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Author:

Zydney, Adam Joseph

Title:

Structure of Attractor Region for Natural Extension Map Associated with p-adic Continued Fractions

Area of Honors:

Mathematics

Keywords:

attractor region
natural extension map
p-adic numbers
analysis

File:

Download zydney-thesis-FINAL.pdf

Thesis Supervisors:

Svetlana Katok, Thesis Supervisor
Svetlana Katok, Thesis Honors Advisor
Misha Guysinsky, Thesis Supervisor
Svetlana Katok, Thesis Supervisor

Author:

Gillespie, Bryan Rae

Title:

Extending Redheffer's Matrix to Arbitrary Arithmetic Functions

Area of Honors:

Mathematics

Keywords:

Redheffer matrix
Mertens function
Redheffer-type matrix
arithmetic functions
embedding
general linear group
Dirichlet convolution
convolution inversion
sums
eigenvalues
characters
volume
Eulerian polynomials

File:

Download bgillespie-honors-thesis.pdf

Thesis Supervisors:

Robert Charles Vaughan, Thesis Supervisor
Robert Charles Vaughan, Thesis Supervisor
Svetlana Katok, Thesis Honors Advisor

Author:

Somers, Elizabeth Anne

Title:

ASSESSING THE EFFECTIVENESS OF MULTIPLE CHOICE MATH TESTS

Area of Honors:

Mathematics

Keywords:

multiple choice exams
data analysis
difficulty
effectiveness

File:

Download Somers_Thesis.pdf

Thesis Supervisors:

Stanley S Smith, Thesis Supervisor
Mark Levi, Thesis Honors Advisor
Stanley S Smith, Thesis Supervisor

Author:

Sofo, Ignacio

Title:

Using the Finite Element Method for Solving the Schrödinger Equation

Area of Honors:

Mathematics

Keywords:

Finite Element Method
error analysis

File:

Download Ignacio_SofoHonorsThesis2.pdf

Thesis Supervisors:

Victor Nistor, Thesis Supervisor
Victor Nistor, Thesis Supervisor
Svetlana Katok, Thesis Honors Advisor

Author:

Walsh, Mark Edward

Title:

The Propagation of Shallow-Water Waves

Area of Honors:

Mathematics

Keywords:

shallow-water waves
wave propagation
Korteweg-deVries equation

File:

Download MWalsh_Thesis.pdf

Thesis Supervisors:

Diane Marie Henderson, Thesis Supervisor
Dr. Diane Marie Henderson, Thesis Supervisor
Nigel David Higson, Faculty Reader
Dr. Diane Marie Henderson, Thesis Honors Advisor

Author:

Levi, Max Richard

Title:

Overlapping Neighborhoods, Local Interaction Model

Area of Honors:

Mathematics

File:

Download TeachMeHowToDougie.pdf

Thesis Supervisors:

Dr. Christopher Byrne, Thesis Supervisor
Dr. Diane Marie Henderson, Thesis Honors Advisor
Dr. Christopher Byrne, Thesis Supervisor

Author:

Huang, Ying-Hui

Title:

CASE STUDY OF BEHAVIOR DIFFERENCES BETWEEN DEFINED BENEFIT AND DEFINED CONTRIBUTION PENSION PLANS

Area of Honors:

Mathematics

Keywords:

defined benefit
defined contribution
pension
retirement rate
withdrawal rate

File:

Download Ying-Hui_Huang_final.pdf

Thesis Supervisors:

David Arthur Cather, Thesis Supervisor
David Arthur Cather, Thesis Supervisor
Dr. Diane Marie Henderson, Thesis Honors Advisor

Author:

Immendorf, Robert Erik

Title:

An Examination of the Assignment Scheduling Capability for Unmanned Aerial Vehicles (asc-u) Model

Area of Honors:

Mathematics

Keywords:

Army
Mathematics
Linear Programming
Optimization
Operations Research

File:

Download Immendorf_Honors_Thesis-Final-Version.pdf

Thesis Supervisors:

Leonid N Vaserstein, Thesis Supervisor
Luen Chau Li, Thesis Honors Advisor

Author:

Li, Qiyuan

Title:

Construction of Cantor Sets

Area of Honors:

