Sets, logic and computability | Math History | NJ Wildberger
In this video we give a very quick overview of a highly controversial period in the development of modern mathematics: the rise of set theory, logic and computability in the late 19th and early 20th centuries. Starting with the pioneering but contentious work of Georg Cantor in creating S
From playlist MathHistory: A course in the History of Mathematics
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
Commutative algebra 53: Dimension Introductory survey
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an introductory survey of many different ways of defining dimension. Reading: Section Exercises:
From playlist Commutative algebra
(PP 6.2) Multivariate Gaussian - examples and independence
Degenerate multivariate Gaussians. Some sketches of examples and non-examples of Gaussians. The components of a Gaussian are independent if and only if they are uncorrelated.
From playlist Probability Theory
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. Nevertheles
From playlist MathHistory: A course in the History of Mathematics
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
You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.
From playlist Abstract algebra
Commutative algebra 1 (Introduction)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. https://link.springer.com/book/10.1007/978-1-4612-5350-1 This is a short introductory lecture, and gives a few examples of the
From playlist Commutative algebra
This lecture is part of an online course on Galois theory. This is an introductory lecture, giving an informal overview of Galois theory. We discuss some historical examples of problems that it was used to solve, such as the Abel-Ruffini theorem that degree 5 polynomials cannot in genera
From playlist Galois theory
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
Recent progress in multiplicative number theory – Kaisa Matomäki & Maksym Radziwiłł – ICM2018
Number Theory Invited Lecture 3.5 Recent progress in multiplicative number theory Kaisa Matomäki & Maksym Radziwiłł Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (suc
From playlist Number Theory
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