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

## 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.

Below are links for this course (Be sure to refresh the page)

### Homework:

Be sure to ask me questions in advance. I will not answer questions the night before any homework is due.
• Read Chapter 2 and do exercises 1-12 (Due Wednesday January 23 at the start of class)
• Read Chapter 3 and do exercises 1-14 (Due Friday January 25 at the start of class)

### Past Homework

• Read Chapter 1 and do exercises 1-7 (Due by email on Wednesday January 16th at noon)

## Preparation for Linear Algebra (Math 290 Students Only)

For each reading assignment, you will write a brief paragraph telling me what you learned and a paragraph or several telling me what isn't clear. Due dates for these responses are below.
• Read Section 1.1 and 1.2 [Due Friday Jan 18]
• Notes for questions on 1.1 and 1.2
• Read Section 1.3 and 1.4 [Due Friday Jan 25]
• Read Section 1.5 and 1.6 [Due Friday Feb 1]
• Read Section 1.7 and 1.8 [Due Friday Feb 8]
• Read Section 1.9 and 1.10 [Due Friday Feb 15]
• Read Section 1.11 and 2.1 [Due Friday Feb 22]

### Homework

These problems come from the textbook.
• 1.1: 2, 4, 6, 10, 16, 18,22, 25,30; 1.2: 2, 4, 14, 18, 23,24,33 [Due Wednesday Jan 23]
• 1.3:2, 4, 6, 8, 10, 12, 14, 18, 20, 22;1.4: 4, 6, 8, 12, 14, 20, 22, 30 [Due Wednesday Jan 30]

## 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.

Below are links for this course (Be sure to refresh the page)

### Homework

Be sure to ask questions in advance. I will not take questions the evening before the homework is due.
• Homework 2 (Due January 24 at the beginning of class)
• Homework 3 (Due January 28 at the beginning of class)
• Homework 4 (Due January 29 at the beginning of class)
• Homework 5 (Due January 30 at the beginning of class)
• Jan 28 In Class assignment
• Homework 6 (Due January 31 at the beginning of class)

## Partnering With Industry

This course will link students with industrial partners in our community. The course will strenthen skills necessary for success as a mathematician in non academic careers.

Below are links for this course (Be sure to refresh the page)

The Math 490 professor is Dr. Tom Asaki.

First Day Stuff

## Differential Geometry

In this class, students will get an introduction in the area of differential geometry. By the end, students should know the basic theory and notation. Students should also know how to do computational tasks in differential geometry.

Below are links for this course (Be sure to refresh the page)

### Homework

(Check this regularly. I like adding to this list.):
• Homework 1: Read Ch 1 Sections 1-4. Do: 1.1: 1,4; 1.2: 1,3,4,5; 1.3: 1-5;1.4:1,3,4,9 [Due Wednesday Jan 23]

## Info For Reasearch Students

This is the page to find out what my students have done (this will come later) and if you are my student, what I expect this week.