- published: 18 Nov 2020
- views: 2578
Create your page here
-
remove the playlistComputability Theory
- remove the playlistComputability Theory
back to playlist
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 6 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press,
https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Lecture 6. Computability
What is computability? Kurt Gödel defined a robust class of computable functions, the primitive recursive functions, and yet he gave reasons to despair of a fully satisfactory answer. Nevertheless, Alan Turing’s machine concept of computability, growing out of a careful philosophical analysis of the nature of human computability, proved robust and laid a foundation for the contemporary computer era; the widely accepted Church-Turing thesis asserts that Turing had the right notion. The distinction between computable decidability and computable enumerability, highlighted by the undecidability of the halting problem, shows that not all mathematical problems can be solved by machine, and a vast hierarchy looms in the Turing degrees, an infinitary information theory. Complexity theory refocuses the subject on the realm of feasible computation, with the still-unsolved P versus NP problem standing in the background of nearly every serious issue in theoretical computer science.
Theory of Computation
https://uvatoc.github.io/week10
21.1 Proving Computability and Noncomputability
- Ways to Prove a Function is Computable or Uncomputable
- Example: Adding is Computable
David Evans and Nathan Brunelle
University of Virginia
- published: 26 Oct 2020
- views: 647
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheless, it went on to support the Zermelo-Fraenkel axiomatic approach to sets which we have a quick look at.
Then we introduce Alan Turing's ideas of computability via Turing machines and some of the consequences.
The lecture closes with a review of historical positions on the contentious idea of completed infinite sets, quoting illustrious mathematicians from Aristotle to A. Robinson, along with G. Cantor himself.
In summary, it appears that this is not a closed chapter in the History of Mathematics. For those interested in a more in depth discussion of these and other interesting issues, see my MathFoundations series of YouTube videos--also at this channel.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
- published: 21 May 2015
- views: 24229
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?".
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=SUtq4JXBbxM
- published: 22 Jan 2016
- views: 3788
Alan Turing almost accidentally created the blueprint for the modern day digital computer. Here Mark Jago takes us through The Halting Problem.
Turing Machines Explained: https://youtu.be/dNRDvLACg5Q
Busy Beaver: https://youtu.be/CE8UhcyJS0I
VR Simulator: http://youtu.be/Lm0lA0enPSk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Thanks to Assistant Professor Mark Jago of the University of Nottingham.
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
- published: 21 Aug 2014
- views: 706517
Let's see how this goes!
My Set Theory Notes (Introduction for Newbies)
https://drive.google.com/file/d/1jSultyuwOBhwLyUVlmOSwo47j69N8wM0/view?usp=sharing
My Computability Notes
https://drive.google.com/file/d/1aLves0iSwrXVmSywioN0hGGmPTbGOfYV/view?usp=sharing
- published: 06 Sep 2020
- views: 831
This video is part of an online course, Intro to Theoretical Computer Science. Check out the course here: https://www.udacity.com/course/cs313.
- published: 23 Feb 2015
- views: 12480
developed with YouTube
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched. The field has since grown to include the study of generalized computability and definability. Invention of the central combinatorial object of recursion theory, namely the Universal Turing Machine, predates and predetermines the invention of modern computers. Historically, the study of algorithmically undecidable sets and functions was motivated by various problems in mathematics that turned out to be undecidable; for example, word problem for groups and the like. There are several applications of the theory to other branches of mathematics that do not necessarily concentrate on undecidability. The early applications include the celebrated Higman's embedding theorem that provides a link between recursion theory and group theory, results of Michael O. Rabin and Anatoly Maltsev on algorithmic presentations of algebras, and the negative solution to Hilbert's Tenth Problem. The more recent applications include algorithmic randomness, results of Soare et al. who applied recursion-theoretic methods to solve a problem in algebraic geometry, and the very recent work of Slaman et al. on normal numbers that solves a problem in analytic number theory.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Computability_theory
-
What is Computability?
