Menger's theorem

Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem

In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

Dirichlet Eta Function - Integral Representation

Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna

From playlist Integrals

Intro to Menger's Theorem | Graph Theory, Connectivity

Menger's theorem tells us that for any two nonadjacent vertices, u and v, in a graph G, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths in G. The Proof of Menger's Theorem: https://youtu.be/2rbbq-Mk-YE Remember that

From playlist Graph Theory

Lecture 20 - Trees and Connectivity

This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Differential Equations | Abel's Theorem

We present Abel's Theorem with a proof. http://www.michael-penn.net

From playlist Differential Equations

Amaury Pouly

A (truly) universal polynomial differential equation Lee A. Rubel proved in 1981 that there exists a universal fourth-order algebraic differential equation P(y,y',y'',y''')=0 (1) and provided an explicit example. It is universal in the sense that for any continuous function f from R to

From playlist DART X

Proof: Menger's Theorem | Graph Theory, Connectivity

We prove Menger's theorem stating that for two nonadjacent vertices u and v, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths. If you want to learn about the theorem, see how it relates to vertex connectivity, and see

From playlist Graph Theory

Cong He: Right-angled Coxeter Groups with Menger Curve Boundary

Cong He, University of Wisconsin Milwaukee Title: Right-angled Coxeter Groups with Menger Curve Boundary Hyperbolic Coxeter groups with Sierpinski carpet boundary was investigated by {\'S}wi{\c{a}}tkowski. And hyperbolic right-angled Coxeter group with Gromov boundary as Menger curve was s

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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)

How to determine the max and min of a sine on a closed interval

👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

What are Vertex Separating Sets? | Graph Theory

What are vertex separating sets in graph theory? We'll be going over the definition of a vertex separating set and some examples in today's video graph theory lesson! Let G be a graph and S be a vertex cut of G. As in, S is a set of vertices of G such that G - S is disconnected. Then, let

From playlist Set Theory

The Beauty of Fractal Geometry (#SoME2)

0:00 — Sierpiński carpet 0:18 — Pythagoras tree 0:37 — Pythagoras tree 2 0:50 — Unnamed fractal circles 1:12 — Dragon Curve 1:30 — Barnsley fern 1:44 — Question for you! 2:05 — Koch snowflake 2:26 — Sierpiński triangle 2:47 — Cantor set 3:03 — Hilbert curve 3:22 — Unnamed fractal squares 3

From playlist Summer of Math Exposition 2 videos

The Second Fundamental Theorem of Calculus

This video introduces and provides some examples of how to apply the Second Fundamental Theorem of Calculus. Site: http://mathispower4u.com

From playlist The Second Fundamental Theorem of Calculus

Kurt Gödel Centenary - Part III

John W. Dawson, Jr. Pennsylvania State University November 17, 2006 More videos on http://video.ias.edu

From playlist Kurt Gödel Centenary

What is the max and min of a horizontal line on a closed interval

👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

Commutative algebra 55: Dimension of local rings

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 4 definitions of the dimension of a Noetherian local ring: Brouwer-Menger-Urysohn dimension, Krull dimension, degree o

From playlist Commutative algebra

Weil conjectures 1 Introduction

This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie

From playlist Algebraic geometry: extra topics

Jeff Erickson - Lecture 4 - Two-dimensional computational topology - 21/06/18

School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Jeff Erickson (University of Illinois at Urbana-Champaign, USA) Two-dimensional computational topology - Lecture 4 Abstract: This series of lectures will describe recent

From playlist Jeff Erickson - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects

Recognising Fractals from a reasonable distance - Linear Distance Estimation Edition!

Welcome to the second part of the series on recognising fractals from a reasonable distance! This is the Linear Distance Estimation Edition, featuring the following fractals: Amazing box - Mod 2 Abox - Mod Kali-V3 Abox - SurfBox Generalized Fold Box - Octahedron Generalized Fold Box - Oc

From playlist Nerdy Rodent Uploads!

The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg

In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t

From playlist Algebraic Calculus One