The BSc level course Domain-Specific Languages of Mathematics (course code DAT326 at Chalmers and DIT982 at UGOT) presents classical mathematical topics from a computing science perspective: giving specifications of the concepts introduced, paying attention to syntax and types, and ultimately constructing DSLs of some mathematical areas mentioned below.
Lectures:
- Introduction: Haskell, complex numbers, syntax, semantics, evaluation, approximation
- Basic concepts of analysis: sequences, limits, convergence, ...
- Types and mathematics: logic, quantifiers, proofs and programs, Curry-Howard, ...
- Type classes, derivatives, differentiation, calculational proofs
- Domain-Specific Languages and algebraic structures, algebras, homomorphisms
- Polynomials, series, power series
- Power series and differential equations, exp, sin, log, Taylor series, ...
- Linear algebra: vectors, matrices, functions, bases, dynamical systems as matrices and graphs
- Laplace transform: exp, powers series cont., solving PDEs with Laplace
The course has been running yearly from 2016 and from 2022 there is a course book published by College Publications.
