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- Multiple special numbers;
symmetric rational functions and applications;
elliptic hypergeometric series identities and q-series identities associated
to root systems; optimal estimation applications in mathematical biology; speech processing
Recent Grant Awards:
- Advanced Research Program (ARP) grant, Inverse scattering and spectral problems in human speech,
(jointly with T. Aktosun), The Texas Higher Education Coordinating Board (THECB), 2008-2011, $108,000. Role: PI.
The poster presents some of the results obtained in this project.
Pending and Previous Grant Applications and Awards
- A detailed list of ~30 grant applications to and awards by Texas A&M University-Commerce, and federal organizations including NSF and NIH
Selected Journal Publications:
- Electronic copies of some of the articles are available in preprint form through the arxiv. The links below point to more recent revised versions.
- Algebraic Combinatorics:
- - H. Coskun, Various families of multiple polygonal numbers, in preparation.
- - H. Coskun, Multiple Stirling numbers of first and second kind,
Advances in Math, expected date of publication: 03/2012.
- - H. Coskun,
Multiple Bernoulli numbers and related probability distributions,
Advances in Applied Math, expected date of publication: 05/2012.
- - H. Coskun,
Multiple Fibonacci numbers and applications,
Discrete Mathematics, expected date of publication: 07/2012.
- - H. Coskun, A multilateral Bailey Lemma and multiple Andrews-Gordon Identities, The Ramanujan Journal, 26 (2011) 2, 229-250. (pdf)
- - H. Coskun,
Multiple analogues of binomial coefficients and related special numbers, Discrete Mathematics, 310 (2010) 17, 2280-2298. (pdf)
- - H. Coskun,
Multilateral basic hypergeometric summation identities and hyperoctahedral group symmetries, Advances and Applications in Discrete Mathematics, Volume 5 (2010), 2, 145-157. (pdf)
- - H. Coskun, An Elliptic BCn Bailey Lemma, Multiple
Rogers-Ramanujan Identities and Euler's Pentagonal Number Theorems, AMS
Transactions, 360 (2008), 5397-5433. (pdf)
- - H. Coskun, The well-poised Macdonald functions Wλ and
Jackson coefficients ωλ on BCn (jointly with
R. A. Gustafson), Jack, Hall-Littlewood and Macdonald Polynomials,
September 2003, ICMS, AMS Contemporary Mathematics, Volume 417 (2006),
127-155. (pdf)
- Mathematical Biology:
- - H. Coskun,
Speaker recognition via vocal tract modeling based on inverse
scattering theory,
Inverse Problems in Science and Engineering, submitted, expected date of publication: 05/2012.
- - H. Coskun,
Statistical computing applications in optimal parameter estimation of biological system models, (jointly with H. Coskun and N. Yildirim),
Applied Mathematics and Computation, expected date of publication: 04/2012.
- - H. Coskun,
Cell physician: Reading cell motion. A mathematical diagnostic technique through analysis of single cell motion, (jointly with H. Coskun), The Bulletin of Mathematical Biology, Volume 73, Issue 3 (2011), pp. 658.
(pdf)
An annotated movie of crawling neutrophil chasing bacteria demonstrates the Anchor Model introduced in this paper.
This work has been featured in various scientific media channels including Science Daily.
- - H. Coskun,
Quantitative analysis of canary (Canarius serinus) vocalization, (jointly with G. Angle), Bioacoustics Journal, submitted, expected date of publication: (pdf)
Other Publications:
- A more complete list of publications
- - H. Coskun, Inverse scattering and spectral problems in human speech,
Advanced Research Program Technical Progress Report, Texas Higher Education Coordinating Board, Project Number: 003656-0046-2007, accepted, 2009, (abstract) .
- - H. Coskun, A BCn Bailey Lemma and Generalizations of Rogers-Ramanujan Identities, Ph.D. Thesis, Texas A&M University, College Station, TX, December 2003.
Editorial Boards:
- - Journal of Algebra, Number Theory and Applications
- - Advances and Applications in Discrete Mathematics
- - Far East Journal of Mathematical Sciences (FJMS)
- - Far East Journal of Applied Mathematics
- - Surveys in Mathematics and Mathematical Sciences
Presentations and Invited Talks
- A detailed list of ~30 presentations and
invited talks at national and international conferences, meetings and seminars
-
- - Math 335 Linear Algebra
- - Math 502 Mathematical Statistics II
- - Math 515 Dynamical Systems
Courses Taught in Past Semesters:
- Texas A&M University-Commerce, Fall 2003-present:
(T: traditional lecture style, W: web-based/online, DE: distance education. T is the default unless otherwise indicated.)
Most courses are delivered as web-enhanced courses through eCollege. Every course in the list had a technology component: all introductory level undergraduate courses integrated TI calculators or Excel application, and most upper level undergraduate and graduate courses integrated computer mathematics and statistics software including R, Mathematica, MATLAB and Geometer's Sketchpad.
The strategies I use for integrating technology in classroom instruction was featured by the IT & DE Department at A&M-Commerce on the October 2010 issue of the Faculty Spotlight.
- - Undergraduate Courses:
- Business Math I and II,
College Algebra,
Precalculus,
Calculus I and II,
Mathematical Technologies (W),
Introduction to Abstract Algebra,
Linear Algebra,
Discrete Mathematics,
Introduction to Mathematical Statistics,
Differential Equations, Interdisciplinary Research Experiences:
Numerical Analysis,
Introduction to Analysis,
Functions of a Complex Variable
- - Graduate Courses:
- Advanced Calculus I and II,
Complex Variables I and II,
Mathematical Statistics I and II,
Abstract Algebra I and II,
Methods of Applied Mathematics (T & DE),
Fundamental Techniques in Mathematical Economics,
Differential Equations and Applications,
Theory of Numbers (T & DE),
Optimization,
Foundations of Geometry,
Fourier Analysis and Wavelets,
Probability and Statistics,
Statistical Computing and Design of Experiments (T & DE),
Dynamical Systems,
Numerical Solutions to Partial Differential Equations,
Numerical Analysis,
Thesis,
Research Literature & Techniques
Sample Lecture:
- A short (33min) excerpt from a taped
lecture covering discussions on some homework exercises in a distance education class on applied linear algebra
Supervised Theses & Papers:
- A detailed list of ~15 graduate theses,
reearch papers and undergraduate research projects
Humor:
- - got math test?
- - proof by intimidation
- - ma & pa kettle (video clip)
- - phdcomics.com
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