Joel David Hamkins, Professor of Logic, Oxford University This lecture is based on chapter 6 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press, https://mitpress.mit.edu/books/lectures-philosophy-mathematics. Lecture 6. Computability What is computability? Kurt Gödel defined a robust class of computable functions, the primitive recursive functions, and yet he gave reasons to despair of a fully satisfactory answer. Nevertheless, Alan Turing’s machine concept of computability, growing out of a careful philosophical analysis of the nature of human computability, proved robust and laid a foundation for the contemporary computer era; the widely accepted Church-Turing thesis asserts that Turing had the right notion. The distinction between computable decidability...
published: 18 Nov 2020 -
Proving Computability and Noncomputability
Theory of Computation https://uvatoc.github.io/week10 21.1 Proving Computability and Noncomputability - Ways to Prove a Function is Computable or Uncomputable - Example: Adding is Computable David Evans and Nathan Brunelle University of Virginia
published: 26 Oct 2020 -
Computability and problems with Set theory | Math History | NJ Wildberger
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheless, it went on to support the Zermelo-Fraenkel axiomatic approach to sets which we have a quick look at. Then we introduce Alan Turing's ideas of computability via Turing machines and some of the consequences. The lecture closes with a review of historical positions on the contentious idea of completed infinite sets, quoting illustrious mathematicians from Aristotle to A. Robinson, along with G. Cantor himself. In summary, it appears that this is not a closed chapter in the History of Mathematics. Fo...
published: 21 May 2015 -
Computability theory
If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 Computability theory Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=SUtq4JXBbxM
published: 22 Jan 2016 -
computability theory 1 Computable Functions
published: 30 Oct 2020 -
Turing & The Halting Problem - Computerphile
Alan Turing almost accidentally created the blueprint for the modern day digital computer. Here Mark Jago takes us through The Halting Problem. Turing Machines Explained: https://youtu.be/dNRDvLACg5Q Busy Beaver: https://youtu.be/CE8UhcyJS0I VR Simulator: http://youtu.be/Lm0lA0enPSk What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc Thanks to Assistant Professor Mark Jago of the University of Nottingham. http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: http://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
published: 21 Aug 2014 -
Preliminary Philosophy (Computability Theory Lecture 1)
Let's see how this goes! My Set Theory Notes (Introduction for Newbies) https://drive.google.com/file/d/1jSultyuwOBhwLyUVlmOSwo47j69N8wM0/view?usp=sharing My Computability Notes https://drive.google.com/file/d/1aLves0iSwrXVmSywioN0hGGmPTbGOfYV/view?usp=sharing
published: 06 Sep 2020 -
Computability Or Complexity Theory - Intro to Theoretical Computer Science
This video is part of an online course, Intro to Theoretical Computer Science. Check out the course here: https://www.udacity.com/course/cs313.
published: 23 Feb 2015 -
TOC:Computability Complete in Just 15 Min
published: 12 Dec 2019
developed with YouTube
1:24:10
What is Computability?
- Order: Reorder
- Duration: 1:24:10
- Uploaded Date: 18 Nov 2020
- views: 2578
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 6 of my book, Lectures on the Philosophy of Mathematics, published wi...
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 6 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press,
https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Lecture 6. Computability
What is computability? Kurt Gödel defined a robust class of computable functions, the primitive recursive functions, and yet he gave reasons to despair of a fully satisfactory answer. Nevertheless, Alan Turing’s machine concept of computability, growing out of a careful philosophical analysis of the nature of human computability, proved robust and laid a foundation for the contemporary computer era; the widely accepted Church-Turing thesis asserts that Turing had the right notion. The distinction between computable decidability and computable enumerability, highlighted by the undecidability of the halting problem, shows that not all mathematical problems can be solved by machine, and a vast hierarchy looms in the Turing degrees, an infinitary information theory. Complexity theory refocuses the subject on the realm of feasible computation, with the still-unsolved P versus NP problem standing in the background of nearly every serious issue in theoretical computer science.
https://wn.com/What_Is_Computability
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 6 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press,
https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Lecture 6. Computability
What is computability? Kurt Gödel defined a robust class of computable functions, the primitive recursive functions, and yet he gave reasons to despair of a fully satisfactory answer. Nevertheless, Alan Turing’s machine concept of computability, growing out of a careful philosophical analysis of the nature of human computability, proved robust and laid a foundation for the contemporary computer era; the widely accepted Church-Turing thesis asserts that Turing had the right notion. The distinction between computable decidability and computable enumerability, highlighted by the undecidability of the halting problem, shows that not all mathematical problems can be solved by machine, and a vast hierarchy looms in the Turing degrees, an infinitary information theory. Complexity theory refocuses the subject on the realm of feasible computation, with the still-unsolved P versus NP problem standing in the background of nearly every serious issue in theoretical computer science.
- published: 18 Nov 2020
- views: 2578
7:57
Proving Computability and Noncomputability
- Order: Reorder
- Duration: 7:57
- Uploaded Date: 26 Oct 2020
- views: 647
Theory of Computation
https://uvatoc.github.io/week10
21.1 Proving Computability and Noncomputability
- Ways to Prove a Function is Computable or Uncomputable
...
Theory of Computation
https://uvatoc.github.io/week10
21.1 Proving Computability and Noncomputability
- Ways to Prove a Function is Computable or Uncomputable
- Example: Adding is Computable
David Evans and Nathan Brunelle
University of Virginia
https://wn.com/Proving_Computability_And_Noncomputability
Theory of Computation
https://uvatoc.github.io/week10
21.1 Proving Computability and Noncomputability
- Ways to Prove a Function is Computable or Uncomputable
- Example: Adding is Computable
David Evans and Nathan Brunelle
University of Virginia
- published: 26 Oct 2020
- views: 647
47:05
Computability and problems with Set theory | Math History | NJ Wildberger
- Order: Reorder
- Duration: 47:05
- Uploaded Date: 21 May 2015
- views: 24229
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these diffi...
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheless, it went on to support the Zermelo-Fraenkel axiomatic approach to sets which we have a quick look at.
Then we introduce Alan Turing's ideas of computability via Turing machines and some of the consequences.
The lecture closes with a review of historical positions on the contentious idea of completed infinite sets, quoting illustrious mathematicians from Aristotle to A. Robinson, along with G. Cantor himself.
In summary, it appears that this is not a closed chapter in the History of Mathematics. For those interested in a more in depth discussion of these and other interesting issues, see my MathFoundations series of YouTube videos--also at this channel.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
https://wn.com/Computability_And_Problems_With_Set_Theory_|_Math_History_|_Nj_Wildberger
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheless, it went on to support the Zermelo-Fraenkel axiomatic approach to sets which we have a quick look at.
Then we introduce Alan Turing's ideas of computability via Turing machines and some of the consequences.
The lecture closes with a review of historical positions on the contentious idea of completed infinite sets, quoting illustrious mathematicians from Aristotle to A. Robinson, along with G. Cantor himself.
In summary, it appears that this is not a closed chapter in the History of Mathematics. For those interested in a more in depth discussion of these and other interesting issues, see my MathFoundations series of YouTube videos--also at this channel.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
- published: 21 May 2015
- views: 24229
8:42
Computability theory
- Order: Reorder
- Duration: 8:42
- Uploaded Date: 22 Jan 2016
- views: 3788
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Computability theory
Computabil...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?".
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=SUtq4JXBbxM
https://wn.com/Computability_Theory
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?".
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=SUtq4JXBbxM
- published: 22 Jan 2016
- views: 3788
12:04
computability theory 1 Computable Functions
- Order: Reorder
- Duration: 12:04
- Uploaded Date: 30 Oct 2020
- views: 204
- published: 30 Oct 2020
- views: 204
6:14
Turing & The Halting Problem - Computerphile
- Order: Reorder
- Duration: 6:14
- Uploaded Date: 21 Aug 2014
- views: 706517
Alan Turing almost accidentally created the blueprint for the modern day digital computer. Here Mark Jago takes us through The Halting Problem.
Turing Machines...
Alan Turing almost accidentally created the blueprint for the modern day digital computer. Here Mark Jago takes us through The Halting Problem.
Turing Machines Explained: https://youtu.be/dNRDvLACg5Q
Busy Beaver: https://youtu.be/CE8UhcyJS0I
VR Simulator: http://youtu.be/Lm0lA0enPSk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Thanks to Assistant Professor Mark Jago of the University of Nottingham.
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
https://wn.com/Turing_The_Halting_Problem_Computerphile
Alan Turing almost accidentally created the blueprint for the modern day digital computer. Here Mark Jago takes us through The Halting Problem.
Turing Machines Explained: https://youtu.be/dNRDvLACg5Q
Busy Beaver: https://youtu.be/CE8UhcyJS0I
VR Simulator: http://youtu.be/Lm0lA0enPSk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Thanks to Assistant Professor Mark Jago of the University of Nottingham.
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
- published: 21 Aug 2014
- views: 706517
27:35
Preliminary Philosophy (Computability Theory Lecture 1)
- Order: Reorder
- Duration: 27:35
- Uploaded Date: 06 Sep 2020
- views: 831
Let's see how this goes!
My Set Theory Notes (Introduction for Newbies)
https://drive.google.com/file/d/1jSultyuwOBhwLyUVlmOSwo47j69N8wM0/view?usp=sharing
My Co...
Let's see how this goes!
My Set Theory Notes (Introduction for Newbies)
https://drive.google.com/file/d/1jSultyuwOBhwLyUVlmOSwo47j69N8wM0/view?usp=sharing
My Computability Notes
https://drive.google.com/file/d/1aLves0iSwrXVmSywioN0hGGmPTbGOfYV/view?usp=sharing
https://wn.com/Preliminary_Philosophy_(Computability_Theory_Lecture_1)
Let's see how this goes!
My Set Theory Notes (Introduction for Newbies)
https://drive.google.com/file/d/1jSultyuwOBhwLyUVlmOSwo47j69N8wM0/view?usp=sharing
My Computability Notes
https://drive.google.com/file/d/1aLves0iSwrXVmSywioN0hGGmPTbGOfYV/view?usp=sharing
- published: 06 Sep 2020
- views: 831
0:55
Computability Or Complexity Theory - Intro to Theoretical Computer Science
- Order: Reorder
- Duration: 0:55
- Uploaded Date: 23 Feb 2015
- views: 12480
This video is part of an online course, Intro to Theoretical Computer Science. Check out the course here: https://www.udacity.com/course/cs313.
This video is part of an online course, Intro to Theoretical Computer Science. Check out the course here: https://www.udacity.com/course/cs313.
https://wn.com/Computability_Or_Complexity_Theory_Intro_To_Theoretical_Computer_Science
This video is part of an online course, Intro to Theoretical Computer Science. Check out the course here: https://www.udacity.com/course/cs313.
- published: 23 Feb 2015
- views: 12480
15:28
TOC:Computability Complete in Just 15 Min
- Order: Reorder
- Duration: 15:28
- Uploaded Date: 12 Dec 2019
- views: 3815
- published: 12 Dec 2019
- views: 3815
1:24:10
What is Computability?
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter...
published: 18 Nov 2020
What is Computability?
What is Computability?
- Report rights infringement
- published: 18 Nov 2020
- views: 2578
Joel David Hamkins, Professor of Logic, Oxford University
This lecture is based on chapter 6 of my book, Lectures on the Philosophy of Mathematics, published with MIT Press,
https://mitpress.mit.edu/books/lectures-philosophy-mathematics.
Lecture 6. Computability
What is computability? Kurt Gödel defined a robust class of computable functions, the primitive recursive functions, and yet he gave reasons to despair of a fully satisfactory answer. Nevertheless, Alan Turing’s machine concept of computability, growing out of a careful philosophical analysis of the nature of human computability, proved robust and laid a foundation for the contemporary computer era; the widely accepted Church-Turing thesis asserts that Turing had the right notion. The distinction between computable decidability and computable enumerability, highlighted by the undecidability of the halting problem, shows that not all mathematical problems can be solved by machine, and a vast hierarchy looms in the Turing degrees, an infinitary information theory. Complexity theory refocuses the subject on the realm of feasible computation, with the still-unsolved P versus NP problem standing in the background of nearly every serious issue in theoretical computer science.