Mathematics

Keywords:

Cantor set
Hausdorff measure
Kolmogorov complexity

File:

Download thesis.pdf

Thesis Supervisors:

Jan Severin Reimann, Thesis Supervisor
Stephen George Simpson, Thesis Honors Advisor

Author:

Fuller, Samantha Ashlee

Title:

Representation Theory of sl(2,C) and sl(3,C)

Area of Honors:

Mathematics

Keywords:

representation theory
irreducible representations
Lie algebras

File:

Download Thesis.pdf

Thesis Supervisors:

Nigel David Higson, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Taylor, Benjamin David

Title:

Analogies in Linear Algebra and Group Theory

Area of Honors:

Mathematics

Keywords:

math
linear algebra
group theory
abstract algebra

File:

Download Final_Thesis.pdf

Thesis Supervisors:

Mihran Papikian, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Shi, Yixuan

Title:

Bernoulli polynomials and riemann zeta function

Area of Honors:

Mathematics

Keywords:

bernoulli polynomial
riemann zeta function

File:

Download Final_draft_of_thesis_for_SHC.pdf

Thesis Supervisors:

Misha Guysinsky, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Shen, Sijia

Title:

a model of economic growth driven by competitive innovation

Area of Honors:

Mathematics

Keywords:

economy
math
piazza
periodic orbit
ODE

File:

Download Thesis_FormatReview.pdf

Thesis Supervisors:

Alberto Bressan, Thesis Supervisor
Luen Chau Li, Thesis Honors Advisor

Author:

Jin, Cheng

Title:

Chinese Remainder Theorem

Area of Honors:

Mathematics

Keywords:

Chinese Remainder Theorem
Rings
Commutative Algebra

File:

Download ChengJin_CRT_5.0.pdf

Thesis Supervisors:

Dr. Karl Schwede, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Yang, Jing

Title:

medical malpractice insurance and its premium

Area of Honors:

Mathematics

Keywords:

malpractice insurance
premium
medical

File:

Download 2-malpractice_insurance.pdf

Thesis Supervisors:

Ron Gebhardtsbauer, Thesis Supervisor
Mark Levi, Thesis Honors Advisor

Author:

Cai, Wente B

Title:

An Optimal Control Problem Arising from an Evolutionary Game

Area of Honors:

Mathematics

Keywords:

game theory
evolutionary game theory
optimal control

File:

Download Thesis_Edited.pdf

Thesis Supervisors:

Christopher H Griffin, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Author:

Li, Boya

Title:

Stochastic Modeling and Pricing Of Mortality-linked Securities

Area of Honors:

Mathematics

Keywords:

stochastic mortality model
the Wang transform
mortality-linked securities
pure mortality bond
maximum likelihood estimation

File:

Download honors_thesis_final_draft-_Boya_Li.pdf

Thesis Supervisors:

Zhongyi Yuan, Thesis Supervisor
Dr. Diane Marie Henderson, Thesis Honors Advisor

Author:

Zhan, Hongyuan

Title:

Numerical Methods for Hamiltonian Systems: Theory, Numerics and Case Studies

Area of Honors:

Mathematics

Keywords:

numerical methods
Hamiltonian system

File:

Download thesis_hzz5039.pdf

Thesis Supervisors:

Xiantao Li, Thesis Supervisor
Dr. Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Battaglia, Emily Louise

Title:

Two Mathematical Models of Inequality in Economics

Area of Honors:

Mathematics

Keywords:

Income Inequality
Solow Model
Agent-based Model

File:

Download Battaglia_Thesis.pdf

Thesis Supervisors:

Christopher H Griffin, Thesis Supervisor
Dr. Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Yang, Zhaoning

Title:

SPACES OF POLYNOMIALS RELATED TO MULTIPLIER MAPS

Area of Honors:

Mathematics

Keywords:

polynomial space
dimension
multiplier map

File:

Download ZYang_HonorsThesis.pdf

Thesis Supervisors:

Yuriy G Zarkhin, Thesis Supervisor
Dr. Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Paulson, Elisabeth C

Title:

A Reformulation of the CSSR Algorithm and Application to Optimal Deception Strategy in Two Player Games

