Research Interests:

Ergodic Theory
Dynamical systems
Random Dynamical systems
Stochastic processes
Frobenius- Perron operator,
Applications of stochastic processes and dynamical systems in Finance.

Honors research student: Willium Liu (Summer 2010--Winter 2011)

Teaching:
Fall 2011:
Math 151 A: Introductory Calculus I
Math 151 B: Introductory Calculus I

Winter 2012:
Math 152C: Introductory Calculus II

Fall 2010:
Math 151 C: Introductory Calculus I
Math 151 D: Introductory Calculus I

Winter 2011:
Math 151: Introductory Calculus I
Math 152C: Introductory Calculus II
Math 152D: Introductory Calculus II

Winter 2010:
Math 385: Mathematics of Finance
Math 111B: Finite mathematics
Math 252: Intermediate Calculus II

Fall 2009:
Math 151 A: Introductory Calculus I
Math 151 B: Introductory Calculus I

Fall 2006-Summer 2009 at UPEI:
Math 385, Math 151, Math 152, Math 252, Math 111, Math 112;

Fall 2005 - Summer 2006 at University of Lethbridge:
Analysis I, Calculus I, Linear Algebra II, Linear Algebra I;

Fall 1998 - Summer 2005 at Concordia:
Math 208: Finite mathematics, Math 204: vector and matrices, Math 206: Algebra and Functions;

Feb 1995 - July 1998 at Shah Jalal University:
Topology, Ring theory and modules, Analysis, Calculus I, Differential Equations, Linear algebra, Numerical analysis and Fortan, Complex analysis;

Publications:

Articles in progress:

1. Islam, Shafiqul & Pawel Gora: Chebyshev approximation for stochastic perturbation of discrete time dynamical systems (in progress);

2. Islam, Shafiqul: Deterministic representation of Markov switching position dependent random maps (in progress);

Articles published in refereed Journals:

1. Anatoliy Swishchuk and M. Shafiqul Islam: Normal Deviation and Poison approximation of
the Geometric Markov Renewal Processes}, accepted for publication in Communications in Statistics.

2. Swishchuk, Anatoliy and Islam, Shafiqul: Diffusion approximation of the geometric Markov renewal processes and option price formulas, Inter. J. Stochastic Analysys, 2010 ;

3.Islam, Shafiqul: Maximum entropy method for invarinat measures for position dependent random maps, Int. J. Bifurcation and Chaos (to appear), 2011;

4. Swishchuk, Anatoliy and Islam, Shafiqul: The geometric Markov renewal processes with application to finance, Journal of Stochastic analysis and applications (accepted, 2010).

5. Islam, Shafiqul and Gora, Pawel: Invariant measures of stochastic perturbations of dynamical systems using Fourer approximations, accepted for publication in Bifurcation and Chaos, 2010.

6. Islam, Shafiqul and Gora, Pawel: Smoothness of invariant densities for random maps, Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) (to appear),2009.

7. Islam, Shafiqul, Invariant measures for Higher dimensional Markov switching position dependent random maps,International Journal of Bifurcation and Chaos, Vol. 19, No. 1 (2009) 409-417..

8. Islam, Shafiqul, Piecewise linear probability density functions of invariant measures for position dependent random maps, Global Journal of Pure and Applied Mathematics, Volume 3, Number 3, 2007.

9. Doosti, H., Islam, S., Chaubey, V. and Gora P.,Two-Dimensional Wavelets for Nonlinear Autoregressive Models with an application in Dynamical system, Italian journal of pure and applied mathematics, 2008.

10. Pawel Gora, Abraham Boyarsky and Shafiqul Islam, Invariant densities of random maps have lower bounds on their supports, J. Appl. Math. Stoch. Anal. 2006.

11. Shafiqul Islam, Absolutely continuous invariant measures of linear interval maps. Int. J. Pure Appl. Math. 27 (2006), no. 4.

12. Pawel Gora, Abraham Boyarsky, Shafiqul Islam and Wael Bahsoun, Absolutely Continuous Invariant Measures that cannot be observed experimentally , SIAM J. Appl. Dyn. Syst. 5 (2006), no. 1.

13. Shafiqul Islam, Pawel Gora and Abraham Boyarsky, A generalization of Straube's Theorem: Exixtence of absolutely continuous invariannt measures for random maps, J. Appl. Math. Stoch. Anal. 2005, no. 2.

14. Abraham Boyarsky, pawel Gora and shafiqul islam, Randomly chosen chaotic maps give rise to nearly ordered behavior, Phys. D 210 (2005), no. 3-4.

14. Islam, Shafiqul, Gora, Pawel and abraham Boyarsky: Approximation of absolutely continuous invariannt measures for Markov switching position dependent random maps , Int. J. Pure Appl. Math. 25 (2005), no. 1, 51--78.

15. Islam, Shafiqul: Existence, approximation and properties of absolutely continious invariant measures for random maps, Ph. D. thesis, Dept. of Mathematics and Statistics., Concordia University,Montreal, Canada, 2004, Under direction of Pawel Gora and Abraham Boyarsky.

Reports published in proceedings:

1. Islam, Shafiqul (with Rita Aggarwala and et al): "Statistical Design of an experimental problem in harmonics", Proceedings of the third IPSW ,PIMS IPSW 3(2000), Canada.

2. Islam, Shafiqul (with Colin Please and and et al): "Temperature effects on a river or estuary Due to the construction of a power station", Proceedings of the third PIMMC,2000, PIMS, Canada.

M. Sc. Thesis:

Islam, Shafiqul: Absolutely continuous invariant measures for piecewise linear interval maps both contracting and expanding, M. Sc. thesis, Dept. of Mathematics. and Statistics, Concordia University , 2000, Under direction of Pawel Gora.

Islam, Shafiqul: Studies on fuzzy topological structures and prefilter convergence, M. Sc. thesis, Dept. of Mathematics, University of Dhaka, Bangladesh, 1993, Under direction of R. A.F.M. Khodadad Khan.