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
Noorah Aldaghlas, Natalie Bax, Jasmine Choi, Elena Ea, and Augustus Williams, Statistics (STAT) 2024, Beyond the Average: Exploring the Relationship Between Income Inequality and the Mortality Distribution of US Counties using Quantile Regression
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
Zachary Glaser, Mathematics (MATH) 2024, Voting Systems: Values, Weaknesses, Impossibilities
Alejandro Gonzalez, Sophie Boileau, Hugh Shanno, Grace Hanson, and Ammy Lin, Mathematics (MATH) 2024, Binary Quadratic Forms: Properties, Groups, and Ideals
Benjamin Griesel, Statistics (STAT) 2024, The Impact of Obstetric Periodontal Therapy and Interactions on Preterm Birth: A Survival Analysis
Andrew Hong, Mathematics (MATH) 2024, An Introduction to Ergodic Theory
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
