Sperner's lemma

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

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

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

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

RIngs 22 Hensel's lemma

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

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

Topics in Combinatorics lecture 2.5 --- Sperner's theorem

How many subsets of {1,...,n} can you choose if no set in your collection is allowed to be a subset of another? An obvious construction is to take all sets of size n/2 (or (n-1)/2 if n is odd). Sperner's theorem tells us that this is the best we can do. It has a miraculously short and simp

From playlist Topics in Combinatorics (Cambridge Part III course)

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

Splitting Rent with Triangles | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi You can find out how to fairly divide rent between three different people even when you don’t know the third person’s preferences! Find out how with Sperner’s Lemma. T

From playlist An Infinite Playlist

NYT: Sperner's lemma defeats the rental harmony problem

TRICKY PROBLEM: A couple of friends want to rent an apartment. The rooms are quite different and the friends have different preferences and different ideas about what's worth what. Is there a way to split the rent and assign rooms to the friends so that everybody ends up being happy? In t

From playlist Recent videos

Problem Solving Session (Sperner's Lemma) by Mayank Bhardwaj & Amal Roy

Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f

From playlist Summer Research Program On Dynamics Of Complex Systems 2019

Henry Adams (9/3/20): Fair division

Title: Fair division Abstract: Suppose five roommates need to pay $3,000 dollars of rent per month for their five-bedroom apartment. The five bedrooms are not equivalent: one is bigger, one is smaller, one has more windows, one is closer to the kitchen, one is painted neon green. So it is

From playlist AATRN 2020

Nevanlinna Prize Lecture: Equilibria and fixed points — Constantinos Daskalakis — ICM2018

Equilibria, fixed points, and computational complexity Constantinos Daskalakis Abstract: The concept of equilibrium, in its various forms, has played a central role in the development of Game Theory and Economics. The mathematical properties and computational complexity of equilibria are

From playlist Special / Prizes Lectures

How can you cut a square into equal triangles? | Nathan Dalaklis

You've read the title, it seems like a simple question, but an answer requires the p-adic norm, Sperner's lemma, and some more mathematical machinery. In this video, we give a proof of Sperner's lemma for the 2-dimensional case and introduce the p-adic norm in order to provide a proof for

From playlist The New CHALKboard

Algorithmic Game Theory by Siddharth Barman

Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f

From playlist Summer Research Program On Dynamics Of Complex Systems 2019

My Favorite Theorem: The Borsuk-Ulam Theorem

Many thanks for 10k subscribers! Fun video for you from Topology: The Borsuk-Ulam Theorem. One interpretation of this is that on the surface of the earth, there must be some point where it and its antipode (the spot exactly opposite it) have the exact same temperature and pressure. More ge

From playlist Cool Math Series

Number Theory | Hensel's Lemma

We prove Hensel's Lemma, which is related to finding solutions to polynomial congruences modulo powers of primes. http://www.michael-penn.net Thumbnail Image: By Unknown - Universität Marburg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=9378696

From playlist Number Theory