These digital collections include theses, dissertations, and faculty publications from the Department of Mathematics.

Collections in this community

Recent Submissions

  • Moduli spaces of rational graphically stable curves 

    Author(s):Fry, Andy J.
    Date Issued:2021
    Format:born digital; doctoral dissertations
    We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a ...
  • Generalizations of persistent homology 

    Author(s):McCleary, Alexander J.
    Date Issued:2021
    Format:born digital; doctoral dissertations
    Persistent homology typically starts with a filtered chain complex and produces an invariant called the persistence diagram. This invariant summarizes where holes are born and die in the filtration. In the traditional ...
  • Conjugacy extension problem, The 

    Author(s):Afandi, Rebecca
    Date Issued:2021
    Format:born digital; doctoral dissertations
    In this dissertation, we consider R-conjugacy of integral matrices for various commutative rings R. An existence theorem of Guralnick states that integral matrices which are Zp-conjugate for every prime p are conjugate ...
  • Topological, geometric, and combinatorial aspects of metric thickenings 

    Author(s):Bush, Johnathan E.
    Date Issued:2021
    Format:born digital; doctoral dissertations
    The geometric realization of a simplicial complex equipped with the 1-Wasserstein metric of optimal transport is called a simplicial metric thickening. We describe relationships between these metric thickenings and topics ...
  • k-simplex volume optimizing projection algorithms for high-dimensional data sets 

    Author(s):Stiverson, Shannon J.
    Date Issued:2021
    Format:born digital; doctoral dissertations
    Many applications produce data sets that contain hundreds or thousands of features, and consequently sit in very high dimensional space. It is desirable for purposes of analysis to reduce the dimension in a way that preserves ...
  • Combinatorial structures of hyperelliptic Hodge integrals 

    Author(s):Afandi, Adam
    Date Issued:2021
    Format:born digital; doctoral dissertations
    This dissertation explores the combinatorial structures that underlie hyperelliptic Hodge integrals. In order to compute hyperelliptic Hodge integrals, we use Atiyah-Bott (torus) localization on a stack of stable maps to ...
  • Wave propagation: laser propagation and quantum transport 

    Author(s):Bragdon, Sophia Potoczak
    Date Issued:2021
    Format:born digital; doctoral dissertations
    This dissertation consists of two independent projects, where wave propagation is the common theme. The first project considers modeling the propagation of laser light through the atmosphere using an approximation procedure ...
  • Persistence stability for metric thickenings 

    Author(s):Moy, Michael
    Date Issued:2021
    Format:born digital; masters theses
    Persistent homology often begins with a filtered simplicial complex, such as the Vietoris–Ripscomplex or the Čech complex, the vertex set of which is a metric space. An important result, the stability of persistent homology, ...
  • Arithmetic properties of curves and Jacobians 

    Author(s):Bisogno, Dean M.
    Date Issued:2020
    Format:born digital; doctoral dissertations
    This thesis is about algebraic curves and their Jacobians. The first chapter concerns Abhyankar's Inertia Conjecture which is about the existence of unramified covers of the affine line in positive characteristic with ...
  • Laplacian Eigenmaps for time series analysis 

    Author(s):Rosse, Patrick J.
    Date Issued:2020
    Format:born digital; masters theses
    With "Big Data" becoming more available in our day-to-day lives, it becomes necessary to make meaning of it. We seek to understand the structure of high-dimensional data that we are unable to easily plot. What shape is it? ...
  • Weak Galerkin finite element methods for elasticity and coupled flow problems 

    Author(s):Harper, Graham Bennett
    Date Issued:2020
    Format:born digital; doctoral dissertations
    We present novel stabilizer-free weak Galerkin finite element methods for linear elasticity and coupled Stokes-Darcy flow with a comprehensive treatment of theoretical results and the numerical methods for each. Weak ...
  • Comparing sets of data sets on the Grassmann and flag manifolds with applications to data analysis in high and low dimensions 

    Author(s):Ma, Xiaofeng
    Date Issued:2020
    Format:born digital; doctoral dissertations
    This dissertation develops numerical algorithms for comparing sets of data sets utilizing shape and orientation of data clouds. Two key components for "comparing" are the distance measure between data sets and correspondingly ...
  • Electrical impedance tomography with Calderón's method in two and three dimensions 

    Author(s):Shin, Kwancheol
    Date Issued:2020
    Format:born digital; doctoral dissertations
    Electrical impedance tomography (EIT) is a non-invasive imaging technique in which electrical measurements on the electrodes attached to the boundary of a subject are used to reconstruct the electrical properties of the ...
  • Two-field finite element solver for linear poroelasticity, A 

    Author(s):Wang, Zhuoran
    Date Issued:2020
    Format:born digital; doctoral dissertations
    Poroelasticity models the interaction between an elastic porous medium and the fluid flowing in it. It has wide applications in biomechanics, geophysics, and soil mechanics. Due to difficulties of deriving analytical ...
  • Success in Calculus I: implications of students' precalculus content knowledge and their awareness of that knowledge 

    Author(s):Sencindiver, Benjamin D.
    Date Issued:2020
    Format:born digital; doctoral dissertations
    High failure rates in Calculus I contribute to the course acting a filter, rather than a pump, for STEM disciplines. One often cited source of difficulty for students in Calculus I is their weak precalculus content knowledge. ...
  • Finitely generated modules over Noetherian rings: interactions between algebra, geometry, and topology 

    Author(s):Flores, Zachary J.
    Date Issued:2020
    Format:born digital; doctoral dissertations
    In this dissertation, we aim to study finitely generated modules over several different Noetherian rings and from varying perspectives. This work is divided into four main parts: The first part is a study of algebraic ...
  • Vietoris–Rips metric thickenings and Wasserstein spaces 

    Author(s):Mirth, Joshua
    Date Issued:2020
    Format:born digital; doctoral dissertations
    If the vertex set, X, of a simplicial complex, K, is a metric space, then K can be interpreted as a subset of the Wasserstein space of probability measures on X. Such spaces are called simplicial metric thickenings, and a ...
  • Supporting and empowering students in online pre-calculus 

    Author(s):Golden, Shannon Nicole
    Date Issued:2020
    Format:born digital; masters theses
    The Paced Algebra to Calculus electronically Program (PACe) offers pre-calculus through five 1-credit courses in a fully online and mastery-based setting. The mathematics department at Colorado State University realized ...
  • Metric thickenings and group actions 

    Author(s):Heim, Mark T.
    Date Issued:2020
    Format:born digital; masters theses
    Let G be a group acting properly and by isometries on a metric space X; it follows that the quotient or orbit space X/G is also a metric space. We study the Vietoris–Rips and Čech complexes of X/G. Whereas (co)homology ...
  • Three projects in arithmetic geometry: torsion points and curves of low genus 

    Author(s):Camacho-Navarro, Catalina
    Date Issued:2019
    Format:born digital; doctoral dissertations
    This paper is an exposition of three different projects in arithmetic geometry. All of them consider problems related to smooth curves with low genus and the torsion points of their Jacobians. The first project studies ...

View more