# Undergraduate Senior Thesis in Mathematics

The Department of Mathematics at UC Davis offers undergraduate students the opportunity to participate in original mathematical research that will culminate in a senior undergraduate thesis. A student taking advantage of this opportunity would work under the guidance of a faculty mentor, pursuing original research.

### Eligibility

To be eligible to write a senior thesis, advanced undergraduate students must

- Have a GPA of 3.5 or above in upper level courses in Mathematics OR be in the Honors Program.
- Find an appropriate research mentor willing to supervise their research project. Research supervisors can be faculty from the Mathematics Department or faculty from the Graduate Group in Applied Mathematics (GGAM).
- Students that do not meet the GPA requirement may also be permitted to write a senior thesis. However, they must be nominated by a faculty member who is willing and able to supervise them in a research project, and the nomination must be approved by Undergraduate Research Committee.

### Requirements for completion of an undergraduate thesis

- Students must complete two full quarters of research prior to graduation.
- While pursuing their research, students must complete MAT 199 (Special Studies for Advanced Undergraduates) and/or MAT 194 (Undergraduate Thesis) for a total of at least 6 units of credit over two quarters.
- Students must complete a thesis of sufficient quality and substance. Both the research supervisor and the Undergraduate Research Committee (URC) will evaluate a student's thesis. In some cases, the URC will appoint an ad hoc committee to review the thesis.
- The URC must receive a draft of the thesis no later than the beginning of the eighth week of the quarter in which the student plans to graduate. The URC must also receive the supervisor's evaluation of the thesis at this time. The final copy of the thesis must be submitted to the department by the end of finals week.

Students in the Honors Program who complete theses may be considered for graduation with High Honors or Highest Honors. All students completing theses will be recognized at the June Graduation Reception and in the Fall Department Newsletter.

