Computable analysis

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Computable analysis

Code: 213154
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Zvonko Iljazović - Lectures
Load:

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES:
Students should be able to:
- use fundamental concepts of computable analysis
- solve problems that include computability, analysis, and topology

COURSE DESCRIPTION AND SYLLABUS:

- Basic and more complex examples of computability in analysis and motivation for the notion of a recursive number.
- Recursive real functions. Recursive rational functions, recursive real functions, examples.
- Recursive Numbers. Examples, characterization of recursive numbers, examples of nonrecursive numbers.
- Computable functions of real variable. Sequential computability, effective uniform continuity, examples, properties, Kleene tree, computable functions without recursive zeropoints.
- Computability in Euclidean Space. Computable sets, computably enumerable sets, co-computably enumerable sets, properties
- Computable metric spaces. Motivation, examples, properties, computable sets, computably enumerable sets, co-computably enumerable sets, computability on compact sets.
Literature:
  1. M. B. Pour-El, J. I. Richards: Computability in Analysis and Physics
  2. K. Weichrauch: Computable Analysis
  3. E. Bishop, D. Bridges: Constructive Analysis
Prerequisit for:
Enrollment :
Passed : Computability
1. semester
Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

2. semester
Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

3. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

4. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics
Consultations schedule: