Shelly Wismath is a Professor of mathematics, whose research is in the area of Universal or General Algebra. She studies hyperidentities and hypersubstitutions, especially for varieties of semigroups, varieties of bands and varieties of star-bands; the Galois connection between sets of hypersubstitutions and collections of varieties, and Galois connections in general; complexity measurements for terms, identities and varieties, and k-normal varieties; and class operators on lattices of varieties, including inflations and generalized inflation. Her research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
Math was never my first choice as an undergraduate, but something I liked and could do well. To me it is more a whole way of looking at the world, a context rather than a particular interest. But I've always liked logic and structure, which suits the research I do now. I first got really intrigued by the interplay of these two areas in an abstract algebra course in university, when I realized that if we change the rules of algebra we can get different results. For example, does 9 + 6 always equal 15? Well, if the question is "what time will it be if you start work at 9 a.m. and work for 6 hours", the sensible answer is actually 3! That is, on a 12-hour clock, 9 + 6 = 3! And on a 3-hour clock,2 + 2 = 1 makes sense. Learning about this really made me think about the world of mathematics in a new way!
Not at all! What I do is very abstract algebra, and on the surface at least has little connection to physical reality. But mathematics often has a very long lag-time, before it becomes applicable. For example, the earliest work on Boolean Algebra in the mid-1800s was purely theoretical, but a hundred years later people figured out how to use Boolean algebra to make computers!
I am very proud of the two teaching awards I have received at the U of L: the Distinguished Teaching Award in 1989 and the inaugural Board of Governors' Chair in Teaching in 2009.
Students are not really necessary to my research, and students would need at least some third year algebra courses (and preferably fourth) before they would understand my research area. But I have enjoyed working with senior undergraduate student research assistants over the years, and have been pleasantly surprised by how much research work they can accomplish, given careful guidance.
Over the years I have become very interested in the teaching of mathematics, especially to students who are not in math or science, and in how to make the logical skills of mathematics accessible to a general audience. This connects strongly to my interest
and involvement in the Liberal Education program at the U of L. So if I had unlimited money, I would fund programs to investigate and enhance the teaching of critical thinking skills, including quantitative skills, in undergraduate students.