 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

# Mathematical Structures in Computer Science

The course is not on the list Without time-table
Code Completion Credits Range Language
NI-MSI Z,ZK 4 2P+1C Czech
Lecturer:
Tutor:
Supervisor:
Department of Applied Mathematics
Synopsis:

Mathematical semantics of programming languages.

Data types as continous lattices, Scott topology.

Procedures as continuous mappings.

The Scott model of lambda calculus.

Introduction to category theory.

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:

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.

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:
Data valid to 2023-02-07
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6167106.html