Research

Metric Geometry:

  Continuous Dynamics on Metric Spaces
(1.8MB) Version 1.0   Book exploring very general
dynamical systems, 185 pages
     
  Foliating Metric Spaces
      Generalized Frobenius' Theorem

  Generating Flows on a Metric Space
(with David Bleecker, U of Hawaii)
 Journal of Mathematical Analysis and Applications,  248, pp. 645-677 (2000)    
 Generalization of the well-posedness of ODEs

  Metric Coordinate Systems
(with Axel Boldt, Michael Green, and David Bleecker)
   Communications in Mathematical Analysis, 6 (2009), No. 2, pp. 79-108.   

  University of Hawaii Thesis: Arc Fields


Analysis:

  Lipschitz Flow-box Theorem (with Axel Boldt)
Journal of Mathematical Analysis and Applications,  338, 2, pp. 1108-1115 (2008)

  Linear Combinations of  Gaussians with a Single Variance are Dense in L^{2
The 2008 International Conference of Applied and Engineering Mathematics (ICAEM)}

  Approximating with Gaussians (with Axel Boldt)
New families of non-orthogonal approximating functions



Fractals:
  Movies

I think that modern physics has definitely decided in favor of Plato.  In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.                        --Werner Heisenberg

Courses

Math 101: Exploring Functions

Math 110: Math for Liberal Arts
  Syllabus and Homework Wed. Spring '09
  Syllabus and Homework Fri. Spring '09 

Math 115:  College Algebra
  1st Day Review (do these problems before coming to class)
  Syllabus and Homework

Math 210: Calculus I
  Syllabus and Homework

Math 211: Calculus II
  Syllabus and Homework

Math 215: Discrete Mathematics
  Syllabus and Homework

Math 251: Intro to Probability and Statistics

Math 301: Introduction to Analysis
  Syllabus and Homework

Math 310: Multivariable Calculus
  Syllabus and Homework

Math 315: Linear Algebra
  Syllabus and Homework

Math 340: Mathematical Modeling

Math 350: Ordinary Differential Equations
  Syllabus and Homework

Math 370: Modern Geometry
  Syllabus and Homework

Math 405: Partial Differential Equations
  Syllabus and Homework

Math 420: Numerical Analysis
  Syllabus and Homework

Math 450: Operations Research
  Syllabus and Homework

Math 471: Abstract Algebra
  Syllabus and Homework

Math 499: Senior Seminar

Independent Studies:
  Point Set Topology
  Real Analysis
  Complex Analysis
  Dynamical Systems


Zhejiang Normal University, Jinhua China (Sabbatical 2006-7)
  Functional Analysis
  Algebra
  Space Analytic Geometry
  Differential Equations

                     My wife's photos from our family's stay in China