Graduate Student Presentations

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Math Graduate Student Presentations


Spring Semester 2018

Date Speaker Title / Abstract
April 30, 2018 12:15pm
ENG 239
Allison Donahue TITLE:  Topology of Cantor Sets 

ABSTRACT: PDF
Date Speaker Title / Abstract
April 13, 2018 Meng Li TITLE:  A Simulation on Campus Pedestrian Traffic 

ABSTRACT: With the ever-growing population of university campuses, the understanding of pedestrian flow throughout them becomes more and more important as time goes on. In this project aim to model the paths that people on a university campus will take to get from one place to another. The project simulates the UCCS campus pedestrian traffic based on the data from Fall 2014. The project also addresses the path choosing processes considering the capacities of each available paths on UCCS main campus. The model considers the idle students locations with stochastic approach.
Date Speaker Title / Abstract
April 13, 2018 Justin Garrish TITLE:  Radial basis function-generated finite differences (RBF-FDs): supplementation with polynomials and application to a steady-state flow problem 

ABSTRACT: RBF-FD methods have been gaining popularity to approximate solutions of partial differential equations due to their combination of simplicity, accuracy, and flexibility, especially in irregular geometries. That being said, direct substitution of RBFs for traditional basis functions (e.g. cubic splines) is not enough to guarantee accurate or stable computational solutions. Supplementation of RBF-FD with polynomials will be presented as an approach to overcome these shortcomings, and the impact of polynomial degree on its efficacy will be illustrated on a benchmark problem. A modern approach to domain discretization permitted by this method will be demonstrated. In particular, we apply RBF-FD with supplementary polynomials to the compressible Euler equations in order to simulate two-dimensional steady-state flow around an object enclosed in a tube.

Math Graduate Student Presentations


Spring Semester 2017

Date Speaker Title / Abstract
April 7, 2016 12:00-1:30pm
OSB A215
Tommy McDowell TITLE:  Numerical Study of the Stem in 3142-Soliton Solution of KP 

ABSTRACT: PDF

Math Graduate Student Presentations


Spring Semester 2016

Date Speaker Title / Abstract
April 7, 2016 12:00pm OSB A327 Ikko Saito TITLE: Traceless Matrices that are not Commutators which each equivalence class contains a unique possessing these ABSTRACT: By a classical result, for any field F and a positive integer n, a matrix Mn(F) is a comumutator if and only if it has trace zero. This is no longer true if F is replaced with an arbitrary ring R. But the only known example of matrices which have trace zero and are not commutators are of the size 2x2. The purpose of this thesis is to construct an nxn matrix for any positive integer n>2 which has trace zero but is not a commutator.
April 7, 2016 1:00pm OSB A327 Katherine Cliff TITLE: An Introduction to Information Geometry equivalence mentation class contains a unique possessing these ABSTRACT: Information Geometry is the application of differential geometry to probability theory. After introducing the basic notation and vocabulary of information geometry, we will examine some fundamental results relations to the asymptotic theory of information and the relationships between statistical manifolds

Math Graduate Student Presentations


Spring Semester 2015

Date Speaker Title / Abstract
September 22, 2015 12:30pm-1:00pm ENG 239 Reece Adragna TITLE: An Introduction to Information Geometry equivalence mentation class contains a unique possessing these ABSTRACT: Information Geometry is the application of differential geometry to probability theory. After introducing the basic notation and vocabulary of information geometry, we will examine some fundamental results relations to the asymptotic theory of information and the relationships between statistical manifolds

Math Graduate Student Presentations


Spring Semester 2016

Date Speaker Title / Abstract
July 16, 2015 Luke Harmon TITLE: A set-theoretic foundation of mathematical induction ABSTRACT: We will use Godel-Bernays set theory, with the 'standard' axiom of infinity replaced by Tarski's infinity axiom, to rigorously construct the set of natural numbers. This construction will then be used to justify the ubiquitous Induction Principle.
August 6, 2015 Kathryn Arthur TITLE: Markov Chains

Math Graduate Student Presentations


Spring Semester 2013

Date Speaker Title / Abstract
December 17, 2013 Henri Ndaya Coding Theory - Error correcting codes: A special look at the Reed-Muller Codes ABSTRACT:The purpose of my presentation is to focus on linear codes and conclude with a special look at a family of codes (the Reed-Muller Codes) defined recursively with interesting properties and easy code decoding algorithms.

