Semantic Methods

10 credits

Syllabus, Master's level, 1MA057

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA057
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

BSc, 90 credit points Mathematics and Computer Science

Learning outcomes

In order to pass the course (grade 3) the student should be able to

give an account of important concepts and definitions in the area of the course;

exemplify and interpret important concepts in specific cases;

formulate important results and theorems covered by the course;

describe the main features of the proofs of important theorems;

express problems from relevant areas of applications in a mathematical form suitable for further analysis;

use the theory, methods and techniques of the course to solve mathematical problems;

present mathematical arguments to others.

Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.

Content

Fixed points. Various domain concepts: cpo, algebraic cpo, Scott–Ershov domains. Domain constructions, domain equations and the theory for their solutions. Briefly about topological concepts related to domain theory. Alternative ways to present domains: neighbourhood systems, information systems. Briefly about computable domains, power domains, universal domains and formal topological spaces.

Category theoretical concepts: Adjoints, initial and final algebras, monads, monoidal categories and functor categories.

Models of lambda calculus. Game semantics and models of linear logic. Semantics for quantum programming languages.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.