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

  • Thomas J. Asaki and HM "Anisotropic Variation Formulas for Imaging Applications." AIMS Mathematics, 2019, No. 3.PDF
  • 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.

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

Exams

  • The Final Exam is: Monday Dec 9

Matlab/Octave Code

Homework:

Be sure to ask me questions in advance.

Past Homework

LaTeX, R, and Matlab

This course provides students some exercises to better their skills in LaTeX, R, and Matlab

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

Homework

Integrated Science

This course is a team-taught, place-based course designed to provide an introduction to multiple scientific disciplines, including biology, chemistry, computer science, earth science, mathematics, and physics around the theme of the greater Lewiston-Clarkston valley watershed. Course content is integrated in order to allow the students the opportunity to use multiple scientific disciplines to understand the world in which they live. Weekly laboratories will be used to provide students with hands on learning experiences that directly related to the topics covered in lecture and may include field experiences. The course will include emphasis on college reading, college writing, collaboration, and using math to solve real world problems. This course is designed for science majors who place into intermediate algebra, however, any student is welcome to contact the instructor(s) for permission to enroll in the course.

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

Class Assignments and Labs

  • Don't forget to email me telling me you saw this before noon on Tuesday Aug 20.

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 2: Read Ch 1 Sections 7. Do: 1.7: 1, 2, 3, 4,5,6,8,10,11 [Due Friday February 15]

Past Homework

  • Homework 2: Read Ch 1 Sections 5,6. Do: 1.5:1,2,3,5,7,9,10; 1.6:1, 4, 5,7,8 [Due Wednesday Jan 30]
  • 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.

Below are links and info

Links: