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.