Since Spring 2013, our department offers a Thesis option to our Masters students. A thesis, unlike a project, consists on original research done by the student. Next we list the Thesis our department has produced.

Theses in Progress

Student: Richard Adams
Advisor: Khang Tran
Graduation Date: December 2018
Thesis Title: On hyperbolic polynomials and four-term recurrence with linear coefficients
Abstract: Study necessary and sufficient conditions for the hyperbolicity of polynomials satisfying a four-term recurrence whose first and third power coefficients are linear.

Past Theses

 

Student: Sarah McGahan
Advisor:
Carmen Caprau
Graduation Date: 
May 2017
Thesis Title: 
A Categorical Model for the Virtual Singular Braid Monoid

Abstract: Different approaches are used to study the algebraic structure of the virtual singular braid monoid.

 

Student: Nicholas Newsome
Advisor:
Maria Nogin and Adnan H. Sabuwala
Graduation Date: 
May 2017
Thesis Title: 
An Investigation of Power Sums of Integers

 

Student: Jeffrey Park
Advisor:
Tamas Forgacs
Graduation Date: 
May 2016
Thesis Title:
Bell Multiplier Sequences

Abstract: An investigation of sequences of real numbers, which - when viewed as linear operators on polynomials - preserve hyperbolicity of polynomials in the Bell basis.

 

Student: Kelsey Friesen
Advisor:
Carmen Caprau
Graduation Date: 
May 2016
Thesis Title:
Polynomial Invariants for Virtual Singular Knots

Abstract: Well-known polynomial invariants for classical knots are extended to virtual singular knots and the properties of the resulting polynomials are studied.

 

Student: Elaina Aceves
Advisor:
Carmen Caprau
Graduation Date: 
May 2016
Thesis Title: 
A Study of Projections of 2-Bouquet Graphs

Abstract: The concepts of trivializing and knotting numbers are extended from classical knots to spatial graphs and 2-bouquet graphs, in particular. The trivializing and knotting numbers for projections and pseudodiagrams of 2-bouquet spatial graphs are calculated based on the number of precrossings and the placement of the precrossings in the pseudodiagram of the spatial graph.

 

Student: Bing Xu
Advisor:
Maria Nogin
Graduation Date: 
May 2016
Thesis Title:
Investigation of the Topological Interpretation of Modal Logics

Student: Jennifer Elder
Advisor:
 Oscar Vega
Graduation Date: 
May 2016
Thesis Title: 
Generalizing the Futurama theorem
Abstract:Every permutation x can be written as a product of cycles that have not been used in the construction of x, as long as two new elements are incorporated in the transpositions. This results generalizes Keeler's Theorem A.K.A. The Futurama Theorem.

Student: Hillary Bese
Advisor:
 Oscar Vega
Graduation Date: 
May 2015
Thesis Title: 
The Well-covered Dimension of the Adjacency Graph of Generalized Quadrangles
Abstract: The well-covered space of the adjacency graph of the classical generalized quadrangle W_q is trivial, for every prime power q.

Student: David Heywood
Advisor:
 Tamas Forgacs
Graduation Date: 
May 2015
Thesis Title: 
Multiplier Sequences of the Second Kind
Abstract: An investigation of sequences of real numbers, which - when viewed as standard diagonal linear operators on polynomials - preserve the real rootedness of polynomials with only real zeroes of the same sign.

Student: Megan Kuneli
Advisor:
Oscar Vega
Graduation Date:
May 2014
Thesis Title:
Spreads and Parallelisms
Abstract:
Study of partitions of the lines in a projective plane into lines that partition the points in such plane.

Student: Katherine Urabe
Advisor:
Carmen Caprau
Graduation Date:
May 2014
Thesis Title:
The Dubrovnik Polynomial of Rational Knots
Abstract:
Finding a closed form expression for the Dubrovnik polynomial of a rational knot or link diagram in terms of the entries of its associated vector. The resulting closed form allows a Mathematica program which efficiently computes the Dubrovnik polynomial of rational knots and links.

Student: Karen Willis
Advisor:
Oscar Vega
Graduation Date:
May 2014
Thesis Title:
Blocking Polygons in Finite Projective Planes
Abstract:
Study of configurations of points in a finite projective plane that do not allow the existence of polygons that are disjoint from such set.