Math Graduate Student Presentations


Spring Semester 2013

Date Speaker Title / Abstract
April 25, 2013 Robert Marion Method of Multiple Scales with an Application to Water Waves
April 25, 2013 Katie Hendricks Algebraic Topology: Fundamental Groups
April 25, 2013 Andrea Essler Linear Programming The Simplex Method
April 25, 2013 Gaetan Delavignette Modeling the Risk of Cancer
April 25, 2013 Kevin Ewing The Richardson Arms Race Model-An Elementary Analysis and a Nonlinear Modification
April 25, 2013 Ben Schoonmaker An Examination of the K0 Groups of the Leavitt Path Algebras of some Cayley Graphs

Math Graduate Student Presentations


Fall Semester 2012

Date Speaker Title / Abstract
Dec 6, 2012 David England Psudospectral Methods for Optimal Control
Dec 6, 2012 Joshua Carnahan Nelder-Mead Method and Applications

Math Graduate Student Presentations


Spring Semester 2012

Date Speaker Title / Abstract
April 18, 2012 James Parmenter Graphs of Leavitt Path Algebras: e A natural equivalence relation on finite acyclic directed graphs arises from the graded isomorphisms between finite dimensional Leavitt path algebras. We will identify graph-theoretic properties for which each equivalence class contains a unique possessing these properties.
May 1, 2012 Tracey Moreland Gravitational Effects on Blood Flow Velocity: How fast does blood flow through the arteries with each heart beat? In this presentation I will look at Womersley flow, a classical approach to calculating blood flow velocity. This approach assumes flow through a rigid tube, and uses concepts from fluid mechanics to model the flow velocity. Bessel functions and the Navier-Stokes equations are used in the model, and Fourier series are used to model the pressure gradient function. I will also examine an extension to the model to include gravitational effects on blood flow. Results will be given for various gravitational fields and for different animals.
May 1, 2012 Jim Eberle Abstract: When data is transmitted via satellite, or when you use a CD, errors can occur in the process of getting the data to you. When it is important that the data is correct, an error correction code must be embedded in the data. One of the popular means of encoding and decoding is "Convolutional Error Correcting Codes". These codes will be discussed in how data can be encoded and decoded, and how these codes are used.

Math Graduate Student Presentations


Spring Semester 2011

Date Speaker Title / Abstract
April 28, 2011 Markus Tyboroski An overview of the finite element method
April 28, 2011 Richard Neely The Statistics Behind Cancer

Math Graduate Student Presentations


Spring Semester 2010

Date Speaker Title / Abstract
May 5, 2010 Jennifer Holmes Brownian Motion and the Counterintuitive Aspects of Arcsine Law
May 5, 2010 McKenna Roberts Evaluation of parameter effects in estimating non-linear uncertainty propagation

Math Graduate Student Presentations


Fall Semester 2009

Date Speaker Title / Abstract
Nov 13, 2009 Steve Hartman Properties of the Hyperbolic Area Function

Math Graduate Student Presentations


Spring Semester 2009

Date Speaker Title / Abstract
April 23, 2009 Matt Gerholdt Modeling the Chaotic Waterwheel
April 23, 2009 Merida Bass Imaginary Numbers: A History
April 23, 2009 Joseph Montgomery Moving Frames In Differential Geometry
May 5, 2009 Robyn Macivor Using Fractals to Study the Structure of Trees
May 5, 2009 Jason Ocvirk Stochastic Processes with Sports Standings
June 16, 2009 Jeremy Riehl Elliptical Geometry: A Closer Look

Math Graduate Student Presentations


Spring Semester 2008

Date Speaker Title / Abstract
April 24, 2008 Brian White An introduction to the field of game theory, focusing on two person, zero-sum games with a short proof of von Neumann's Minimax Theorem
April 24, 2008 Mihalo Popovic Topology of Pointwise Convergence of Sequences of Real Functions. (An example of non-metrizable topology)
April 24, 2008 Jeff Marsh The Kuramoto Model
May 2, 2008 Dustin Keck The “Art” of Algebraic Groups and Tessellations

Math Graduate Student Presentations


Summer Semester 2007

Date Speaker Title / Abstract
July 2, 2007 Dustin Schmidt Effects of Selection on Information Entropy in a Weasel Program

Math Graduate Student Presentations


Spring Semester 2007

Date Speaker Title / Abstract
April 24, 2007 Travis Spero Macroscopic Traffic Modeling
April 19th, 2007 Eric Sullivan Mathematics on the Rocks
May 1, 2007 Shane Passon Methods of Control