A degree with honors in mathematics will be awarded by the department to students who have achieved excellence in the work of the major and also meet the following further requirements:

- at least two additional semesters of work at the 300 level or above (this includes Supervised Work 403).
- completion of a meritorious project consisting of a written honors thesis, which may be an expository paper or some original research, and an oral presentation of the thesis.
- a major grade point average of at least 3.6, calculated at the end of the senior year.

An honors project normally requires two semesters of independent study with a faculty member. A student interested in pursuing honors should approach faculty members at the end of her junior year to determine the availability of a project of mutual interest. The written thesis must be completed by the last day of classes in the spring semester, and preferably a week before the oral presentation is given. *The formal decision on honors is determined by a vote of the math faculty after the oral presentation and after the final version of the written thesis has been submitted.*

### Honors Theses

**2018**

Student |
Title of Thesis |
Adviser |

Benedetto, Dina | Optimal Control Theory: Finding the Optimal Cancer Treatment Protocol for Various Anti-Cancer Approaches | Graham |

Nguyen, Linh | Portfolio Selection Problem: Optimal Portfolio and Minimum Analysis Approach | Cheng |

Nguyen, Phuong |
An Application of Queueing Theory: Optimizing Queues at JFK Airport |
Graham |

Nguyen, Thu | Valuation and Hedging of Barrier Options | Cheng |

Rendleman, Hunter | Mathematical Methods of Studying Disease: Formal and Statistical Approaches | Cheng |

Sheng, Yu | On Some Supercongruence Conjectures for Hypergeometric Series | Milićević |

Terry, Rachel | Valuation of Lookback Options on LVMH Stock | Cheng |

Wang, Wenqi | Persistent Homology: From Data to Barcodes | Melvin |

**2017**

Student |
Title of Thesis |
Adviser |

Bai, Yiling | Pricing Up-And-Out Call Options | Cheng |

Ball, Prianka | An Analysis of the Viability of Wind Turbines | Donnay |

He, Tianyi | Valuation of Lookback Options | Cheng |

Kaplan-Kelly, Rose | Multi-crossing Projections of Legendrian Knots | Traynor |

Li, Jingling | Well-Quasi Ordering and its Relation to Terminating Rewrite System | Cheng |

Mildenhall, Westley | Chaotic Systems of Geodesics on Surfaces of Revolution | Donnay |

Qu, Kewei | Well-Quasi Ordering and Confluence | Cheng |

Wang, Yichen | Generalized Two-parameter Exponential Distribution and its Parameter Estimation | Cheng |

**2016**

Student |
Title of Thesis |
Adviser |

Geng, Xiaoqi | Estimation Maximization Algorithm: Its Application and Implementation in R | Nancy Zhang at Upenn |

Koukoutchos, Melina | Harshad Numbers and Shantid Numbers | Grundman |

Lin, Bingxi | Persistent Homology and Its Application to Data Analysis | Melvin |

Manhartova, Zuzana | Financial Models: Theory with Examples using Real Data | Cheng |

Mohattane, Yamina | Applications of the Hull-White One-Factor Model | Cheng |

Sun, Shuhong (Paula) | An Introduction to Computational Persistent Homology | Melvin |

Tang, Siran | Portfolio Management with a Focus on Monte Carlo Simulation | Cheng |

Williams, Simon | Generalizations of Happy Numbers | Grundman |

Yan, Ziyi | Geometric Brownian Motion in Financial Mathematics | Cheng |

Zhai, Yuping | A Development of Basic Stochastic Calculus and its Applications | Cheng |

**2015**

Capovilla-Searle, Orsola | Surgery Strings of Legendrian Knots | Traynor |

Dong, Xinyuan | Stock Price Movement: Simulations and Theories | Cheng |

Johnson, Madeleine | Geodesic Path of a Surface of Revolution | Donnay |

Li, Lydia | New p-adic Sextic Supercongruences of Ramanujan Type |
Milićević |

Liu, Yifan | Valuation of American Options | Cheng |

Luo, Danqi | Option Valuation Under Risk Neutral Measures | Cheng |

Narasimhan, Swetha | Analyzing Music Through Geometry | Traynor |

Preziuso, Danielle | Powering Our Future with Sun and Wind: A Renewable Energy Model for Delaware, New Jersey, and Pennsylvania | Donnay |

Ramaswamy, Lipika | Fixed Point Theorems and Applications to Economics | Traynor |

Tang, Jessie | Mathematical Modeling of Ebola | Donnay |

**2014**

Ahsin, Taha | A Development of Basic Stochastic Calculus and Its Applications | Cheng |

Curl, Emelie | The Omega Primality Function in Consecutively Generated Embedding Dimension Three Monoids, or How Studying Chicken McNuggets Helped Me Explain Complex Algebraic Structure | Cheng |

Mirbey, Jeanne | The Mathematics of Medical Imaging | Cheng |

Oh, Sookyung | Brownian Motion | Cheng |

Shrestha, Kriti | Incomplete Character Sums |
Milićević |

Zhao, Sophie | City Network: The Dynamics of Location, Education, and Production | Traynor |

**2013**

Ammar, Lynne | Harmonic Analysis: the bounded Oscillatory Integrals | Cheng |

Boranda, Bianca | Games, Games, Games: Multistage Stochastic Games | Traynor |

Ha, Hoang | Gonorrhea Transmission Dynamic and Netlogo Simulation | Donnay |

Jiang, Hao | Introduction of Valuation of Financial Derivatives | Cheng |

Kang, Sunny | L^{p} Estimates for a Certain Class of Oscillatory Integral Operators |
Cheng |

Martinez, Brenda | Netlogo Simulations of HPV | Donnay |

Neal, Meagan | Reproducing Kernal Hilbert Spaces in Multi-Task Machine Learning | Cheng (jointly with Visiting Assistant Professor of Computer Science Eric Eaton) |

Pandya, Meghan | Symmetry in Dance and Art: Group Theory and its Applications | Cheng |

Pradhan, Alisha | Hedging using Options and Futures | Cheng |

Weinstein, Hannah | Mathematical Modeling of West Nile Virus and Climate Change | Donnay |

Wu, Qian | Cooperative Games and the Nash Bargaining Model | Traynor |

Xie, Pan | Stochastic Process and Option Pricing Models | Cheng |

Yan, Shuning | The Set of Signed Unknotting Numbers | Traynor |

**2012**

Dunusinghe, Kaushiki | An Analysis of Energy Use in Bryn Mawr College Buildings | Donnay |

Hien, Winnie | Vanilla and Exotic Options: Valuation and Hedging | Cheng |

Link, Katie | Guinea Worm Disease: Opening a mathematical can of worms | Donnay |

Murphy, Aidan | An Inverse Zero-Sum Conjecture | Grundman |

Nelson, Sarah | Valuation of Options | Cheng |

Owens, Catherine | A Theorem on the Weighted Davenport constant | Grundman |

Savage, Jennifer | Oscillatory intergral Operators and Improved Hormander's Theorem | Cheng |

Wu, Tong | Options, Hedging and Portfolio Management | Cheng |

**2011**

Azuma, Bethany | Construction of Smooth Curves and Surfaces | Melvin |

Bereznak, Sasha | Valuation of Barrier Options | Cheng |

Caniglia, Ellie | Modeling the Joint Epidemics of HIV and TB | Donnay |

Davidson, Sara | Mathematics in Medical Imaging | Cheng |

Dewar, Romy | Valuation of Options and Hedging | Cheng |

Kumar, Anagha | Valuation of European and American Call Options | Cheng |

Lee, Alex | Configuration Spaces of Graphs | Traynor |

Mirbey, Adele | Mathematics in Crystallography | Cheng |

Panosia, Alison | Using Phylogenetic Trees to Understand the Evolution of Genes | Traynor |

**2010**

Iles, Caitlin | HIV - A Controllable Disease | Donnay |

Hamermesh, Naomi | Mathematical Modeling of Climate Change: Examining the Diurnal Temperature Range | Donnay |

Martin, Alyssa | The Mathematics of Catastrophe Risk | Cheng |

Raj, Leah | Why ESPN Needs More Mathematicians | Cheng |

Van Sciver, Alicia | Options on Futures | Cheng |

**2009**

Brown, Jillian | Mathematically Modeling the Immunological Spread of HIV/AIDS | Donnay |

Durante, Catherine | Analysis of the Black Scholes Model: An Imperative in Option Pricing | Cheng |

Hayde, Kendra | Fingerprint Compression using Wavelets | Cheng |

Lu, Amanda | Valuation of Barrier Options | Cheng |

Macko, Melania | Bond Pricing | Cheng |

Waterhouse, Hannah | Climate Changes, Fisheries, and Mathematical Modeling | Donnay |

**2008**

Edwalds, Melanie | Geometric and Topological properties of the Mobius Band | Melvin | |

Feldman, Dena | Langevin Equations: Modeling Particle Motion and Trail Formation | ||

Krieger, Jody | Analysis of the Black-Scholes Model: A Catalyst for Financial Mathematics | Cheng | |

Redzic, Milena | Helffer-Sjostrand Proof of the Spectral Theorem | Hughes |

**2007**

Haymaker, Katie | Isospectral Lattices and Quadratic Forms | Melvin | |

Huynh, Huong | The Mathematical Dissection of Social Networks | Donnay | |

O'Brien, Genevieve Stein | Spectral Theorem for Compact Hermitian Operators | Kasius | |

Petonic, Cara | Intrinsic Linking Numbers of Complete Graphs | Melvin | |

Porreca, Camille | Bounded Mean Oscillation Space | Cheng | |

Tang, Danny | Thurston-Bennequin Bound of Legendrian Links | Melvin | |

Won, Priscilla | Social Network Analysis: Applications to School District Management | Donnay |

**2006**

Benfold, Nicole | Simplest Cubic Fields and Class Numbers | Grundman |

Do, Cindy | Credit Risk Management | Stromquist |

Hammer, Emily | Stable Solvability of a Family of Quartic Thue Equations | Grundman |