Past Event: Babuška Forum

The Mathematics of Programming

Robert van de Geijn, Department of Computer Science, UT Austin

Abstract

Many a computational software scientist starts as a “domain scientist” who discovers that computation can accelerate scientific discovery and ends up contributing to the software infrastructure for scientific exploration. As a domain scientist, he/she is expected to understand the mathematics that underlies the domain (physics, chemistry, etc.). Yet once they become software scientists, few master the fundamental mathematics that underlies programming: the so-called Hoare Calculus that underlies goal-oriented programming. Did you know that you can prove a program correct? That the Principle of Mathematical Induction is fundamental to understanding loops? That you can derive programs hand-in-hand with their proofs of correctness? That the derivation process yields families of algorithms from which the highest performing can be chosen? In this talk, we illustrate how the science of programming matrix operations has allowed us to develop open source software libraries that are exceptionally robust and high performing. Bio: Robert van de Geijn is professor of computer science and member of the Institute for Computational Engineering and Sciences. He received his Ph.D. in Applied Mathematics from the University of Maryland, College Park. His interests are in linear algebra, high-performance computing, parallel computing, and formal derivation of algorithms. He heads the FLAME project, a collaboration between UT Austin, Universidad Jaume I (Spain), and RWTH Aachen University (Germany). This project pursues foundational research in the field of linear algebra libraries and has led to the development of the libflame library, a modern, high-performance dense linear algebra library that targets both sequential and parallel architectures. One of the benefits of this library lies with its impact on the teaching of numerical linear algebra, for which van de Geijn received the UT President’s Associates Teaching Excellence Award. He has published several books and more than 100 refereed publications.