Area of Honors:

Mathematics

Keywords:

hidden markov models
probabilistic finite-state machine
deception strategy
game theory

File:

Download merged_document_2.pdf

Thesis Supervisors:

Christopher H Griffin, Thesis Supervisor
Svetlana Katok, Thesis Honors Advisor
Svetlana Katok, Faculty Reader

Author:

Cobern, Sara Catherine

Title:

The q-catalan numbers of Macmahon and a related identity of Andrews

Area of Honors:

Mathematics

Keywords:

q-Catalan numbers
Mathematics
Combinatorics

File:

Download Cobern_Final_Thesis.pdf

Thesis Supervisors:

Ae Ja Yee, Thesis Supervisor
Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Cotner, Nicholas H

Title:

Fock Spaces

Area of Honors:

Mathematics

Keywords:

Fock spaces
quantum field theory
math
tensor products
Hilbert spaces

File:

Download Cotner_fockspace_thesis.pdf

Thesis Supervisors:

Adrian Ocneanu, Thesis Supervisor
Mark Levi, Thesis Honors Advisor

Author:

Antinori, Lilith Zaila

Title:

Toward a graph theoretical model of functional connectivity in chronic developmental traumatic stress disorders

Area of Honors:

Mathematics

Keywords:

traumatic stress
graph theory
functional connectivity
neuroscience

File:

Download Actual_Formatted_Thesis-1-1-edited4.pdf

Thesis Supervisors:

Andrew Leonard Belmonte, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Author:

Inciardi, Allegra Marie

Title:

Mathematical Modeling Of Influenza At Penn State: a Study Of Incidence Patterns And Effect Of Vaccination

Area of Honors:

Mathematics

Keywords:

influenza
mathematical model
influenza vaccination

File:

Download Inciardi_Thesis.pdf

Thesis Supervisors:

Timothy Charles Reluga, Thesis Supervisor
Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Zhang, Xingyu

Title:

Approximate Ramsey Theory

Area of Honors:

Mathematics

Keywords:

math
Ramsey theory
combinatorics

File:

Download Zhang_Xingyu_approximateramseytheory.pdf

Thesis Supervisors:

Jan Severin Reimann, Thesis Supervisor
Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Henry, Seth Michael

Title:

Application of Computational Linear Algebraic methods to a Reliability Simulation

Area of Honors:

Mathematics

Keywords:

Markov chain
reliability theory
computational methods
Gauss-Seidel
Conjugate Gradient
Successive over-relaxation

File:

Download NewThesis.pdf

Thesis Supervisors:

Christopher H Griffin, Thesis Supervisor
Victoria V Sadovskaya, Thesis Honors Advisor

Author:

Tang, Yuan

Title:

A B-spline Hierarchical Model on HIV Prevalence Data

Area of Honors:

Mathematics

Keywords:

b-spline
hierarchical model
HIV prevalence
mixed model
Bayesian inference
Markov Chain Monte Carlo
sparse and imbalanced data

File:

Download final_thesis_Yuan_Tang.pdf

Thesis Supervisors:

Le Bao, Thesis Supervisor
Luen Chau Li, Thesis Honors Advisor

Author:

Nataraj, Karthik

Title:

Problems in Partition Theory

Area of Honors:

Mathematics

Keywords:

Rogers-Ramanujan
integer partitions
distinct parts

File:

Download Nataraj_Karthik_ProblemsInPartitionTheory.pdf

Thesis Supervisors:

George E. Andrews, Thesis Supervisor
Aissa Wade, Thesis Honors Advisor

Author:

Kellock, Cameron Annetta

Title:

The Effect of Adding Contribution Tiers to Employer-sponsored Health Insurance Plans

Area of Honors:

Mathematics

Keywords:

Vertical Product Differentiation
Game Theory
Patient Protection and Affordable Care Act

File:

Download Cameron_Kellock.pdf

Thesis Supervisors:

Eli Christopher C Byrne, Thesis Supervisor
Eli Christopher C Byrne, Thesis Supervisor
Dr. Diane Marie Henderson, Thesis Honors Advisor

Author:

Shi, Hanjie

Title:

Option Pricing: Study of Generalized Binomial Model

Area of Honors:

Mathematics

Keywords:

financial mathematics
option pricing
binomial model
markov chain
Black-Scholes Model

File:

Download thesis.pdf

Thesis Supervisors:

Manfred Heinz Denker, Thesis Supervisor
Luen Chau Li, Thesis Honors Advisor

Author:

Easton, Matthew Daniel

Title:

Persistence Of Dynamic Fairness And Altruism In The Ultimatum Game

Area of Honors:

Mathematics

Keywords:

game theory
mathematics
economics

File:

Download EASTON_MATTHEW_THESIS.pdf

Thesis Supervisors:

Andrew Leonard Belmonte, Thesis Supervisor
Aissa Wade, Thesis Honors Advisor

Author:

Miller, Justin Davis

Title:

Extending First Order Logic to Quantify Over Formulas

Area of Honors:

Mathematics

Keywords:

First Order Logic
Mathematical Logic
Mathematics
Foundations of Mathematics

File:

Download master.pdf

Thesis Supervisors:

Jason Michael Rute, Thesis Supervisor
Anne Kirsten Eisentraeger, Thesis Honors Advisor

Author:

Gaertner, Carol Lynn

Title:

More Efficient Choices of Linear Bases in Numerical Methods

Area of Honors:

Mathematics

Keywords:

numerical methods
finite element method
differential equations
linear basis

File:

Download Carol_Gaertner_Math_Honors_Thesis.pdf

Thesis Supervisors:

Victor Nistor, Thesis Supervisor
Svetlana Katok, Thesis Honors Advisor

Author:

Zhou, Hangyu

Title:

Topology and Data Analysis

Area of Honors:

Mathematics

Keywords:

hoomology
topological data analysis
persistent homology
algebraic topology

File:

Download Zhou_Hangyu_Topology_and_Data_Analysis.pdf

Thesis Supervisors:

John Roe, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Zhu, Mengxue

Title:

Mathematical Interpretation of the Financial Terms in Interest Models Theory and Practice

Area of Honors:

Mathematics

Keywords:

Interest rate model
mathematical interpretation

File:

Download thesis0406.pdf

Thesis Supervisors:

Manfred Heinz Denker, Thesis Supervisor
Luen-Chau Li, Thesis Honors Advisor

Author:

Liu, Shikun

Title:

Variational Generative Models

Area of Honors:

Mathematics

Keywords:

variational inference
generative model
3D Shape Learning

File:

Download psu_thesis.pdf

Thesis Supervisors:

Clyde Lee Giles, Thesis Supervisor
Sergei Tobachnikov, Thesis Honors Advisor

Author:

Litman, Matthew Chad

Title:

Sphere Eversion: Analysis of a Veridical Paradox

Area of Honors:

Mathematics

Keywords:

topology
sphere eversion
mathematics

File:

Download M_Litman_Thesis.pdf

Thesis Supervisors:

Sergei Tabachnikov, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Author:

Nicodemus, Patrick Blair

Title:

A Recursive Presentation of the Graphon Space

Area of Honors:

Mathematics

Keywords:

graph theory
graphon
descriptive set theory
effective descriptive set theory
graph homomorphisms
effective Polish space
recursive presentation

File:

Download Nicodemus_Patrick_RecursivePresentation.pdf

Thesis Supervisors:

Jan Severin Reimann, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Author:

Shen, Yuefei

Title:

ON CUBIC PARTITIONS AND PARTITIONS CLASSIFIED BY SMALLEST MISSING PART

Area of Honors:

Mathematics

Keywords:

partitions
cubic partitions
combinatorics

File:

Download thesis.pdf

Thesis Supervisors:

George E. Andrews, Thesis Supervisor
Anne Kirsten Eisentraeger, Thesis Honors Advisor

Author:

Wu, Kaiyi

Title:

Markov Chain Monte Carlo Methods and Applications

Area of Honors:

Mathematics

Keywords:

Markov Chain Monte Carlo
Adaptive method

File:

Download Kaiyi_Wu.pdf

Thesis Supervisors:

Ludmil Tomov Zikatanov, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Xiao, Yifei

Title:

Graph Observability: Definition, Condition and Algorithm

Area of Honors:

Mathematics

Keywords:

graph theory
observability
colored graphs
trackable graphs
graph algorithm

File:

Download Thesis_Yifei_Xiao.pdf

Thesis Supervisors:

Ting He, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Slocum, Samuel Thomas

Title:

A Model of Bank Behavior under Market, Credit, and Liquidity Risk

Area of Honors:

Mathematics

Keywords:

Economics
Banking
Numerical Analysis

File:

Download samuelslocum_thesis_vita.pdf

Thesis Supervisors:

Jenny Xiaoe Li, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Author:

Cassady, Connor Dane

Title:

The Riemann Hypothesis for Elliptic Curves over Finite Fields

Area of Honors:

Mathematics

Keywords:

Riemann Hypothesis
Finite Fields
Elliptic Curves
Number Theory

File:

Download Cassady_Connor_RiemHypElipCurves.pdf

Thesis Supervisors:

Mihran Papikian, Thesis Supervisor
Nathanial Patrick Brown, Thesis Honors Advisor

Author:

Luo, Weiyu

Title:

Boundary Operators Associated with Conformally Covariant Tri-Laplacian Operator

Area of Honors:

Mathematics

Keywords:

GJMS operator
Poincaré-Einstein manifold
Boundary operator
conformally covariant operator
fractional Laplacian
Sobolev trace inequality

File:

Download Luo_Weiyu_Boundary_Operator.pdf

Thesis Supervisors:

Jeffrey Steven Case, Thesis Supervisor
Sergei Tabachnikov, Thesis Honors Advisor

Author:

Minner, Lauren Jeanette

Title:

Elliptic Curves and Their Integration into an Existing Undergraduate Number Theory Course

Area of Honors:

Mathematics

Keywords:

mathematics
elliptic curves
number theory
finite fields
cryptography
cryptology

File:

Download Minner_Lauren_EllipticCurves.pdf

Thesis Supervisors:

Paul Becker, Thesis Supervisor
Daniel Joseph Galiffa, Thesis Honors Advisor

Author:

Dorabiala, Olga M

Title:

PREDICTIVE EFFECTIVENESS OF ON-DEMAND PRE-EXPOSURE PROPHYLAXIS TO PREVENT HIV

Area of Honors:

Mathematics

Keywords:

PrEP
HIV
pre-exposure prophylaxis
PK/PD Model
early infection model of HIV
on-demand PrEP
HIV virus dynamics
HIV disease prevention
pharmacokinetic-pharmacodynamic model
mathematical model of HIV

File:

Download master.pdf

Thesis Supervisors:

Dr. Jessica Conway, Thesis Supervisor
Dr. Diane Marie Henderson, Thesis Honors Advisor

Author:

Cotner, Sean Thomas

Title:

Diophantine Approximation and Complexity Measures

Area of Honors:

Mathematics

Keywords:

Diophantine approximation
Kolmogorov complexity

File:

Download Final_thesis.pdf

Thesis Supervisors:

Jan Severin Reimann, Thesis Supervisor
Anne Kirsten Eisentraeger, Thesis Honors Advisor

Author:

Falk, David Benjamin

Title:

DYNAMICS OF MINIMAL PERMITTED MOTIFS IN COMBINATORIAL THRESHOLD-LINEAR NETWORKS

Area of Honors:

Mathematics

Keywords:

CTLN
neural network
threshold linear
mathematical modeling
mathematical neuroscience
mathematical biology
minimal permitted motif
nonlinear dynamics
differential equations
graph theory
combinatorics
discrete mathematics
symmetry
neurons
clique union
cyclic union

File:

Download David_Falk_Thesis.pdf

Thesis Supervisors:

Carina Pamela Curto, Thesis Supervisor
Mark Levi, Thesis Honors Advisor

Author:

Keller, Jacob James

Title:

Intersection Theory

Area of Honors:

Mathematics

Keywords:

Algebraic Geometry
Intersection Theory
Enumerative Geometry

File:

Download KellerHThesisFinal.pdf

Thesis Supervisors:

Jack William Huizenga, Thesis Supervisor
Ludmil Tomov Zikatanov, Thesis Honors Advisor