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Matematikens domänspecifika språk

Göteborgs universitet
Sammanfattning
Fristående kurser (grundnivå)
Göteborg
7.5 hp
Deltid
Klassrum
Startdatum: Vår 2021 - Göteborg

Matematikens domänspecifika språk

Software engineering involves modelling very different domains (e.g., business processes, typesetting, natural language, etc.) as software systems.  The main idea of this course is that this kind of modelling is also important when tackling classical mathematics.  In particular, it is useful to introduce abstract datatypes to represent mathematical objects, to specify the mathematical operations performed on these objects, to pay attention to the ambiguities of mathematical notation and understand when they express overloading, overriding, or other forms of generic programming.  We shall emphasize the dividing line between syntax (what mathematical expressions look like) and semantics (what they mean).  This emphasis leads us to naturally organize the software abstractions we develop in the form of domain-specific languages, and we will see how each mathematical theory gives rise to one or more such languages, and appreciate that many important theorems establish "translations" between them.

Mathematical objects are immutable, and, as such, functional programming languages are a very good fit for describing them.  We shall use Haskell as our main vehicle, but only at a basic level, and we shall introduce the elements of the language as they are needed. The mathematical topic treated have been chosen either because we expect all students to be familiar with them (for example, limits of sequences, continuous functions, derivatives) or because they can be useful in many applications (e.g., analytic functions, Laplace transforms).

Förkunskaper

The student should have successfully completed 7.5 credits in discrete mathematics as for example DIT980 Discrete Mathematics for Computer Scientists. 15 credits in mathematics, for example MMGD20 Linear Algebra D and MMGD30 Calculus D 15 credits in computer science, for example DIT440 Introduction to Functional Programming or MVG300 Programming with Matlab and DIT012 ImperativeProgramming with Basic Object-orientation Additional 22.5 credits of any mathematics or computer science Courses.

Göteborgs universitet

Göteborgs universitet

Göteborgs universitet möter samhällets utmaningar med mångsidig kunskap. 37 000 studenter och 6 000 medarbetare gör universitetet till en stor och inspirerande arbetsplats, flödande av kunskap och idéer. Öppenheten är ett signum som genomsyrar verksamheten. Universitetet tar plats i debatten...


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