John Williams, PhD
Dana Hall 239
PhD Indiana University | BS Rose-Hulman Institution
My academic career started in Complex Variables, in particular Univalent Function Theory. I was interested in the geometry of the omitted set of certain extreme univalent functions defined on the exterior of the unit disk. The equivalent problem on the interior of the unit disk, the Bieberbach conjecture was solved just when I graduated from Indiana University but the problem on the exterior remains unsolved. Not only unsolved but without a good conjecture. I remain interested in the problem and keep up with the new results in this area. My current interests is in the use of technology in pedagogy. That includes both student centered technology such as graphing calculators, CAS and online homework systems to presentation technology such as clickers and chalkless lectures. I see that most students learn in a way that is different than my peers did thirty years ago and I feel an obligation to adapt my teaching to their learning styles. The ability to illuminate complex mathematical ideas with technology is a game changer. The idea that all our students carry a full computer algebra system in their hand changes the focus of education. When students graduate, they will access to even more technology and our job in academia is to prepare them for a life of learning.