Mathematical Structures in Computer Science

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Code	Completion	Credits	Range	Language
MI-MSI	Z,ZK	4	2P+1C	Czech

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

Mathematical semantics of programming languages.

Requirements:

Basic courses on programming and algebra.

Syllabus of lectures:

1. Motivation, semantics of programming languages. Order relations.

2. Orders, lattices, complete lattices.

3. Monotone mappings, fixed popints.

4. Topology: neighbourhood, closure, basis, subbasis.

5. Separation. Convergence. Continuity.

6. Data types as lattices. Scott topology.

7. Procedures as continous mappings.

8. Complex data types. Types of functions.

9. Continuous lattices as injective spaces.

10. Inverse limits. A lattice model of lambda calculus.

11. Categories: lbjects and morphisms. Mono- and epimorphisms.

12. Products, sums, equalizers. Diagrams and limits.

13. Exponents, eval. Cartesian closed categories.

Syllabus of tutorials:

Study Objective:

Study materials:

S. Abramsky, A. Jung, Domain Teory

A. Asperti, G. Longo, Categories, Types and Structures

M. A. Arbib, E. G. Manes, The Categorial Imperative

G. Birkhoff, Lattice Theory

L. S. Bobrow, M. A. Arbib, Discrete Mathematics

H. Herrlich, G. E. Strecker, Category Theory

E. G. Manes, Categorial Theory Applied to Computation and Control

S. Mac Lane, G. Birkhoff, Algebra

S. Mac Lane, Categories for the Working Mathematician

B. C. Pierce, Basic Category Theory for Computer Scientists

D. Scott, Data types as lattices

Note:

Further information:

https://courses.fit.cvut.cz/MI-MSI/

No time-table has been prepared for this course

The course is a part of the following study plans: