Berge's lemma, an animated proof
Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should
From playlist Summer of Math Exposition Youtube Videos
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Burnside's Lemma (Part 2) - combining math, science and music
Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be
From playlist Traditional topics, explained in a new way
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
Perfectoid spaces (Lecture 2) by Kiran Kedlaya
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
The Case for Jackson Pollock | The Art Assignment | PBS Digital Studios
You’ve heard of Jackson Pollock and know of his infamous “drip paintings,” but what is it that you’re supposed to do when you look at his work today? Why did it cause shockwaves in 1947, and what does it mean now? We explore the life, evolution, and legacy of Jackson Pollock. Thanks to o
From playlist The Case For
From the Curator: Jackson Pollock Abstract Expressionist New York The Museum of Modern Art, October 3, 2010--April 11, 2011 MoMA.org/abexny Filmed by Plowshares Media Images courtesy of Pollock-Krasner Foundation; Artists Rights Society (ARS), New York; Nina Leen; Time & Life Pict
From playlist Expressionism to Pop Art | Art History | Khan Academy
László Lovász: The many facets of the Regularity Lemma
Abstract: The Regularity Lemma of Szemerédi, first obtained in the context of his theorem on arithmetic progressions in dense sequences, has become one of the most important and most powerful tools in graph theory. It is basic in extremal graph theory and in the theory of property testing.
From playlist Abel Lectures
In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral
From playlist Real Analysis
Trending Artists of the 17th Century
Have you heard of Italian Baroque artist Artemisia Gentilschi? Find out why her popularity, and that of other artists, has risen dramatically since the 1970s. And vote for America's favorite novel here!: https://to.pbs.org/2Jes2X5. Chart the frequency of mention of any artist, maker, gen
From playlist We Think Art is Interesting
Proof & Explanation: Gauss's Lemma in Number Theory
Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Quadratic Residues
Paint Application Studies of Jackson Pollock's Mural
Scientists from the Getty Conservation Institute attempt to recreate the method and materials used by Jackson Pollock to create his monumental painting, Mural. Watch additional videos about the discoveries of Jackson Pollock's Mural made by Getty conservation scientists and curators. http
From playlist Expressionism to Pop Art | Art History | Khan Academy
From the Curator: Mark Rothko Abstract Expressionist New York The Museum of Modern Art, October 3, 2010--April 11, 2011 MoMA.org/abexny Filmed by Plowshares Media Images courtesy of Kate Rothko Prizel & Christopher Rothko; Barnett Newman Foundation; The Franz Kline Estate; The Wil
From playlist Expressionism to Pop Art | Art History | Khan Academy
How to paint like Jackson Pollock – One: Number 31, 1950 – with Corey D'Augustine | IN THE STUDIO
Learn how to paint like artist Jackson Pollock, one of the key figures of the postwar abstract expressionist art movement, with IN THE STUDIO instructor Corey D’Augustine. Explore the techniques of other New York School painters like de Kooning, Rothko, and Pollock in MoMA's new free, o
From playlist Expressionism to Pop Art | Art History | Khan Academy
Can the U.S. Pursue Interests and Values at the Same Time? with Michael McFaul
Watch, learn and connect: https://stanfordconnects.stanford.edu/ As a democratic nation, America champions ideals such as freedom and liberty. Drawing from his government service and extensive background in foreign policy, Professor McFaul proposes a framework for thinking about democracy
From playlist STANFORD+CONNECTS
Commutative algebra 51: Hensel's lemma continued
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. This lecture continues the discussion of Hensel's lemma. We first use it to find the structure of the group of units of the p-
From playlist Commutative algebra
Desire Is the Theme of All Life: Helen Frankenthaler in 1950s New York with Alexander Nemerov
At the dawn of the 1950s, a promising young painter named Helen Frankenthaler, fresh out of college, moved back to New York City, where she grew up. By the decade’s end, she had succeeded in establishing herself as an important American artist of the postwar period. In the years in between
From playlist Stanford Alumni Faculty Talks