Domain-Specific Languages of Mathematics: Presenting Mathematical Analysis Using Functional Programming

TL;DR

This paper introduces a pedagogical approach that uses functional programming to teach mathematical analysis, helping students better understand and apply complex mathematical concepts through domain-specific languages.

Contribution

It proposes a novel educational method integrating functional programming and domain-specific languages to improve learning in advanced mathematics courses.

Findings

Students better understand mathematical functions and types.

Enhanced ability to create calculational proofs.

Improved engagement with mathematical syntax.

Abstract

We present the approach underlying a course on "Domain-Specific Languages of Mathematics", currently being developed at Chalmers in response to difficulties faced by third-year students in learning and applying classical mathematics (mainly real and complex analysis). The main idea is to encourage the students to approach mathematical domains from a functional programming perspective: to identify the main functions and types involved and, when necessary, to introduce new abstractions; to give calculational proofs; to pay attention to the syntax of the mathematical expressions; and, finally, to organise the resulting functions and types in domain-specific languages.