TEACHING EXPERIENCE:
Undergraduate Courses:
TRIGONOMETRY, COLLEGE ALGEBRA, BUSINESS CALCULUS, CALCULUS I, II, III,
CALCULUS I, II AND III FOR HONORS STUDENTS, HONORS SEMINAR
ORDINARY DIFFERENTIAL EQUATIONS,
LINEAR AND MATRIX ALGEBRA,
MODERN GEOMETRIES
Graduate Courses:
TOPICS IN ADVANCED CALCULUS,
APPROXIMATION THEORY,
SPECIAL FUNCTIONS, SPLINE FUNCTIONS,
FOUNDATIONS OF ANALYSIS (TOPOLOGY),
COMPLEX ANALYSIS
REAL ANALYSIS
Master Research Reports Supervised:
Charles Teagues, Jr. ``Portrait of Hermite Error Formula'', 1992.
Jeffrey L. Billeter ``Gibbs Phenomena in Cubic Splines Least Squares Approximation'', 1994.
Thomas Rutenkroger ``Solution of Boundary Value Problems by Cubic Splines'', 1995.
Holly K. Carley ``Markov Type Inequalities'', 1998.
Mark Varvak ``Comptational Experiment and Analysis of Bernstein's Conjecture'', 1999.
RESEARCH EXPERIENCE
Grants:
- Scientific Computing Environment for Research, National Science Foundation, 1998-2000
- Numerical Approximation of Integrals, Office of Sponsored Research, University of Central Florida, 1993-1994.
Presentation of Research Papers:
International Meetings:
- Mean convergence of rational functions interpolating on the unit circle, Asymptotics and Special Functions,
Hong Kong, June, 1999.
- Rational interpolation to functions on the unit circle, Analytic Theory of Continued Fractions and Related
Topics, Boulder, Colorado, May 26-30, 1998.
- Convergence of interpolating Laurent polynomials on an Annulus, Continued Fractions: from analytic number
theory to constructive approximation, Columbia, Missouri, May 20-23, 1998.
- Regularity of orthogonal rational functions on the unit circle, Continued Fractions and Geometric Function
Theory, Trondheim, Norway, June 24-28, 1997.
- Orthogonal Polynomials and Bernstein Inequalities and Separation Theorem of Chebyshev-A.Markov-Stieltjes
for Laurent Polynomials Orthognal on $(0,+\infty)$, Workshop on "Special Functions, q-Series and Related
Topics", The Fields Institute for Research in Mathematical Sciences, (June 12-23, 1995, Toronto, Ontario)
- On the asymptotics of the columns in the table of orthogonal polynomials with varying measures, Workshop
on "Orthogonal Polynomials on the Unit Circle", (Madrid, Spain, 6/1994), two lectures, Invited Speaker.
- On the convergence of double least-squares inveres, International Conference on Computational Methods
and Function Theory (Penang, Malyasia, 3/1994).
- Nonsquare doubly stochatic matrices, AMS-SIAM-IMS Summer Conference on Mathematical Research ``Distributions
with Fixed Marginals, Doubly Stochastic Matrices, and Markov Operators'' (Seattle, WA., 8/1993).
- Remarks on orthogonal polynomials with respect to varying measures and related problems, Seventh International
Symposium on Approximation Theory (Austin, Texas 1/1992).
- On Saff's contamination principle in $L_2$ approximation on ${\bf R}$, US-USSR Workshop on "Methods
of Approximation Theory in Complex Analysis and Mathematical Physics", (Leningrad, Former Soviet Union, 5/1991).
- On Markov's inequality on ${\bf R}$ for Hermite weight, the American Mathematical Society Southeast
section Meeting, (Tampa, FL., 1991).
- Uniform convergence of polynomials associated with varying Jacobi weights, US-Norway Workshop on "Pade
Approximation and Related Topics", (Boulder, CO., 1988).
Regional Meeting and Seminars:
- Rational approximation in Hardy spaces, colloqium, Department of Mathematics, Norweigian Institute of
Technology, (Trondhaim, Norway, November, 1998)
- Approximation by rational functions, American Mathematical Society Meeting #919, (Memphis, Tennessee,
March 21-22, 1997)
- Using TI-92 in teaching trigonometric functions, Workshop on TI-92, (Orlando, August, 1996)
- On the convergence of rational functions orthogonal on the unit circle and The K-result for the R-process,
Workshop on "Analytic Theory of Continued Fractions and Related Topics", (Boulder, CO., 7/1994)
- On polynomials orthogonal with respect to Sobolev inner product on the unit circle, Workshop on "Analytic
Theory of Continued Fractions and Related Topics", (Boulder, CO., 7/1993)
- On Lagrange Interpolation, Approximation Seminar, University of South Florida, (Tampa, FL., 7/29/1992).
- $C^1$ Functions to which the Lagrange interpolation yields the Jackson order of approximation, Analysis
Seminar, UCF, (Orlando FL., 1992).
- Start with Cauchy's integral formula, Mathematics Colloquium, UCF, (Orlando FL., 1992).
Seminar Conducted:
Approximation Seminar (every semester regularly).
Other Professional Activities:
Served as referee for:
Journal of Approximation Theory
Constructive Approximation
SIAM Journal on Mathematical Analysis
International Journal of Mathematics and Mathematical Sciences
Methods and Applications of Analysis
Journal of Mathematical Analysis and its Applications
Journal of Computational and Applied Mathematics
Transaction of the American Mathematical Society
1995 AMS Southeast Section Meeting Committee:
Organizor of special session "Approximation Theory and Special Functions"
PROFESSIONAL SERVICE
Department Committee:
Search Committee (1998-present)
Computer Committee (chair, 1998-present)
Undergraduate Curriculum Committee (1993-present)
Tanure and Promotion Committee (1997-8)
Department Library Committee (1992-4)
Graduate Student Mentor Committee (1990-present)
Mathematics/Business Articulation (1992-3)
College Algebra Textbook Selection Committee (1992-3)
Ordinary Differential Equation Textbook Selection Committee (1992-3)
Calculus II course, Coordinator (1992-3)
University Committee:
Faculty Seneta (1998-2000)
Undergraduate Curriculum Committee (1998-2000)
Public Service:
Judge in the 42nd International Science and Engineering Fair, Orlando, May 8, 1991.
Judge in the 38th Annual State Science and Engineering Fair of Florida, Orlando, April 15, 1993.
Contributing exam problems for the Mathematics Olympic for students from community colleges in Florida, March 1994.
Back to Xin Li's homepage
vita