Cosets generated by elements of cosets
What were to happen should we generate a left or right coset with an element of a coset? In this video I explore how we simply end up with the same coset.
From playlist Abstract algebra
A graphical representation of cosets using Caley tables, gives us a deeper insight. In this video we explore two cases. In the first, the element of G that creates the coset of the subgroup is in the subgroup and in the second, it is not.
From playlist Abstract algebra
In this video I do an example problem calculating the right coset of a set, H, with an element from the symmetric group on four elements.
From playlist Abstract algebra
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Abstract Algebra - 7.1 Cosets and Their Properties
In this video, we explore the definition of both left and right cosets and an example of each. In addition, we take a look at 9 properties that cosets share. Video Chapters: Intro 0:00 What is a Coset/Left Coset Example? 0:06 Example of Right Cosets 4:31 The First 3 Coset Properties 8:19
From playlist Abstract Algebra - Entire Course
The Hoover Dam: an Engineering and Artistic Masterpiece
Located on the border between Arizona and Nevada, the Hoover Dam is an iconic structure that has stood the test of time for nearly a century. Built in the 1930s to provide hydroelectric power and help control floods in the Colorado River, the Hoover Dam is a testament to human ingenuity an
From playlist Iconic Builds
In this first video on cosets, I show you the equivalence relation on a group, G, that will turn out to create equivalence classes, which are actually cosets. We will prove later that these equivalence classes created by an element in the group, G, are equal to the set of element made up
From playlist Abstract algebra
What to do with all those old PCBs from stuff you've taken apart...
From playlist Projects & Installations
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
GT4. Normal Subgroups and Quotient Groups
EDIT: At 2:00, the columns for cosets of H={e, (12)} are switched. Abstract Algebra: We define normal subgroups and show that, in this case, the space of cosets carries a group structure, the quotient group. Example include S3, the modular integers, and Q/Z. U.Reddit course materia
From playlist Abstract Algebra
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagr
From playlist Visual Group Theory
GT3. Cosets and Lagrange's Theorem
Abstract Algebra: Let G be a group with subgroup H. We define an equivalence relation on G that partitions G into left cosets. We use this partition to prove Lagrange's Theorem and its corollary. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theor
From playlist Abstract Algebra
This lecture is part of an online graduate course on Galois theory. As an application of Galois theory, we prove Gauss's theorem that it is possible to construct a regular heptadecagon with ruler and compass.
From playlist Galois theory
Complete Derivation: Universal Property of the Tensor Product
Previous tensor product video: https://youtu.be/KnSZBjnd_74 The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universa
From playlist Tensor Products
Why Normal Subgroups are Necessary for Quotient Groups
Proof that cosets are disjoint: https://youtu.be/uxhAUmgSHnI In order for a subgroup to create a quotient group (also known as factor group), it must be a normal subgroup. That means that when we conjugate an element in the subgroup, it stays in the subgroup. In this video, we explain wh
From playlist Group Theory
Abstract Algebra | Subgroups and quotient groups of the quaternions.
We present a description of all subgroups and quotient groups of the quaternions. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Induction of p-Cells and Localization - Lars Thorge Jensen
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Induction of p-Cells and Localization Speaker: Lars Thorge Jensen Affiliation: Member, School of Mathematics Date: November 19, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Visual Group Theory, Lecture 3.5: Quotient groups
Visual Group Theory, Lecture 3.5: Quotient groups Like how a direct product can be thought of as a way to "multiply" two groups, a quotient is a way to "divide" a group by one of its subgroups. We start by defining this in terms of collapsing Cayley diagrams, until we get a conjecture abo
From playlist Visual Group Theory
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapters 19 & 20