7:57
Proving Computability and Noncomputability
Theory of Computation
https://uvatoc.github.io/week10
21.1 Proving Computability and Nonc...
published: 26 Oct 2020
Proving Computability and Noncomputability
Proving Computability and Noncomputability
- Report rights infringement
- published: 26 Oct 2020
- views: 647
Theory of Computation
https://uvatoc.github.io/week10
21.1 Proving Computability and Noncomputability
- Ways to Prove a Function is Computable or Uncomputable
- Example: Adding is Computable
David Evans and Nathan Brunelle
University of Virginia
47:05
Computability and problems with Set theory | Math History | NJ Wildberger
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of...
published: 21 May 2015
Computability and problems with Set theory | Math History | NJ Wildberger
Computability and problems with Set theory | Math History | NJ Wildberger
- Report rights infringement
- published: 21 May 2015
- views: 24229
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheless, it went on to support the Zermelo-Fraenkel axiomatic approach to sets which we have a quick look at.
Then we introduce Alan Turing's ideas of computability via Turing machines and some of the consequences.
The lecture closes with a review of historical positions on the contentious idea of completed infinite sets, quoting illustrious mathematicians from Aristotle to A. Robinson, along with G. Cantor himself.
In summary, it appears that this is not a closed chapter in the History of Mathematics. For those interested in a more in depth discussion of these and other interesting issues, see my MathFoundations series of YouTube videos--also at this channel.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
8:42
Computability theory
If you find our videos helpful you can support us by buying something from amazon.
https:/...
published: 22 Jan 2016
Computability theory
Computability theory
- Report rights infringement
- published: 22 Jan 2016
- views: 3788
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?".
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=SUtq4JXBbxM
12:04
computability theory 1 Computable Functions
published: 30 Oct 2020
computability theory 1 Computable Functions
computability theory 1 Computable Functions
- Report rights infringement
- published: 30 Oct 2020
- views: 204
6:14
Turing & The Halting Problem - Computerphile
Alan Turing almost accidentally created the blueprint for the modern day digital computer....
published: 21 Aug 2014
Turing & The Halting Problem - Computerphile
Turing & The Halting Problem - Computerphile
- Report rights infringement
- published: 21 Aug 2014
- views: 706517
Alan Turing almost accidentally created the blueprint for the modern day digital computer. Here Mark Jago takes us through The Halting Problem.
Turing Machines Explained: https://youtu.be/dNRDvLACg5Q
Busy Beaver: https://youtu.be/CE8UhcyJS0I
VR Simulator: http://youtu.be/Lm0lA0enPSk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Thanks to Assistant Professor Mark Jago of the University of Nottingham.
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
27:35
Preliminary Philosophy (Computability Theory Lecture 1)
Let's see how this goes!
My Set Theory Notes (Introduction for Newbies)
https://drive.goog...
published: 06 Sep 2020
Preliminary Philosophy (Computability Theory Lecture 1)
Preliminary Philosophy (Computability Theory Lecture 1)
- Report rights infringement
- published: 06 Sep 2020
- views: 831
Let's see how this goes!
My Set Theory Notes (Introduction for Newbies)
https://drive.google.com/file/d/1jSultyuwOBhwLyUVlmOSwo47j69N8wM0/view?usp=sharing
My Computability Notes
https://drive.google.com/file/d/1aLves0iSwrXVmSywioN0hGGmPTbGOfYV/view?usp=sharing
0:55
Computability Or Complexity Theory - Intro to Theoretical Computer Science
This video is part of an online course, Intro to Theoretical Computer Science. Check out t...
published: 23 Feb 2015
Computability Or Complexity Theory - Intro to Theoretical Computer Science
Computability Or Complexity Theory - Intro to Theoretical Computer Science
- Report rights infringement
- published: 23 Feb 2015
- views: 12480
This video is part of an online course, Intro to Theoretical Computer Science. Check out the course here: https://www.udacity.com/course/cs313.
15:28
TOC:Computability Complete in Just 15 Min
published: 12 Dec 2019
TOC:Computability Complete in Just 15 Min
TOC:Computability Complete in Just 15 Min
- Report rights infringement
- published: 12 Dec 2019
- views: 3815
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched. The field has since grown to include the study of generalized computability and definability. Invention of the central combinatorial object of recursion theory, namely the Universal Turing Machine, predates and predetermines the invention of modern computers. Historically, the study of algorithmically undecidable sets and functions was motivated by various problems in mathematics that turned out to be undecidable; for example, word problem for groups and the like. There are several applications of the theory to other branches of mathematics that do not necessarily concentrate on undecidability. The early applications include the celebrated Higman's embedding theorem that provides a link between recursion theory and group theory, results of Michael O. Rabin and Anatoly Maltsev on algorithmic presentations of algebras, and the negative solution to Hilbert's Tenth Problem. The more recent applications include algorithmic randomness, results of Soare et al. who applied recursion-theoretic methods to solve a problem in algebraic geometry, and the very recent work of Slaman et al. on normal numbers that solves a problem in analytic number theory.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Computability_theory
Related Sites
- thecapitaltheory.com
- dowtheorynews.com
- greekbankingtheory.com
- basetheory.net
- darwiniantheory.net
- zeropointlifetheory.com
- zeropointenergytheory.net
- proportiontheory.com
- teslatheory.org
- theoryanddebate.com
- theoryofrelativities.com
- complexitytheory.org
- ancientalienstheory.com
- amounttheory.com
- unproventheory.com
- fundamentaltheory.net
- theoryofliberty.com
- zeropointenergytheory.org
- cuttingtheory.com
- zerositeenergytheory.com
What is Computability?...
Proving Computability and Noncomputability...
Computability and problems with Set theory | Math ...
Computability theory...
computability theory 1 Computable Functions...
Turing & The Halting Problem - Computerphile...
Preliminary Philosophy (Computability Theory Lectu...
Computability Or Complexity Theory - Intro to Theo...
TOC:Computability Complete in Just 15 Min...
Latest News for: recursion theory
Edit
Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices [Statistical Genetics and Genomics]
The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented ... .
Edit
Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices [Investigation]
The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented ... .
Edit
Eight trends accelerating the age of commercial-ready quantum computing Share on Twitter
Ethan Batraski Contributor. Share on Twitter ... Every major technology breakthrough of our era has gone through a similar cycle in pursuit of turning fiction to reality. It starts in the stages of scientific discovery, a pursuit of principle against a theory, a recursive process of hypothesis-experiment ... That’s until now ... 1. Dark horses of QC emerge ... .
Edit
What Happens to Bitcoin and Ether after DeFi Euphoria Blowout? Analysts View
The rise in COMP token has been extraordinary. The total market capitalization of Compound expanded to nearly 7 times that of MakerDAO ... COMP/USD 1-Hour Chart on FTX (TradingView) ... The 2020 version would need to talk about multi-platform defi game theory attacks and problems with the infinite recursion yield mining model ... Bitcoin and Ethereum ... ....
Edit
The Prophecies of Q
Shortly after Trump’s election, as Pizzagate roared across the internet, Welch started binge-watching conspiracy-theory videos on YouTube ... If the internet is one big rabbit hole containing infinitely recursive rabbit holes, QAnon has somehow found its way down all of them, gulping up lesser conspiracy theories as it goes ... “It’s not a theory.
Edit
Will Bitcoin Mining Confidence Cause A BTC Price Spike To $28k?
You know what follows?” Game Theory And Price. This is a belief echoed by the financial reporter, Max Keiser, who, at the start of the month, made a prediction that Game Theory would play out to result in a $28k Bitcoin price ... Per protocol’s hard-coded Game Theory, hash precedes price.
- 1
