In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be split naturally into connected pieces, each piece is usually called a component (or connected component). (Wikipedia).
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist Topology
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
From playlist Belong: What It's Like to Live in the Hyphen
This video is about connectedness and some of its basic properties.
From playlist Basics: Topology
Adding Connections on LinkedIn
In this video, you’ll learn how to add connections on LinkedIn. Visit https://edu.gcfglobal.org/en/linkedin/adding-connections-on-linkedin/1/ for our text-based lesson. We hope you enjoy!
From playlist LinkedIn
From playlist Week 9: Social Networks
What is a Manifold? Lesson 5: Compactness, Connectedness, and Topological Properties
The last lesson covering the topological prep-work required before we begin the discussion of manifolds. Topics covered: compactness, connectedness, and the relationship between homeomorphisms and topological properties.
From playlist What is a Manifold?
Ahlfors-Bers 2014 "Roots of Polynomials and Parameter Spaces"
Sarah Koch (University of Michigan): In his last paper, "Entropy in Dimension One," W. Thurston completely characterized which algebraic integers arise as exp(entropy(f)), where f is a postcritically finite real map of a closed interval. On page 1 of this paper, there is a spectacular ima
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Metric Spaces - Lectures 15 & 16: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 8th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Theorem 1.10 - part 10.5.2 - Neron-Ogg-Shafarevich - Unramified implies Good (extending properness)
In this video we continue the proof of Neron-Ogg-Shaferevich to show that the whole Neron Model is proper and connected provided the information about the special fiber being proper.
From playlist Theorem 1.10
Section 4b: Graph Connectivity
From playlist Graph Theory
Metric Spaces - Lectures 17 & 18: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 9th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Robert Lazarsfeld: Cayley-Bacharach theorems with excess vanishing
A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and H
From playlist Algebraic and Complex Geometry
Lie Groups and Lie Algebras: Lesson 34 -Introduction to Homotopy
Lie Groups and Lie Algebras: Introduction to Homotopy In order to proceed with Gilmore's study of Lie groups and Lie algebras we now need a concept from algebraic topology. That concept is the notion of homotopy and the Fundamental Group of a topological space. In this lecture we provide
From playlist Lie Groups and Lie Algebras
Types Of Centrality - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Tao Hou (5/13/20): Computing minimal persistent cycles: Polynomial and hard cases
Title: Computing minimal persistent cycles: Polynomial and hard cases Abstract: Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in the purely topological persistence diagrams (also termed as barcodes). In our ear
From playlist AATRN 2020
