# Curriculum Vitae

#### Skills

- Expert knowledge of mathematics and its applications. Strong problem-solving skills. Extensive experience in teaching undergraduate mathematics.
- Programming experience in C/C++, Visual Basic, and Mathematica.
- Familiarity with Windows and Linux operating systems. Basic knowledge of computer hardware. Experience using Microsoft Office.
- Excellent command of written and spoken English. Proficient in German.

#### Education

- Ph.D. Mathematics, University of California, Santa Cruz, CA. 1989.
- M.A. Mathematics, State University of New York, Stony Brook, NY. 1982.
- B.A. Mathematics, University of California, Santa Cruz, CA. 1980.

#### Research Interests

Aspects of differential geometry and mathematical physics, including the geometry of homogeneous and symmetric spaces, classical surface theory, nonlinear partial differential equations and integrable systems, and the discretization of differential geometric structures and related dynamics. Applications and interdisciplinary research.

#### Teaching Experience

*Online tutoring.*

Abstract algebra, linear algebra, calculus, real and complex analysis, functional analysis, special functions, probability and statistics, ordinary differential equations, point-set and algebraic topology, differential geometry, general relativity, middle school competition mathematics.*Upper-division undergraduate courses.*bstract algebra, linear algebra, probability and statistics, mathematical analysis, ordinary differential equations, partial differential equations, complex variables and transforms, history of mathematics.

A*Lower-division undergraduate courses.*

Intermediate algebra, college algebra, trigonometry, precalculus, calculus, introduction to computer programming.*Middle school & high school level mathematics.*

Competition-based instruction in algebra, combinatorics, number theory, probability, and geometry.

#### Professional Experience

*President, Mathematical Synergistics LLC, Aberdeen, SD 57401; July 2012-Present.*Engaged in online tutoring, technical proofreading, and

*Mathematica*consulting.*Faculty, Math Zoom Academy, Irvine, CA 92604; June 2013-July 2013.*Taught mathematics and problem-solving skills to middle school and high school students at Math Zoom Academy Summer Camp at Yale University, New Haven CT. This was an intensive teaching environment that required six contact hours per day for three weeks. Topics included algebra, combinatorics, number theory, probability, and geometry at a level appropriate for MATHCOUNTS, AMC 8, AMC 10, and AMC 12 level mathematics competitions.

*Visiting Faculty, University of Calgary, Calgary, Canada; September 2011-April 2012.*

Engaged in research on the geometry of space curves. This research resulted in a

coauthored paper that is currently under review for publication.*Assistant Professor, Khalifa University, Sharjah, UAE; February 2010-June 2011.*

Taught courses in calculus, ordinary differential equations, and complex variables

and transforms. Coordinated course content alignment and authorship of intercampus uniform finals. Engaged in research on aspects of signal processing, which resulted in a coauthored paper that has been published in a peer-reviewed

journal.*Assistant Professor, Department of Mathematics, Northern State University, Aberdeen, SD; August 2003-January 2010.*

Taught lower-level courses in intermediate algebra, college algebra, trigonometry, precalculus, and calculus. Taught upper-level courses in linear algebra, abstract algebra, probability and statistics, and the history of mathematics. Engaged in research and co/authored two articles that were published in peer-reviewed journals.*Postdoctoral Research Associate, Center for Bioinformatics, Stowers Institute for Medical Research, Kansas City, MO; January 2002-August 2003.*Conducted basic research into the statistical distribution of words in bacterial genomes. Provided statistical data analysis and programming support for resident research biologists. Used

*Mathematica*for data analysis and algorithm prototyping. Implemented algorithms in C++.*Adjunct Faculty, Department of Mathematics, University of Missouri, Kansas City, MO; September 2001-December 2001.*

Taught course in trigonometry.*Adjunct Faculty, Computer and Information Systems, Johnson County Community College, Overland Park, KS; July 2001-August 2001.*

Taught introductory course in Visual Basic.*Consultant, Wimmer Systems, Independence, MO; November 1998-December 1999.*

Developed RSA-based public key encryption software for implementation in*DaCS*, a software package for providing^{TM}*Microsoft Excel*with*21 CFR 11*compliant electronic signature authentication and security. Provided guidance on software system design and documentation.*Programmer/Software Engineer, Petroleum Science Corporation, Prairie Village, KS; October 1995-December 2001.*

Designed algorithms for automatic curve fitting of gas/oil production data and well

pressure test data. Implemented algorithms in softPetroleum Appraiser (TM). Designed and implemented object-based program for rendering two-dimensional plots of well fluid data. This program is an integral part of softPetroleum Operator (TM).*Lecturer, Department of Mathematics, University of the West Indies, Kingston,*

*Jamaica; February 1992-June 1994.*

Taught courses in mathematical analysis, ordinary differential equations, and partial differential equations. Coauthored book chapter.*Postdoctoral Research Associate, Department of Mathematics, University of Technology, Berlin, Germany; September 1989-February 1992.*

Engaged in basic research and coauthored article that was published in a peer reviewed journal.

#### Publications

**Book Chapters**

- M. Melko and I. Sterling,
*Integrable systems, harmonic maps and the classical theory of surfaces,*in Harmonic maps and integrable systems, edited by Allan P. Fordy and John C. Wood, Vieweg :129–144, 1994.

##### **Journal Articles**

- Larry M. Bates and O. Michael Melko,
*On curves of constant torsion I.*Journal of Geometry, 104(2):213-227, 20 July 2013. - Luis Weruaga and O. Michael Melko,
*Asymptotic Cramer-Rao bound for noise-compensated autoregressive analysis,*IEEE Transactions on Circuits and Systems I, 59(9):2017-2024, 2012. - O. Michael Melko,
*Visualizing minimal surfaces: rendering solid models with the aid of 3D printers,*The Mathematica Journal 12:1-28, 2010. - O. Michael Melko and Luc Patry,
*A simple grammar for generating cocompact Fuchsian groups,*International Journal of Pure and Applied Mathematics 46(2):165-170, 2008. - O. Michael Melko and Arcady R. Mushegian,
*Distribution of words with a predefined range of mismatches to a DNA probe in bacterial genomes,*Bioinformatics 20(1):67-74, 2004. - M. Melko and I. Sterling,
*Application of soliton theory to the construction of pseudospherical surfaces in R*Annals of Global Analysis and Geometry 11:65-107, 1993.^{3},

**Preprints**

- Larry M. Bates and O. Michael Melko,
*An exotic symplectic \( \mathbf{R}^6 \).*arXiv:1507.08939 [math.DG]. - Larry M. Bates and O. Michael Melko,
*On curves of constant torsion I.*arXiv:1206.7086v1 [math.DG].

**Conference Proceedings**

- Luis Weruaga and O. Michael Melko,
*On the Cramér-Rao bound of autoregressive estimation in noise,*Circuits and Systems (ISCAS), 2011 IEEE International Symposium on 15-18 May 2011, Rio de Janeiro, Brazil: 373-376. - O. Michael Melko,
*Ergodic theory and its application to the analysis of nucleic acid sequences,*Proceedings of the South Dakota Academy of Sciences, 83:55-63, 2004.