In mathematics, the Klein four-group is a group with four elements, in which each element is self-inverse (composing it with itself produces the identity)and in which composing any two of the three non-identity elements produces the third one.It can be described as the symmetry group of a non-square rectangle (with the three non-identity elements being horizontal and vertical reflection and 180-degree rotation),as the group of bitwise exclusive or operations on two-bit binary values,or more abstractly as Z2 × Z2, the direct product of two copies of the cyclic group of order 2.It was named Vierergruppe (meaning four-group) by Felix Klein in 1884.It is also called the Klein group, and is often symbolized by the letter V or as K4. The Klein four-group, with four elements, is the smallest group that is not a cyclic group. There is only one other group of order four, up to isomorphism, the cyclic group of order 4. Both are abelian groups. The smallest non-abelian group is the symmetric group of degree 3, which has order 6. (Wikipedia).
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Klein Four-Group is the smallest noncyclic abelian group. Every proper subgroup is cyclic. We look at the the multiplication in the Klein Four-Group and find all of it's subgroups.
From playlist Abstract Algebra
There is no better way of understanding product groups than working through and example. In this video we look at the product group of the cyclic group with two elements and itself. The final result is isomorphic to what we call the Klein 4 group.
From playlist Abstract algebra
Finding the Elements of the Quotient Group Klein Four-Group Example
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding the Elements of the Quotient Group Klein Four-Group Example
From playlist Abstract Algebra
Finding the Cosets of a Cyclic Subgroup of the Klein Four Group
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding the Cosets of a Cyclic Subgroup of the Klein Four Group
From playlist Abstract Algebra
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/3kIo
From playlist 3D printing
Groups in abstract algebra examples
In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.
From playlist Abstract algebra
The three types of eight-fold way path on the Klein Quartic
Source code and mesh files here: https://github.com/timhutton/klein-quartic
From playlist Geometry
This is an informal talk on sporadic groups given to the Archimedeans (the Cambridge undergraduate mathematical society). It discusses the classification of finite simple groups and some of the sporadic groups, and finishes by briefly describing monstrous moonshine. For other Archimedeans
From playlist Math talks
Professor Gunnar Carlsson , Stanford University, USA
From playlist Public Lectures
Gunnar Carlsson (5/1/21): Topological Deep Learning
Machine learning using neural networks is a very powerful methodology which has demonstrated utility in many different situations. In this talk I will show how work in the mathematical discipline called topological data analysis can be used to (1) lessen the amount of data needed in order
From playlist TDA: Tutte Institute & Western University - 2021
Colloquium MathAlp 2018 - Christian Gérard
Aspects de la théorie quantique des champs en espace-temps courbe La théorie quantique des champs est formulée d'habitude sur l'espace-temps plat de Minkowski. L'extension de ce cadre à des espaces-temps généraux permet de mettre en lumière de nouveaux phénomènes quantiques qui surviennen
From playlist Colloquiums MathAlp
Topology of resolvent problems - Benson Farb
Special Seminar on Hilbert's 13th Problem II Topic: Topology of resolvent problems Speaker: Benson Farb Affiliation: University of Chicago Date: December 6, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Hunt for the Elusive 4th Klein Bottle - Numberphile
Carlo Séquin on his search for the elusive "fourth type of Klein bottle". More videos on Klein Bottles: http://bit.ly/KleinBottles More links & stuff in full description below ↓↓↓ Carlo's paper: http://bit.ly/Carlo_Klein Also featuring Carlo: Mobius House https://youtu.be/iwo7JReFTeg Tor
From playlist Carlo Séquin on Numberphile
Geometry of Surfaces - Topological Surfaces Lecture 3 : Oxford Mathematics 3rd Year Student Lecture
This is the third of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture covers cellular decompositions/subdivisions, triangulations and the
From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Nonlinear algebra, Lecture 10: "Invariant Theory", by Bernd Sturmfels
This is the tenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Made from 24 heptagons. Source code and meshes here: https://github.com/timhutton/klein-quartic
From playlist Geometry
David Nacin - Solutions to Klein Four Puzzles - G4G13 April 2018
A discussion of Ken Ken puzzles over the Klein Four group
From playlist G4G13 Videos