New Directions in the Teaching of Numerical Computing

By André Weideman

New Directions in the Teaching of Numerical Computing, an essay by André Weideman, written for the New Directions in Numerical Computation Conference. All queries should be addressed to Toby Driscoll ([email protected]) and Alex Townsend ([email protected]).

I coded my first Gaussian elimination using a thick stack of punch cards. Today, that involves exactly three characters in MATLAB. Back then, finding a research paper involved a trip to the library. Today, I lift exactly one finger. As an instructor of numerical analysis and scientific computing, I keep asking myself what to take and what to leave from this veritable buffet of technological advances.

Teaching my subject in a computer laboratory has been my mode of instruction for more than two decades. Quadratic convergence, I feel, is much better experienced firsthand than second. Symbolic software has been with us for a while, but these days WolframAlpha understands natural language (most of the time). While I firmly believe students should be able to integrate by parts by hand, symbolic software can do that six term Taylor expansion without jeopardizing understanding. With Google and Wikipedia available, do we even need that expensive text book (the one where only the exercise numbers have been shuffled in the new edition?) Come to think of it, with a lecture from that famous MIT professor only a video link away, have I myself become redundant?

Along with these opportunities for enhanced instruction come hardware and software advances that touch the very heart of our subject. What will the new algorithms look like and what should we teach? Should processor technology be part of the course? I hear a flop is practically free these days, and memory access is what’s important. Should those beautiful flop-counting diagrams in Trefethen & Bau be replaced in the next edition of the book? If so, with what?

Questions are many and answers are few. What is clear is that the classroom (or future equivalent) as well as the course content will look very different two decades from now.

André Weideman is a professor of applied mathematics at Stellenbosch University.