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Research
My main research interest lies at the interface between Probability Theory and Functional Analysis.
In Probability Theory, my interest is mostly in the probability estimate of rare events of random processes;
in Functional Analysis, I focus on the geometric aspect of classical Banach spaces. I typically use analytical
methods to study probability problems, and I use probabilistic methods to tackle problems in Functional Analysis.
I believe both theoretical research and applications are important. Therefore, I am also interested in applications
of theoretical results, especially in statistics and optimization. Having benefited from the interplay between
Analysis and Probability in my own research,
I strongly support the view of developing interdisciplinary research, and have invested some effort on it.
Here are my Recent Publications
Teaching
Universities exist because of the students; consequently, teaching is of essential importance to universities.
As a well recognized basic and important subject, mathematics provides powerful tools for all sciences and engineering. The high quality teaching of mathematics
is crucial to the training of a new workforce in science and engineering.
As a university mathematics professor, I should always try my best to be a good teacher.
To me, a good mathematics teacher must 1) deliver course material effectively; 2) motivate students' learning and further stimulate their interest in the field;
and 3) set a good example of loving mathematics and the mathematical profession.
I believe that the only way to learn mathematics is to do mathematics; and the amount and level of difficulty of the problems given to students determines
the effectiveness of their practice. As a professor, a careful assignment of homework is an essential part of my design of the framework in which
learning can take place most effectively. As my students, you are expected to finish all the assignments, which often include a reasonable amount of
challenging problems.
In the fall 2011, I will be teaching Math 275 (Analytic Geometry and Calculus III ) and Math 571 (Functional Analysis I).
I will also co-teach a Putnam seminar.
Math 275
Math 571b
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