Patrik Jansson

Professor of Computer Science


Computer Science and Engineering

Chalmers University of Technology

Domain-Specific Languages of Mathematics

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.
  • 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. 

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