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.

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

### Exams

• Exam 3 will be an in-class exam on Wednesday Nov 28.

### Homework:

NOTE: I will not accept homework submitted without a .tex, .pdf, and all supporting figures (no .aux, .log, nor .syntex.gz are needed).
• Homework 11: Read Chapter 8. Do all problems whose number is a perfect number, a multiple of a perfect number, or one more than a Mersenne Prime.[Due Monday Nov 12]
• Homework 12. Read Chapter 9. Do all problems whose number is congruent to 2 (mod 4).[Due Monday Nov 26]
• Homework 13. Read Chapter 10. Do all problems that are in the Fibonacci sequence.[Due Monday Nov 26]
• Homework 14. Read Chapter 11. Do the following problems: pg 178 2, 4, 12, pg 183 2, 8, 14, 16, pg 187 2, 8, 12, pg 190 2 pg 194 2, 8. [Due Wednesday Nov 28]
• Homework 15. Read Chapter 12. Do the following problems: pg 200 2, 6, pg 204-205 4, 10, 16, pg 210 2, 6, 8, pg 214 2 (prove it though since you haven't yet), 6 (prove that it is indeed a bijection also), pg 216 2, 6, 12 [Due Monday Dec 3]

### Past Homework

• Homework 10: Rewrite Exam 2 proofs clearly and correctly. Be sure to incorporate my help. [Due Wednesday Nov 7]
• Homework 9: Read Ch 6 and 7. HW: Chapter 6: N=118 and Chapter 7: N is in {129,130}, the Homework problems are in the set
{n|n is even and n is in the set P(N)},
where P(N)={p|p is a problem on page N and if N=118, then p is not 20 nor 22}
All problems not completed in class should be turned in via LaTeX [Due Friday October 26]
• Homework 8: Chapter 5 pg 110 {n|n is even and n is less than 13} Homework 8 Added Problems (PDF)(tex) [Due Wednesday Oct 17]
• Homework 7 (PDF)(tex) [Due Wednesday Oct 10]
• Homework 6 (PDF)(tex) [Due Wednesday Sep 26]
• Homework 5 (PDF)(tex) [Due Wednesday Sep 19]
• Homework 4 (PDF)(tex) [Due Wednesday Sep 12]
• Homework 3 (PDF) (tex) [Due Wednesday Sep 5]
• Homework 2 [Due Wednesday Aug 29]
• Homework 1 [Due Wednesday Aug 22]

## 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.

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

### Exams

• Exam 3 will be this week, next week, or there will be no Exam 3, just a final. Decide and email me before class tomorrow.

### Homework

• Reading Assignment Chapter 7a (pdf)(tex)[Due November 13]
• Coursework Chapter 7a (pdf)[Due November 13]

## 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.

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

## Fourier Analysis

Description Needed

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

### Homework

(Check this regularly. I like adding to this list.):
• Read 3.1 and 3.2 and do pg 67 1, 2,4, pg 71, 1, 4,7
• Finish the things above and read 3.3. Also, recall from Linear Algebra what we are getting when we are projecting a vector onto another and also when we project a vector onto a space.
• Fourier Series code

### Past Homework

• Finish reading Chapter 2 and then use Matlab/Octave to plot several partial sums (choose several values of N (be sure to choose large ones) and plot a new function each time) for the Fourier series given in Table 1 pg 26. Do this for functions, 1, 2, 5, 6, 8, 10. What do you notice? For which functions do you see Gibbs phenomenon? Why?
• Read about Piecewise continuous and Piecewise smooth. Return to your Linear Algebra and recall what information you can obtain when finding projections. Do these problems: pg 37: 1, 4, 5, 6
• 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

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.