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

Intro To Math Reasoning

This course is a first course in logic and proof writing. The course helps transition students to theoretical courses in mathematics. Topics include logic, set theory, counting proofs, mathematical induction, direct proofs, proof by contradiction, and notions of infinity.

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Homework:

NOTE: I will not accept homework submitted without a .tex, .pdf, and all supporting figures (no .aux, .log, nor .syntex.gz are needed).

Past Homework

Differential Equations

This course will focus on solving differential equations and modeling real‐world phenomena using differential equations. Students will develop techniques to solve differential equations, including separation of variables, variation of parameters, method of characteristic roots, undetermined coefficients, power series, and Laplace transforms.

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Code

Homework

Past Homework

PreCalculus

This course combines MATH 147A and MATH 147B into a single course. Topics covered in this course include polynomial functions (division of polynomials, zeros of polynomial functions, complex numbers, the fundamental theorem of algebra), rational functions, exponential functions, logarithmic functions, and elementary matrix operations. Both the right‐triangle and unit‐circle approaches to trigonometry are covered along with trigonometric identities, graphs of trigonometric functions, solving trigonometric functions, the law of sines, the law of cosines, vectors, and polar coordinates.

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Homework

Past Homework

Fourier Analysis

Description Needed

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Homework

(Check this regularly. I like adding to this list.):
  • Read the Chapter 2. Do problems and be ready to present them to me.

Past Homework

  • Read the first chapter. Do the following problems
    • 1.2: 5
    • 1.3: 1,7
    • 2.1: Exercises pg 31
    • 2.2: 2, 4, 5
    and be ready to present them to me.

Info For Reasearch Students

Maybe I'll put things here.

Below are links and info

Links: