, Shift Spaces, S-gap Shifts, and S-limited Shifts

Lianne Siegel, Melissa Bain, Il Shan Ng, and Caitlin Eichten, Mathematics (MATH) 2017, Estimating the Uncertainty in Temperature Trends Due to Internal Climate Variability

Benjamin Madisen White, Mathematics (MATH) 2017, The Distribution of the Longest Run of Heads

shun yang and liyang liu, Mathematics (MATH) 2017, Sketch of an analytic proof of the Prime Number Theorem

Submissions from 2016

Robert Lancaster Emmet, Mathematics (MATH) 2016, Empirical Bayes

Submissions from 2015

Nathan Daniel Bamberger, Devon Shipman Manber, and Nimita Iyer, Mathematics (MATH) 2015, Emergence of Synchrony in Pulse-Coupled Neurons

Larkin Hafer Flodin, Mathematics (MATH) 2015, The Unsolvability of the Word Problem

Matt Godfrey, Will Salon, Preston Carlisle, and Wenth Wang, Mathematics (MATH) 2015, Spatial Economics through a Mathematical Lens: City Structure and the Breakdown of General Equilibrium

Nami Sumida, Jordy Cammarota, Kan Wang, and John Lee, Mathematics (MATH) 2015, Measuring Fractal Sets

Zachary William Walsh, Mathematics (MATH) 2015, A Property of the Number Six

Kathy Yu, Crystal Lai, and Benjamin Russell, Mathematics (MATH) 2015, A solution to the arithmetic problem of finding a number which, divided by given numbers, leaves behind given remainders [translated from the original Latin by Carleton math students]

Submissions from 2014

Trey Aaron Brademan, Sakr Hanan Abo, Michelle Dano Yuen, and Benjamin Kibort Breen, Mathematics (MATH) 2014, abcd...EFG - Ideal Behavior in Fields Relating to Iterated Polynomials

Sophia Catherine Davis, Peter Danforth Briggs, Hilary Curtis Marshall, and Huaiyu Wang, Mathematics (MATH) 2014, Measuring the Mississippi

Katrina Ann Harper, Rachel Ann Ewing, Samuel Ihlenfeldt, and David Stillerman, Mathematics (MATH) 2014, Predictors of Alcohol Use for College Students: A Social Network Approach

Gregory Michel, Kailee Rubin, Ben Caffrey, and Steegh Jonathan Ver, Mathematics (MATH) 2014, Baxter Permutations, Snow Leopard Permutations, and Domino Tilings of Aztec Diamonds

Yan Sun, Mathematics (MATH) 2014, Fourier Analysis in Hilbert Space and An Introduction to Abstract Linear Operator Theory

Submissions from 2013

Milan William Cvitkovic, Mathematics (MATH) 2013, Self-Avoiding Random Walks

Andy Hardt, Pete McNeely, Tung Nguyen Viet Phan, and Justin M. Troyka, Mathematics (MATH) 2013, Combinatorial Species and Graph Enumeration

Asim Viladi Oglu Manizada, Mathematics (MATH) 2013, Generalized Cantor Sets: The Size and The Contents

Laurel Jeffers Orr and Xin Chen, Mathematics (MATH) 2013, Elliptic Functions and Modular Forms

Yansong Pang, Megan Mary Bakkens, Cassie Mullen, and Wenli Rui, Mathematics (MATH) 2013, The Effect of Spinning Machine Speed on Performance of Yarn

Benjamin Adam Strasser, Leo Christopher Olivares, Daoji Huang, and Adam Edward Zweber, Mathematics (MATH) 2013, Plane Trees and Shabat Polynomials

Roy James Wiggins, Matthew James Cusworth Rathkey, and Chelsea Elizabeth Yost, Mathematics (MATH) 2013, Polya Urn Models

David Zelle, Mathematics (MATH) 2013, Stein's Paradox and Bayesian Estimation

Submissions from 2012

Michael Cohen Alexander, Tanner Martin, and Scarlett Tse, Mathematics (MATH) 2012, Counting Moose: A Bayesian Model for Population Estimation

Benjamin Robert Anderson, Erika Rose Warrick, and Kathleen Marie Storey, Mathematics (MATH) 2012, The Medial Axis and its Applications

Russell Joseph Buehler, Mathematics (MATH) 2012, Hilbert's Tenth

Prasit Dhakal, Aman Gupta, and Ben Langfeldt, Mathematics (MATH) 2012, Statistical Analyses of Zooplankton Populations in Lakes in Minnesota

Cory Edward Fauver, Michael William Coughlin, Brian Andrew James, and Jon Anthony Aranda, Mathematics (MATH) 2012, Solitons

Frank Abraham Firke and Abram Zachary Jopp, Mathematics (MATH) 2012, Congruence Subgroups and Symmetry in the Poincaré Upper Half-Plane