In mathematics, the Cayley configuration space of a over a set of its non-edges , called Cayley parameters, is the set of distances attained by over all its , under some -norm. In other words, each framework of the linkage prescribes a unique set of distances to the non-edges of , so the set of all frameworks can be described by the set of distances attained by any subset of these non-edges. Note that this description may not be a bijection. The motivation for using distance parameters is to define a continuous quadratic branched covering from the configuration space of a linkage to a simpler, often convex, space. Hence, obtaining a framework from a Cayley configuration space of a linkage over some set of non-edges is often a matter of solving quadratic equations. Cayley configuration spaces have a close relationship to the flattenability and of graphs. (Wikipedia).
Proof that Cayley table row and column entries are unique and complete
In this video I show a proof of why all the row and column entries in a Cayley table are unique and why all of the elements in the group appear in each row and column. This proof goes a long way towards proving Cayley's theorem.
From playlist Abstract algebra
This video is about Cayley graphs and some of their basic properties.
From playlist Basics: Graph Theory
Visual Group Theory, Lecture 1.2: Cayley graphs
Visual Group Theory, Lecture 1.2: Cayley graphs In this lecture, we introduce a visual way to "map out" a group using an object called a Cayley graph. This concept is a useful visualization tool, but it is often omitted entirely from traditional Abstract Algebra classes. Course webpage (
From playlist Visual Group Theory
Open educational resources for the day
Another run in Newlands Forest, another upload of open educational resources. I uploaded two videos today. In the abstract algebra video I show a proof of why all row and column entries in a Cayley table contain unique elements as well as all of the elements of the group. This takes us
From playlist Fun!!!
Visual Group Theory, Lecture 3.2: Cosets
Visual Group Theory, Lecture 3.2: Cosets The "regularity" property of Cayley diagrams implies that identical copies of the fragment corresponding to a subgroup appear throughout the rest of the diagram. These subsets are called cosets. In this lecture, we formalize this algebraically and
From playlist Visual Group Theory
Abstract Algebra - 1.2 Cayley Tables and an Introduction to Groups
We further develop our understanding of the symmetries of a square by constructing both a Cayley diagram and Cayley table (multiplication table). We also briefly discuss why the symmetries form a group, though we will leave the official definition of a group to video 2.1. Video Chapters:
From playlist Abstract Algebra - Entire Course
Cauchy Sequence In this video, I define one of the most important concepts in analysis: Cauchy sequences. Those are sequences which "crowd" together, without necessarily going to a limit. Later, we'll see what implications they have in analysis. Check out my Sequences Playlist: https://w
From playlist Sequences
Visual Group Theory, Lecture 5.1: Groups acting on sets
Visual Group Theory, Lecture 5.1: Groups acting on sets When we first learned about groups as collections of actions, there was a subtle but important difference between actions and configurations. This is the tip of the iceberg of a more general and powerful concept of a group action. Ma
From playlist Visual Group Theory
Visual Group Theory, Lecture 3.4: Direct products
Visual Group Theory, Lecture 3.4: Direct products There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and mu
From playlist Visual Group Theory
Lie Group Integrators for Animation and Control of Vehicles - Talk (4/4)
This video is a conference presentation of the paper "Lie Group Integrators for Animation and Control of Vehicles" given by Keenan Crane in August 2009 -- see http://keenan.is/nonholonomic for more information Lie Group Integrators for Animation and Control of Vehicles Marin Kobilarov, Ke
From playlist Lie Group Integrators Talk
Visual Group Theory, Lecture 1.4: Group presentations
Visual Group Theory, Lecture 1.4: Group presentations We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a
From playlist Visual Group Theory
Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics
Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics Groups are always lurking where symmetry arises. In this lecture, we explore many beautiful examples of groups that arise from natural symmetries in science, art, and mathematics. This includes shapes of molecules,
From playlist Visual Group Theory
Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Now we know about vector spaces, so it's time to learn how to form something called a basis for that vector space. This is a set of linearly independent vectors that can be used as building blocks to make any other vector in the space. Let's take a closer look at this, as well as the dimen
From playlist Mathematics (All Of It)
If A Sequence is Cauchy in Space it's Component Sequences are Cauchy Proof
If A Sequence is Cauchy in Space it's Component Sequences are Cauchy Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Cauchy Sequences
Jonathan Novak : Monotone Hurwitz numbers and the HCIZ integral
Recording during the thematic meeting : "Pre-School on Combinatorics and Interactions" the January 13, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Combinatorics
Robert Ghrist, Lecture 3: Topology Applied III
27th Workshop in Geometric Topology, Colorado College, June 12, 2010
From playlist Robert Ghrist: 27th Workshop in Geometric Topology
Defining Microservices | SHORTS
What are microservices? What is microservice architecture for and why are they more complex than they look on the surface? In this #shorts episode, Dave Farley give his definition of microservices. For a fuller exploration of Microservices, see Dave's video "The Problem with Microservices
From playlist Microservices
Acylindrically hyperbolic structures on groups - Balasubramanya
Women and Mathematics Title: Acylindrically hyperbolic structures on groups Speaker: Sahana Hassan Balasubramanya Affiliation: Vanderbilt University Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics