A beautiful combinatorical proof of the Brouwer Fixed Point Theorem - Via Sperner's Lemma
Using a simple combinatorical argument, we can prove an important theorem in topology without any sophisticated machinery. Brouwer's Fixed Point Theorem: Every continuous mapping f(p) from between closed balls of the same dimension have a fixed point where f(p)=p. Sperner's Lemma: Ever
From playlist Cool Math Series
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
Lyapunov Stability via Sperner's Lemma
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of i
From playlist Summer of Math Exposition Youtube Videos
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
The Frobenius Problem - Method for Finding the Frobenius Number of Two Numbers
Goes over how to find the Frobenius Number of two Numbers.
From playlist ℕumber Theory
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
Lagrangian Floer theory in symplectic fibrations - Douglas Schultz
Princeton/IAS Symplectic Geometry Seminar Topic: Lagrangian Floer theory in symplectic fibrations Speaker: Douglas Schultz Affiliation: Rutgers University Date:April 27, 2017 For more info, please visit http://video.ias.edu
From playlist Mathematics
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
We Found a Way To Look Into the Invisible Dark Side of the Galaxy
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about a new discovery of several stars that were previously invisible to us because they were on the "dark side" of our galaxy. We now found a way to see th
From playlist The Milky Way
We Found 39 New Galaxies That Were Invisible to Us Until Now
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about 39 newly discovered massive galaxies from far, far away that were invisible to us until now. Paper: https://arxiv.org/pdf/1908.02372.pdf Support this
From playlist Galaxies, Quasars, Blazars
We Just Took The First Ever Picture of the Cosmic Web
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about the picture of the illusive cosmic web. Paper: https://science.sciencemag.org/content/366/6461/97 Support this channel on Patreon to help me make thi
From playlist Galaxies, Quasars, Blazars
These Paintings Show the Future Imagined by Soviet Artists
Leonov, David Scott as well as Neil Armstrong released this amazing book together: https://amzn.to/2BdAvEu Hello and welcome! My name is Anton, this video is dedicated to Alexei Leonov who passed away in October of 2019 and was buried today, when this video is published. I wanted to dedic
From playlist The Universe
Using Science to Figure Out Where Blade Runner Replicants Were From
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about Tears in Rain clip: https://www.youtube.com/watch?v=NoAzpa1x7jU&t=61s Space travel calculator: http://nathangeffen.webfactional.com/spacetravel/spac
From playlist Mysteries of the Universe
This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra
From playlist Zermelo Fraenkel axioms
Goodbye Comrade - A Tribute To The First Man in Outer Space
Leonov, David Scott as well as Neil Armstrong released this amazing book together: https://amzn.to/2BdAvEu Hello and welcome! My name is Anton, this video is dedicated to Alexei Leonov who passed away in October of 2019 and was buried today, when this video is published. I wanted to dedic
From playlist The Universe
NASA Is Looking Into Using Bacteria to Mine Asteroids!
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about a newly launched mission by NASA called Biorock meant to investigate biomining techniques. More about Biorock mission from NASA: https://www.nasa.gov/
From playlist Interesting NASA Missions
We Found Signs of a Large Planetary Collision 1000s Years Ago
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about a recent discovery of the signs of planetary collision in a system known as BD +20 307 discovered using SOFIA telescope. paper: https://iopscience.iop
From playlist Unusual Exoplanets
Asteroseismology - Listening to Star Vibrations To Learn What's Inside
You can buy Universe Sandbox 2 game here: http://amzn.to/2yJqwU6 Hello and welcome! My name is Anton and in this video, we will talk about the field known as asteroseismology - the study of star harmonics or the music that the stars produce. Music: Home-We're Finally Landing https://soun
From playlist Unusual Stars
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Two Times in History When We Were Certain It Was Aliens
The USB dongle you can use to look for pulsars is here: https://amzn.to/2ozMSYE I wrote a foreword for this awesome Sci-Fi book here: https://amzn.to/3aGrg0I Get a Wonderful Person shirt: https://teespring.com/stores/whatdamath Alternatively, PayPal donations can be sent here: paypal.me/wh
From playlist Galaxies, Quasars, Blazars