About Past Research Real Calculus Linear Optimization COV

About Me

I received my PhD in Mathematics at Washington State University in April 2013. Prior to finishing my PhD, I took 6 years off from graduate school. During that time I worked at Walla Walla Community College as the Director of Instructional Support and as an adjunct Math Instructor. I also spent one year teaching High School in a small town called Helix, Oregon. I even spent a semester at the University of Miami in Florida (which was so not my favorite place to live). I received my Master's Degree in Mathematics from Kansas State University in 2000 and I received my Bachelor's Degree in Mathematics (with a Physics minor) from Eastern Oregon University in 1998.

I love the outdoors. In fact, each of the background pictures is a place outdoors that I loved so much I had to capture with my camera. One day, I want to go backpacking in the wild for at least a month. That would be my dream vacation. I also love sports: running, soccer, volleyball, snowshoeing, skating (ice and roller).. but I'm not great at any. I also crochet, but just for fun. I love to Batik. I'm sure you've seen some of my work.

My Research

Interests

  • Calculus of Variations and variational techniques for real data
  • Partial Differential Equations
  • Pure and Applied Analysis
  • Nonsmooth Analysis and Optimization

Publications

  • HM and Thomas J. Asaki "A Finite Hyperplane Traversal Algorithm For 1-Dimensional $L^1pTV$ Minimization, For $0< p\leq 1$." COAP Vol. 61(3). PDF
  • Matthew B, Rudd and HVD, "Median Values, 1-Harmonic Functions, and Functions of Least Gradient." CPAA March 2013. PDF
  • HVD, Kevin R. Vixie, and Thomas J. Asaki, "Cone Monotonicity: Structure Theorem, Properties, and Comparisons to Other Notions of Monotonicity." Abstract and Applied Analysis. Vol 2013. Hindawi Pub. Corp., 2013. PDF
  • HVD, "A Study of $p$-Variation and the $p$-Laplacian for $0< p\leq 1$ and Finite Hyperplane Traversal Algorithms for Signal Processing." Dissertation May 2013. PDF

Real Analysis

This course is the first course in a two‐course sequence that provides a theory of the real line, properties of real numbers, and real‐valued functions. Topics include convergence of sequences; open and closed sets; density of sets; Cauchy sequences; monotone convergence theorem; pointwise and uniform convergence of functions; continuity; mean value theorem; intermediate value theorem; compactness; and differentiability.

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Linear Algebra

This course provides tools that are useful in physics, engineering, natural sciences, economics and social sciences, and further study in mathematics. Topics include systems of equations, vector and vector spaces, linear operators, basis, change of basis, invertible matrix theorem, determinants, eigenvalues, and eigenvectors.

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  • Syllabus
  • Before the first class, fill out the survey in the email that I sent.
  • Read Chapter 1 Homework: pg 25-26, Exercises 1-7 [DUE: Monday Jan 22]
  • Read Chapter 2 Lab: pg 32-36, Exercises 1-12[Due Wednesday Jan 25]
  • Read Chapter 3 Homework: pg 54-55, Exercises 1,3,5,6,8,12,14

Calculus 3

This course provides students with the tools to perform calculus on functions of several variables. This is the third course in a three‐course sequence. This class is intended for students in engineering, mathematics, and the sciences. Topics include vector algebra and geometry; functions of several variables; partial and directional derivatives; the gradient; the multivariable chain rule; optimization; multiple and iterated integrals; parametric curves and surfaces in 3‐dimensions; vector fields; divergence and curl; line and surface integrals; Green’s theorem; Stokes’ theorem; and the divergence theorem.

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Optimization

This course will cover the optimization techniques used to model and solve problems from various disciplines such as business, engineering, sciences, sports, .... In this course students will be introduced optimization methods for linear and integer programming optimization methods. We will emphasize techniques that expand your understanding of Calculus concepts as well as how to formulate a model; interpret problems mathematically and geometrically; solution techniques in cases where Calculus cannot be used. We will also emphasize the theory behind solution techniques; sensitivity analysis; and how to use Octave/Matlab to solve problems.

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Software Code

Below are the links for provided code that can be used on Matlab or Octave (or octave-online.net) that solves any mixed-integer program (linear programs with possibly some integer variable constraints). The relevant files you will need are here: mip.m, ShowSolution.m , myexample.m and classexample.m.

Calculus of Variations

This course will cover techniques and theory of the Calculus of Variations. In particular, we will look at the theory related to partial differential equations, real analysis, and functional analysis. We will also look at how the Calculus of Variations is used in Image Analysis. This course is an independent study course.

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  • Syllabus
  • For Tuesday Jan 23: Read Chapters 0: Prepare a 20 minute overview of what you read. All questions that arise should be part of this overview.
  • For Tuesday Jan 30: Read Chapter Ch 1 Sections 1 and 2 and do the Exercises. Prepare a presentation of this.