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Ian AndersonIan Anderson
Mathematics Professor


Personal Website

As an undergraduate student at the University of Waterloo, my favorite classes were Advanced Calculus, Tensor Analysis and the Calculus of Variations. All of these subjects are central to Differential Geometry and Mathematical Physics, so it perhaps not a surprise that these are areas which are are close to my research activities today. As an undergraduate, I wasn't very good at abstract algebra so, on the other hand, it is a surprise that algebra (especially Lie algebras) is a very important component of my present work.

Nowadays, Abstract algebra is one the classes I enjoy teaching the most. For my Master's degree, I studied spinor equations in general relativity. All the computational skills I learned at this time proved to be extremely important many years later for my first research project with Charlie Torre on the symmetries of the Einstein equations. In my PhD dissertation I discovered a new formulation of Noether's theorem on the relation between symmetries and conservation laws for differential equations, based upon the upon the inverse problem of the calculus of variations. Over time this work opened many new avenues of research for me, including my work on natural variational principles and the variational bi-complex.

From these experiences, I learned that the mathematical and computations skills that one learns while writing one's thesis or dissertation is often times more important than the subject itself. I keep this in mind when helping students choose their projects. For the kinds of mathematical research I do nowadays, computer algebra is an essential research tool. With the DifferentialGeometry software developed here at USU, I am able to quickly perform mathematical experiments, develop conjectures and work complicated examples quickly and with relative ease. I am really convinced that this approach to research will become more important in the future. I believe that students and post-docs with these computational skill skills will be increasingly sought after by employers.