M7970 Approximation in the mathematical foundations of computer science

Přírodovědecká fakulta
podzim 2005
Rozsah
0/0. 2 kr. 2 kr. zápočet, 3 kr. kolokvium, 4 kr. zkouška. Doporučované ukončení: k. Jiná možná ukončení: zk, z.
Vyučující
Profesor Achim Jung (přednášející), prof. RNDr. Jan Paseka, CSc. (zástupce)
Garance
prof. RNDr. Jan Paseka, CSc.
Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Předpoklady
PREREQUISITES: I hope that this course will be attractive to both mathematicians (interested in applications to computer science) and computer scientists (interested in the mathematical foundations of their subject). Mathematicians should have some background in topology, order theory, category theory, or logic; computer scientists should have some experience of denotational semantics. I hope to be able to fill in the missing bits for both types of participants, and are very willing to have the course move in whichever direction the audience prefers.
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Cíle předmětu
Mathematics often deals with infinite objects without much consideration whether such objects have a representation in a computer. For example, real numbers in general require infinitely many digits to write down, and functions on either the reals or the natural numbers may require an infinite amount of information to specify. Over the last 35 years, computer scientists have revisited many such mathematical structures and examined the ways in which they might be represented in a computer. Central to this enterprise is the notion of "approximation" where the ideal infinite object is seen as the limit of a sequence of finite parts. The course will explore this topic from various angles, and will aim to present the results of some very recent research.
Osnova
  • I. Domain Theory: Scott's "domains" as a technique to model recursion and iteration, and as a way to solve recursive domain equations; continuous domains as a way to deal with real numbers and probability. II. Exact Real Number Computation: Representing real numbers as streams of generalised digits; programming languages for exact real number computation; parallelism and sequentiality. III. Domain Theory in Logical Form: Stone duality as a link between semantics and program logics; Stone type dualities for domains; partial predicates and Stone dualities for continuous domains.
Metody hodnocení
The lectures will be given in a week from 27.6. - 1.7.2005.
Vyučovací jazyk
Angličtina
Další komentáře
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  • Permalink: https://is.muni.cz/predmet/sci/podzim2005/M7970