Assistant Professor, CLI
Office: Broadway Hall
Ph.D., Combinatorics, Brandeis University, MA, 2009
M.A., Mathematics, Brandeis University, MA, 2009
B.Sc., Mathematics, Dhaka University, Bangladesh, 2003
After receiving my Bachelor of Science degree from Dhaka University, Bangladesh, I came to Brandeis University where I finished my M.A. and PhD Degree. Coming from a diverse community I could relate my own experience of learning and teaching in two very different environments and education system to the goal of UMR in a unique way. I believe the future of education is really at a turning point given the vast amount of technology and resources we have at our fingertips.
My goals in teaching mathematics are to present the concepts in the simplest, most transparent way, to ensure that students become fluent and confident in their problem solving skills, and to transmit the sense of joy and excitement I feel as the mathematical structures and possibilities unfold.
My interest in teaching mathematics began when I was doing my undergraduate degree. I believe that although a faculty member serves as the main instructor for a class, for the majority of students, the best way to learn is to spend more time working on problems and discussing them with other students. From my teaching at Brandeis University I have seen that working in groups benefits not only the weaker students in the group, but also the stronger ones as well, because explaining a concept to someone else helps to solidify one’s own knowledge of the subject. This made me realize that learning by teaching and learning from discussion are integral parts of the learning process.
My undergraduate teaching experience prior to arriving at UMR includes a wide variety of courses. These include: Differential Calculus, Integral Calculus, Calculus with Analytic Geometry, Introduction to Probability and Statistics, etc.
At UMR, I play a primary role in the design and delivery of courses across the quantitative science core. I also play a secondary role in other courses across the curriculum.
My main area of research is enumerative combinatorics. I like not only its beauty as a subject but also its wide applicability throughout mathematics. I have diverse mathematical interests, and combinatorics is the bridge that connects them. In general, I am interested in the connections of combinatorics with other fields such as algebra, random matrix theory, biology, geometry, probability, and computer science. I enjoy learning about new problems and trying to solve them using combinatorial techniques.
For me the goal of research is to make concepts understandable both to myself and to others. In combinatorics one finds both open problems which are accessible to undergraduate students, and simply stated problems which prove to have deep and sophisticated solutions.
My current research falls into two categories, enumerative combinatorics and random matrices. On the enumerative side I've been studying generalizations of the Chung-Feller theorem for lattice paths with restrictions using cycle lemma and generating function approaches. I've also studied in compositions of graphs. On the random matrix side I've been studying pde's related to Dyson's non-intersecting Brownian motion with a few outliers, also known as the r-Airy process.
Thesis “Generalized Chung-Feller Theorems for Lattice Paths"
“Compositions of Graphs Revisited", Electron. J. Combin. 14 (2007), N15.