Since Spring 2013, our department has offered a Thesis option to our Masters students. A thesis, unlike a project, consists on original research done by the student. Below are the theses our students have produced.

# Recent Theses

**Student: **Elizabeth Compton** Advisor: **Oscar Vega

**December 2019**

Graduation Date:

Graduation Date:

**Thesis Title:**The Power Graph of Split Metacyclic Groups

**Abstract:**Split metacyclic groups generalize the family of dihedral groups in a natural way. The power graph of a group is a refinement of the group lattice that focuses only on cyclic subgroups. This thesis characterizes the power graph of split metacyclic groups using exclusively group-theoretical tools.

**Student: **John Jimenez**Advisor: **Marat Markin**Graduation Date: **December 2019**Thesis Title:** On the Chaoticity of Rolewicz-Type Operators on Function Spaces**Abstract:** The chaoticity of Rolewicz-type linear operators on certain function spaces is proved
and their spectral structure is revealed.

**Student: **Edward Siche**l Advisor: **Marat Markin

**December 2019**

Graduation Date:

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**Thesis Title:**On Expansive Mappings and Non-Hypercyclicity

**Abstract:**We take a close look at the nature of expansive mappings on certain metric spaces (compact, totally bounded, and bounded), provide a finer classification for such mappings, and use them to characterize boundedness. We also furnish a simple straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator in a complex Hilbert space as well as of a certain collection of its exponentials.

# Past Theses

** Student: **Nathan Thom

**Oscar Vega**

**Advisor:****May 2019**

**Graduation Date:****Thesis Title:**The Veldkamp Space of W(p)

**Abstract:**Characterization of the Veldkamp space of the symplectic generalized quadrangle over a field of prime order. The points of this space are the geometric hyperplanes of W(p), and three points are collinear if all the pairwise intersections coincide.

**Student:** Anthony Vogt**Advisor:** Morgan Rodgers**Graduation Date:** May 2019**Thesis Title:** Using 2-ovoids to generate independent sets in W(q)**Abstract:** Investigation, using tools from geometry, algebra, graph theory and computer software,
of how 2-ovoids could be used to construct independent sets in graphs obtained from
the generalized quadrangle W(q).

**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.

**Student: **Sarah McGahan** Advisor:** Carmen Caprau

**May 2017**

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**A Categorical Model for the Virtual Singular Braid Monoid**

Thesis Title:

Thesis Title:

**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

**May 2017**

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**An Investigation of Power Sums of Integers**

Thesis Title:

Thesis Title:

**Student: **Jeffrey Park** Advisor:** Tamas Forgacs

**May 2016**

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**Bell Multiplier Sequences**

Thesis Title:

Thesis Title:

**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

**May 2016**

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**Polynomial Invariants for Virtual Singular Knots**

Thesis Title:

Thesis Title:

**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

**May 2016**

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**A Study of Projections of 2-Bouquet Graphs**

Thesis Title:

Thesis Title:

**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

**May 2016**

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**Investigation of the Topological Interpretation of Modal Logics**

Thesis Title:

Thesis Title:

**Student: **Jennifer Elder** Advisor:** Oscar Vega

**May 2016**

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**Generalizing the Futurama theorem**

Thesis Title:

Thesis Title:

**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

**May 2015**

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**The Well-covered Dimension of the Adjacency Graph of Generalized Quadrangles**

Thesis Title:

Thesis Title:

**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

**May 2015**

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**Multiplier Sequences of the Second Kind**

Thesis Title:

Thesis Title:

**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

**May 2014**

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**Spreads and Parallelisms**

Thesis Title:

Thesis Title:

**Study of partitions of the lines in a projective plane into lines that partition the points in such plane.**

Abstract:

Abstract:

**Student: **Katherine Urabe** Advisor:** Carmen Caprau

**May 2014**

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**The Dubrovnik Polynomial of Rational Knots**

Thesis Title:

Thesis Title:

**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.**

Abstract:

Abstract:

**Student: **Karen Willis** Advisor:** Oscar Vega

**May 2014**

Graduation Date:

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**Blocking Polygons in Finite Projective Planes**

Thesis Title:

Thesis Title:

**Study of configurations of points in a finite projective plane that do not allow the existence of polygons that are disjoint from such set.**

Abstract:

Abstract: