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 Program Committee Chair (UPC) will evaluate a student's thesis.
 The UPC 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 UPC 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

Recovery of the Trajectory of DNA inside Viral Capsids from Liquid Crystal Vector Fields  (Fall 2020) Zhijie Wang (Mentor Javier Arsuaga)

REMARKS ON COMBINATORIAL WALLCROSSING  (Spring 2020) Xuyilong Chen (Mentor Jose Simental Rodriguez

THE FUNDAMENTAL GROUP OF THE COMPLEMENT OF BRAIDED SURFACES  (Spring 2020) Sari Ogami (Mentor Laura Starkston)

THE COHOMOLOGY OF FLAG VARIETIES AND SCHUBERT POLYNOMIALS  (Spring 2020) Yuze Luan (Mentor Erik Carlsson)

Wave Reflections in Excitable Media Using MorrisLecar Dynamics  (Spring 2020) Vincent Lovero (Mentor Tim Lewis)

Euler characteristics of surfaces  (Spring 2020) Shirley Wang (Mentor Eugene Gorskiy)

PolyPathLab: Software for the Calculation of Monotone Paths on Polytopes (Spring 2020) Limin Huang (Mentor Jesus De Loera)

The equilibrium solutions and visualizations to the incompressible fluid ellipsoids (Spring 2020) Ruicong Zheng (Mentor Joseph Biello)

Applying Deep Learning Methods on Detecting Cycles on Graphs (Spring 2020) Ka Hei Michael Chu (Mentor Jesus De Loera)

Estimating Landau's Function (Spring 2020) Richard Gunter (Mentor Jose Simental Rodriguez)

Modeling GeneTreeSpeciesTree Conflict with Migration Using ContinuousTime Markov Chains (Winter 2020) Haleigh Miller (Mentor Bruce Rannala and Gerry Puckett)
 Catalan Recursion on Externally Ordered Bases of Unit interval Positroids (Fall 2019) Jan Tracy Camacho (Mentor Anastasia Chavez)
 Implementation of the Wang Landau Algorithm to Cubic Lattice Knots (Summer 2019) Zihao Zhu (Mentor Mariel Vazquez)
 Global Solution to a Nonlinear 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 GutierrezCastillo)
 Generating Noise for Langevin Dynamics Simulations (Spring 2019) Lorenzo Mambretti (Mentor Niels GronbechJensen)
 Solving Nonnegative Principal Component Analysis Using the FrankWolfe 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)
 LiebRobinson 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 padic Model of Eternal Inflation, a padic Quantum Mechanical Model, and a padic Antide 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 (MentorJesus DeLoera)
 Garnir Polynomial and their Properties (Spring 2017) Yu Wang (MentorEvgeny 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 Primecoordinate Point Set (Fall 2015) Kevin Barrett Summers (Mentor  Jesus De Loera)
 CutGenerating 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 1Lattice Maximal Polytopes (Spring 2015) Megan Liska (Mentor  Jesus De Loera)
 Asymptotic YamabeProblem ObstructionDensities (Spring 2015) Matthew Halbasch (Mentor  Andrew Waldron)
 Derivation of Finite Sums of Integer tth 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 HalfInfinite 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 KTheory 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 VUnimodal Permutations (Spring 2009) (PDF) Dido SalazarTorres (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)