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Great Ideas in Theoretical Computer Science: Computability

Ryan O'Donnell via YouTube

Overview

This course on computability in theoretical computer science aims to teach students the fundamental concepts and theories related to computation and algorithms. By the end of the course, learners will understand the formal definition of Turing Machines, decidable languages, the Church-Turing Thesis, and the concept of uncomputable functions. The course covers topics such as the finite control, universal Turing Machines, and the Halting Problem. The teaching method includes lectures, programming exercises, and discussions. This course is intended for students and professionals interested in deepening their understanding of theoretical computer science and computability.

Syllabus

15-251: Great Theoretical ideas in Computer Science Lecture 22
What is a computation/algorithm?
Turing's inspiration: computers (usage 2)
The finite control (AKA transition rules)
Formal definition of Turing Machines
Decidable languages
TM programming exercises & tricks
Universal Turing Machine
TM's: good definition of computation?
Church-Turing Thesis: "Any natural / reasonable notion of computation can be simulated by a TM."
Describing Turing Machines
Some uncomputable functions
Does the following program (written in Maple) print out "HELLO WORLD" ?
The Halting Problem is Undecidable

Taught by

Ryan O'Donnell

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