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, cocomputably enumerable sets, properties
 Computable metric spaces. Motivation, examples, properties, computable sets, computably enumerable sets, cocomputably enumerable sets, computability on compact sets.