### Undergraduate Senior Thesis - Archived Submissions

**Implementation of the Wang Landau Algorithm to Cubic Lattice Knots**(Summer 2019) Zihao Zhu (Mentor Mariel Vazquez)**Global Solution to a Non-linear Wave Equation of Liquid Crystal in the Constant Electric Field**(Spring 2019) Linjun Huang (Mentor Qingtian Zhang)**Computing Viscoelastic Fluid Dynamics on GPUs**(Spring 2019) Adam Kagel (Mentor Paloma Gutierrez-Castillo)**Generating Noise for Langevin Dynamics Simulations**(Spring 2019) Lorenzo Mambretti (Mentor Niels Gronbech-Jensen)**Solving Nonnegative Principal Component Analysis Using the Frank-Wolfe and Manifold Proximal Gradient Methods**(Spring 2019) Jiayi Lei (Mentor Shiqian Ma)**Representation of Degenerate Affine Hecke Algebra and its Properties**(Spring 2019) Yupeng Li (Mentor Monica Vazirani)**An Op1q algorithm for the numerical evaluation of the prolate spheroidal wave functions of order 0**(Spring 2019) Xinge Zhang (Mentor James Bremer)**Statistical Analysis of Four Pivot Rules for the Simplex Method**(Winter 2019) Chutong Wu (Mentor Jesus De Loera)**Machine Learning and Real Roots of Polynomials**(Winter 2019) Zekai Zhao (Mentor Jesus De Loera)**Mathematical Paper Author Identification with Neural Network**(Winter 2019) Tzu Feng Leung (Mentor Jesus De Loera)**On the Existence of a Euclidean Algorithm in Number Rings with Infinitely Many Units**(Winter 2019) Jake Parkhurst (Mentor Martin Luu)**Randomly Generated Numerical Semigroups**(Spring 2018) Zachary Spaulding (Mentor Christopher O'Neill)**A SEQUENCE OF QUASIPOLYNOMIALS ARISING FROM****RANDOM NUMERICAL SEMIGROUPS**(Spring 2018) Calvin Leng (Mentor Christopher O'Neill)**A SOFTWARE PACKAGE FOR DECOMPOSING AFFINE****SEMIGROUPS**(Spring 2018) Madeline Chen (Mentor Christopher O'Neill)**PARAMETRIZED AND SHIFTED NUMERICAL SEMIGROUPS**(Spring 2018) Franklin Kerstetter (Mentor Christopher O'Neill)**Factorization in Numerical Semigroup Algebras**(Spring 2018) Sviatoslav Zinevich (Mentor Christopher O'Neill)**Monitoring Pesticide Concentrations: Database Time Series Analysis**(Spring 2018) Huong Vu (Mentor Alexander Aue)**Lieb-Robinson Bounds on 1D Lattices**(Spring 2018) Joel Barnett (Mentor Bruno Nachtergaele)**Anyonic Dispersion Under Weak Perturbations to the Toric Code Model**(Spring 2018) Nicholas Sherman (Mentor Bruno Nachtergaele)**The Tverberg Number of Small Trees**(Spring 2018) Dominic Yang (Mentor Jesus DeLoera)**A Machine Learning Approach to Evaluate Beijing Air Quality (Spring 2018)**Mingye Yang (Mentor Jesus DeLoera)**Recursive Relations for the Hilbert Series for Certain Quadratic Ideals (Spring 2018)**Yuzhe Bai (Mentor Eugene Gorsky)**Humidor: Microbial Community Classification of the 16S Gene by Training CIGAR Strings with Convolutional Neural Networks (Spring 2017)**Douglas Sherman (Mentor- Craig Benham)**Computation on Polyhedral Arrangements and its Applications on Lifting Regions (Spring 2017)**Pejiun Xiao (Mentor- Matthias Koeppe)**A p-adic Model of Eternal Inflation, a p-adic Quantum Mechanical Model, and a p-adic Anti-de Sitter Space (Spring 2017)**Brynn Caddel (Mentor - David Cherney)**Slow Neighborhood Growth on the Hamming Plane (Spring 2017)**J.E. Paguyo (Mentor- Erik Slivken)**Apply Machine Learning on Superconductos Analysis (Spring 2017)**Mengda Xu (Mentor-Jesus DeLoera)**Garnir Polynomial and their Properties (Spring 2017)**Yu Wang (Mentor-Evgeny Gorskiy)**Text Mining Methods on Mathematical Documents: A Case Study in Fields Medalists**(Winter 2017) Trevor Chan (Mentor - Jesus DeLoera)**Characterizing Singular Polynomials for Dunkl Operators**(Spring 2016) Christian Smith (Mentor - Eugene Gorsky)**Math Majors Using Math to Help Math Departments: Two Models for Assigning Teaching Assistants to Courses (Winter 2016)**Samuel Asher (Mentor - Jesus De Loera)**The Helly Number of the Prime-coordinate Point Set (Fall 2015)**Kevin Barrett Summers (Mentor - Jesus De Loera)**Cut-Generating Functions for Integer Linear Programming (Spring 2015**) Masumi Sugiyama (Mentor - Matthias Koeppe)**Coupling in Networks of Neuronal Oscillators (Spring 2015)**Carter Johnson (Mentor - Tim Lewis)**Rigged Configurations and Catalan Objects: Completing a Commutative Diagram with Dyck Paths and Rooted Planar Trees (Spring 2015)**Ryan Reynolds (Mentor - Anne Schilling)**Topological Quantum Field Theory From the Viewpoint of Cellular Graphs (Spring 2015)**Ruan Chen (Mentor - Motohico Mulase)**A Problem in Card Shuffling (Spring 2015)**Gweneth McKinley (Mentor: Anne Schilling)**Classifying 1-Lattice Maximal Polytopes (Spring 2015)**Megan Liska (Mentor - Jesus De Loera)**Asymptotic Yamabe-Problem Obstruction-Densities (Spring 2015)**Matthew Halbasch (Mentor - Andrew Waldron)**Derivation of Finite Sums of Integer t-th Powers: A Historic Perspective (Spring 2015)**(PDF) Benjamin Bairrington (Mentor - Jesus De Loera**Connecting Brownian Motion and Partial Differential Equations with Applications in Statistical and Quantum Mechanics (Fall 2014)**(PDF) Zachary Selk (Mentor - Dirk Deckert)**Assigning Teaching Assistants to Courses: Mathematical Models (Spring 2014)**(PDF) Victor Fuentes (Mentor - Jesus De Loera)**Bound States and Scattering States of a Quantum Particle on Half-Infinite Lattices (Spring 2014)**(PDF) Aaron Hsu (Mentor - Bruno Nachtergaele)**Counting Double Tangents of Closed Curves Without Inflection Points (Spring 2014)**(PDF) Emily Macway (Mentor - Abigail Thompson)**Topological K-Theory of Complex Projective Spaces (Spring 2013)**(PDF) Virgil Chan (Mentor - Dmitry Fuchs)**Compressive Sensing with Highly Coherent Dictionaries (Spring 2012)**(PDF) Sara Cohen (Mentor - Thomas Strohmer)**A Bound for Orderings of Reidemeister Moves (Spring 2012)**(PDF) Julian Gold (Mentor - Alexander Coward)**Fluctuations of Matrix Entries of Polynomial Functions of Wigner Matrices (Spring 2012)**(PDF) Asad Lodhia (Mentor - Alexander Soshnikov)**Characterizing Automorphism and Permutation Polytopes (Spring 2011)**(PDF) Katherine Burggraf (Mentor - Jesus DeLoera)**A New Proof of the Ellipsoid Algorithm (Spring 2011)**(PDF) Samantha Capozzo (Mentor - Jesus DeLoera)**The Euclidean Volume of the Moduli Space (Spring 2011)**(PDF) Kevin Chapman (Mentor - Motohico Mulase)**The Geometry of the Simplex Method and Applications to the Assignment Problems (Spring 2011)**(PDF) Rex Cheung (Mentor - Jesus DeLoera)**The Geometric Structure of Spanning Trees and Applications to Multiobjective Optimization (Spring 2009)**(PDF) Allison O'Hair (Mentor - Jesus DeLoera)**Pattern Avoidance in Unimodal and V-Unimodal Permutations (Spring 2009)**(PDF) Dido Salazar-Torres (Mentor - Brant Jones)**Investigations of Barnette's Graphs (Winter 2008)**(PDF) Luis De La Torre (Mentor - Jesus DeLoera)**An Approach to Bounding the Spectral Gap Above the Ground State of a Quantum Spin Chain (Spring 2008)**(PDF) Amanda Young (Mentor - Bruno Nachtergaele)**Orthosymplectic Differential Geometric Operator Algebras with Conformal Symmetry (Spring 2008)**(PDF) Joshua Burkart (Mentor - Andrew Waldron)**The Effect of Habitat Fragmentation on Population Persistence in Spatially Heterogeneous Landscapes (Spring 2008)**(PDF) Matthew Holden (Mentors - Sebastian Schreiber, Rick Grosberg, and Carole Hom)**Traveling Solitary Wave Solutions in the Resonant Interaction of Equatorial Baroclinic and Barotropic Rossby Waves (Spring 2008)**(PDF) Amanda O'Rourke (Mentor - Joseph Biello)