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

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  • 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 ...
  • Mechanism-enabled population balances and the effects of anisotropies in the complex Ginzburg-Landau equation 

    Author(s):Handwerk, Derek
    Date Issued:2019
    Format:born digital; doctoral dissertations
    This paper considers two problems. The first is a chemical modeling problem which makes use of ordinary differential equations to discover a minimum mechanism capable of matching experimental data in various metal nanoparticle ...
  • Methods for network generation and spectral feature selection: especially on gene expression data 

    Author(s):Mankovich, Nathan
    Date Issued:2019
    Format:born digital; masters theses
    Feature selection is an essential step in many data analysis pipelines due to its ability to remove unimportant data. We will describe how to realize a data set as a network using correlation, partial correlation, heat ...
  • Enacted responsiveness and responsiveness as a disposition: leveraging and valuing student thinking 

    Author(s):Gehrtz, Jessica R.
    Date Issued:2019
    Format:born digital; doctoral dissertations
    Over the past few decades there has been increased attention on instructional practices that incorporate and build on student thinking. To effectively implement these practices, it is essential for an instructor to demonstrate ...
  • Generic support vector machines and Radon's theorem 

    Author(s):Carr, Brittany M.
    Date Issued:2019
    Format:born digital; masters theses
    A support vector machine, (SVM), is an algorithm which finds a hyperplane that optimally separates labeled data points in Rn into positive and negative classes. The data points on the margin of this separating hyperplane ...
  • Improved stick number upper bounds 

    Author(s):Eddy, Thomas D.
    Date Issued:2019
    Format:born digital; masters theses
    A stick knot is a mathematical knot formed by a chain of straight line segments. For a knot K, define the stick number of K, denoted stick(K), to be the minimum number of straight edges necessary to form a stick knot which ...
  • Adaptation of K-means-type algorithms to the Grassmann manifold, An 

    Author(s):Stiverson, Shannon J.
    Date Issued:2019
    Format:born digital; masters theses
    The Grassmann manifold provides a robust framework for analysis of high-dimensional data through the use of subspaces. Treating data as subspaces allows for separability between data classes that is not otherwise achieved ...
  • Properties of tautological classes and their intersections 

    Author(s):Blankers, Vance T.
    Date Issued:2019
    Format:born digital; doctoral dissertations
    The tautological ring of the moduli space of curves is an object of interest to algebraic geometers in Gromov-Witten theory and enumerative geometry more broadly. The intersection theory of this ring has a highly combinatorial ...
  • Recovery of organ boundaries in electrical impedance tomography images using a priori data, optimization, and deep learning 

    Author(s):Capps, Michael
    Date Issued:2019
    Format:born digital; doctoral dissertations
    In this thesis we explore electrical impedance tomography (EIT) and new aspects of the solutions to the inverse conductivity problem. Specifically we will focus on new methods for obtaining additional information from ...

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