Mathematics Is Imprecise
Prabhakar Ragde (University of Waterloo)
TL;DR
This paper explores the bidirectional relationship between mathematics and computer science, highlighting how programming enforces precision and how mathematical imprecision can aid beginner programmers.
Contribution
It provides an experience report on teaching CS with Racket and Haskell, emphasizing the mutual influence of mathematical and programming precision.
Findings
Programming enforces mathematical precision, improving understanding.
Imprecision in mathematical notation can benefit novice programmers.
Using functional languages supports learning in mathematically skilled students.
Abstract
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS course to students with very good mathematical skills focusses on the ways that programming forces one to get the details right, with consequent benefits in the mathematical domain. Conversely, imprecision in mathematical abstractions and notation can work to the benefit of beginning programmers, if handled carefully.
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