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 2019

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

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

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

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

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

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

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

#### Submissions from 2018

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

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

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

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

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

#### Submissions from 2017

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

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

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

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

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

#### Submissions from 2016

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

#### Submissions from 2015

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

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

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

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

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

**Kathy Yu, Crystal Lai, and Benjamin Russell**, 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], 2015, Mathematics (MATH)

#### Submissions from 2014

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

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

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

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

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

#### Submissions from 2013

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

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

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

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

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

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

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

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

#### Submissions from 2012

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

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

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

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

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

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

**Jonathan Hahn, Rebecca Cordes, and Collin Hazlett**, Visualizing the Hecke Group: Fractions and Wallpaper Symmetry in Hyperbolic Space, 2012, Mathematics (MATH)

**Isaac A. Hodes**, Counting Below the Curve: Combinatorial Proofs of Integral Formulas, 2012, Mathematics (MATH)

**Erin Michael Jones, Erika Denise Mackin, and Kian Anton Flynn**, Voting Theory and Cake Cutting, 2012, Mathematics (MATH)

#### Submissions from 2011

**Cory Pate Barnes, Michael Phan Knudson, and Thomas William McCauley**, PDE Solutions and Cauchy-Riemann Geometry, 2011, Mathematics (MATH)

**Amy Becker, Lillian Naomi Betke-Brunswick, and Anna Zink**, Plane partitions, 2011, Mathematics (MATH)

**Andrew Thomas Bergman, Akinboye Ibiyemi Akinwande, Mary Elizabeth Cross, and Veronica Tan**, Tic-Tac-Toe with a Twist, 2011, Mathematics (MATH)

**Gabriel Talbot Davis, Aaron Maurer, and Julie Michelman**, An Open Problem in the Combinatorics of Macdonald Polynomials, 2011, Mathematics (MATH)

**Alex John Evangelides, Samuel Vaughn Tucker, Mary Ellen Bushman, and Nathan Mark King**, The Combinatorics of Symmetric Functions: (3 + 1)-free Posets and the Poset Chain Conjecture, 2011, Mathematics (MATH)

**Qi Li, Chen Sun, and Jeremy Grevet**, DNA Recombination: Looking at a Biological Process through the Lens of Knot Theory, 2011, Mathematics (MATH)

**Andrew Douglas Mering, Christopher Daniel Wilen, Celine Annabelle Yeh, and Hang Thi Viet Nguyen**, Dynamics of Pulse-Coupled Integrate-and-Fire Oscillators, 2011, Mathematics (MATH)

**James Martin Munson and Elizabeth Collins-Wildman**, Munshi's Theorem: Zero Places and Infinite Spaces, 2011, Mathematics (MATH)

#### Submissions from 2010

**Chrisna Aing, Sarah Halls, and Kiva Oken**, Using Occupancy Theory and Hierarchical Models to Estimate Otter Population in Southeastern Minnesota, 2010, Mathematics (MATH)

**Erica Rochelle Chesley, Zachary Starer-Stor, and Emma Zhou**, A Finite Simple Puzzle of Order 44,352,000, 2010, Mathematics (MATH)

**Grace Allsman Elwell, Henry Heitzer, and Erik Williams**, Synchronicity of Biological Oscillators, 2010, Mathematics (MATH)

**Tomoki Isogai**, Differences Between Single and Several Complex Variable Analysis, 2010, Mathematics (MATH)

**Becky Jean Patrias, Matthew Bernard Cordes, Beatrice Burlingame White, and Zheng Zhu**, Shadows of the Cantor Set, 2010, Mathematics (MATH)

#### Submissions from 2009

**Hannah L. Breckbill, Aparna Dua, Luke B. Hankins, and Robert W. Trettin**, Challenge Math -- 2nd grade, 2009, Mathematics (MATH)

**Christina Knudson, Edward Kuhn, and Bassirou Sarr**, A Bayesian spatial temporal model of ozone, 2009, Mathematics (MATH)

**David Lonoff and Daniel McDonald**, Bijective proofs: a comprehensive exercise, 2009, Mathematics (MATH)

**Ryan Andrew Smith and Yuan Tian**, Analytic proof of the prime number theorem, 2009, Mathematics (MATH)