Faculty
Science
Supervisor Name
Rasul Shafikov
Keywords
computability theory, turing machines, undecidability, computable numbers, computable functions, computable real functions
Description
In this paper, I present an introduction to computability theory and adopt contemporary mathematical definitions of computable numbers and computable functions to prove important theorems in computability theory. I start by exploring the history of computability theory, as well as Turing Machines, undecidability, partial recursive functions, computable numbers, and computable real functions. I then prove important theorems in computability theory, such that the computable numbers form a field and that the computable real functions are continuous.
Acknowledgements
I would like to thank Professor Rasul Shafikov for his exceptional guidance and feedback during the USRI and my writing of this paper.
Document Type
Paper
Included in
Analysis Commons, Number Theory Commons, Other Mathematics Commons, Theory and Algorithms Commons
Contemporary Mathematical Approaches to Computability Theory
In this paper, I present an introduction to computability theory and adopt contemporary mathematical definitions of computable numbers and computable functions to prove important theorems in computability theory. I start by exploring the history of computability theory, as well as Turing Machines, undecidability, partial recursive functions, computable numbers, and computable real functions. I then prove important theorems in computability theory, such that the computable numbers form a field and that the computable real functions are continuous.