In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?". In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" model of computation (see Church–Turing thesis). It might seem that the potentially infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory. So in principle, any problem that can be solved (decided) by a Turing machine can be solved by a computer that has a finite amount of memory. (Wikipedia).
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Theory of Computation 1. Finite State Machines ADUni
From playlist [Shai Simonson]Theory of Computation
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
The mother of all representer theorems for inverse problems & machine learning - Michael Unser
This workshop - organised under the auspices of the Isaac Newton Institute on “Approximation, sampling and compression in data science” — brings together leading researchers in the general fields of mathematics, statistics, computer science and engineering. About the event The workshop ai
From playlist Mathematics of data: Structured representations for sensing, approximation and learning
Hands on learning of computational theory for software developers from all walks of life. Using semantics and the barebones of the Ruby programming language, learn the meaning of programs and why specific algorithms do their job.
From playlist Programming Podcast
Theory of Computation 11. The Bullseye ADUni
From playlist [Shai Simonson]Theory of Computation
Shadows of Computation - Lecture 5 - What is Computation?
Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In the fifth lecture Will sp
From playlist Shadows of Computation
Theory of Computation 12. Turing Machines ADUni
From playlist [Shai Simonson]Theory of Computation
Intro to Number Theory and The Divisibility Relation
This video introduces the divisibility relation and provided several examples. mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Emergent geometry: The duality between gravity and quantum field theory - Juan Maldacena
Emergent geometry: The duality between gravity and quantum field theory - Juan Maldacena Juan Maldacena Institute for Advanced Study; Faculty, School of Natural Science February 20, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
Teena Gerhardt - 1/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
David Deutsch - Why is the Quantum so Strange?
To know reality, one must confront the quantum. It is how our world works at the deepest level. What's the quantum? It is bizarre, defying all common sense. Particles in two positions at the same time. Spooky action at a distance. It would sound absurd if it weren't true. For more on info
From playlist Closer To Truth - David Deutsch Interviews
David Deutsch - Why is the Quantum so Strange?
To know reality, one must confront the quantum. It is how our world works at the deepest level. What's the quantum? Click here to watch more interviews with David Deutsch http://bit.ly/1xAaXvW Click here to watch more interviews on quantum mechanics http://bit.ly/2yJFX1w Click here to b
From playlist Closer To Truth - David Deutsch Interviews
PiTP - High Energy scattering at strong coupling via AdS/CFT - Juan Maldacena
PiTP - High Energy scattering at strong coupling via AdS/CFT Juan Maldacena Institute for Advanced Study July 25, 2007
From playlist PiTP 2007
Computing Reality (Lecture - 01) by David B Kaplan
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Computational Complexity Classes, Homotopy Classes and N-machines
Examined herein is the possible correspondence between computational complexity classes in computational graphs and higher homotopy classes between computability paths via the application of two methods. The first method is the use of category theory for formalizing a model of (categorifie
From playlist Wolfram Technology Conference 2021
Tests, Games, and Martin-Lof's Meaning Explanations for Intuitionistic Type Theory - Peter Dybjer
Peter Dybjer November 30, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Scattering amplitude in Chern-Simons matter theories by Sachin Jain
ORGANIZERS : Pallab Basu, Avinash Dhar, Rajesh Gopakumar, R. Loganayagam, Gautam Mandal, Shiraz Minwalla, Suvrat Raju, Sandip Trivedi and Spenta Wadia DATE : 21 May 2018 to 02 June 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore In the past twenty years, the discovery of the AdS/C
From playlist AdS/CFT at 20 and Beyond
SketchySVD - Joel Tropp, California Institute of Technology
This workshop - organised under the auspices of the Isaac Newton Institute on “Approximation, sampling and compression in data science” — brings together leading researchers in the general fields of mathematics, statistics, computer science and engineering. About the event The workshop ai
From playlist Mathematics of data: Structured representations for sensing, approximation and learning
Entanglement entropy and dilaton effective action
Discussion Meeting: Entanglement from Gravity(URL: http://www.icts.res.in/discussion_meeting/EG2014/) Dates: Wednesday 10 Dec, 2014 - Friday 12 Dec, 2014 Description: In the last few years, quantum entanglement considerations have led to profound insights in the connection with gravity.
From playlist Discussion Meeting: Entanglement from Gravity