Eigenmumbles

My training is in mathematics and computer science, but engineering has always been part of my intellectual environment. My circle of close friends consists disproportionately of engineers. My father is an engineer. One of my brothers is an engineer. I was co-advised by a civil engineer, and did a graduate minor in mechanical engineering. And I came to Cornell in part for the strength of the engineering program. I spend a lot of time learning from colleagues in engineering about the cool things they think about. Sometimes, I get the chance to help them out; but even if I don’t, it’s fun to learn.

I work in computational science and engineering (CSE), and most of my work involves using computers to analyze mathematical models from the sciences and engineering. A lot of what I do is essentially engineering applied to computational mathematics. Our models of the world are generally incomplete, and even very simplified models often admit no close form solution, nor even a very simple analysis. The goal of most scientific computing answer is to devise methods that are fast enough and get solutions that are right enough to a problem arising from a model that is good enough, where “fast enough”, “right enough” and “good enough” are concepts defined by some underlying problem. Ideally, I want my work to result in artifacts – theories, codes, design rules, or approximation methods – that are useful tools for someone else who is doing something cool.

The basic skills needed to do numerical computing seem like everyday fare: a solid understanding of calculus and linear algebra, some programming ability, and a bit of common sense about what things are actually worth computing. But none of these skills are actually so everyday as what one might initially think (which keeps teaching entertaining). Of these skills, common sense is the most elusive, uncommon, and important. And of these skills, the common-sense appraisal, the understanding of what is actually needed to achieve a goal and the trade-offs in how to get there, is what I most associate with engineering.