Teaching

This briskly paced course can be viewed as equivalent to MATH 13 in terms of prerequisites, but is designed especially for first-year students who have successfully completed a BC calculus curriculum in secondary school. In particular, as part of its syllabus it includes most of the multivariable calculus material present in MATH 8 together with the material from MATH 13. Topics include vector geometry, equations of lines and planes, and space curves (velocity, acceleration, arclength), limits and continuity, partial derivatives, tangent planes and differentials, the Chain Rule, directional derivatives and applications, and optimization problems. It continues with multiple integration, vector fields, line integrals, and finishes with a study of Green's and Stokes' theorem.

Our capacity to fathom the world around us hinges on our ability to understand quantities which are inherently unpredictable. Therefore, in order to gain more accurate mathematical models of the natural world we must incorporate probability into the mix. This course will serve as an introductions to the foundations of probability theory. Topics covered will include some of the following: (discrete and continuous) random variable, random vectors, multivariate distributions, expectations; independence, conditioning, conditional distributions and expectations; strong law of large numbers and the central limit theorem; random walks and Markov chains. 

Beginning with techniques for counting-permutations and combinations, inclusion-exclusion, recursions, and generating functions, the course then takes up graphs and directed graphs and ordered sets and concludes with some examples of maximum-minimum problems of finite sets. Topics in the course have application in the areas of probability, statistics, and computing.

An advanced graduate course on representations of the symmetric group with mathematical applications. We begin with basic facts about the representation theory of finite group (over a field of characteristic zero). This course goes on to construct of the Specht modules – the irreducible representations of the symmetric group. Then the representation theory of the symmetric groups is applied in a number of mathematical settings, many of which involve finite dimensional algebraic complexes.

Sports organizations are becoming increasingly aware that analytics are an important component of team success. This course will introduce students to various statistical techniques used in modern sports analysis and teach participants how statistical methods can be used to analyze game outcomes and evaluate players and strategies. The course will include lectures, in-class exercises using the R statistical computing environment, and guest speakers from the sports industry.