In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y. The set of all double cosets is denoted by (Wikipedia).
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
Proof: Cosets are Disjoint and Equal Size
Explanation for why cosets of a subgroup are either equal or disjoint and why all cosets have the same size. Group Theory playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ6a6 0:00 Cosets are disjoint 3:15 Cosets have same size Subscribe to see more new math
From playlist Group Theory
Have you ever wondered what a double integral is and what it has to do with cake? If so, watch this video and find out. Here I show step-by-step how to calculate a double integral, which is the multivariable calculus analog of an integral, enjoy! Double and Triple Integrals: https://www.y
From playlist Double and Triple Integrals
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Covariance (1 of 17) What is Covariance? in Relation to Variance and Correlation
Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of
From playlist COVARIANCE AND VARIANCE
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
(Updated Version Available)Double Angle Identities
Updated Version: https://youtu.be/4NznoskozDY Visit http://mathispower4u.wordpress.com/ for a categorized and searchable list of all videos.
From playlist Trigonometric Identities
Solve an equation with double angle of cosine
đ Learn how to use the double angle identities to solve trigonometric equations. When we have equations with a double angle we will apply the identities to create an equation that can help solve by inverse operations or factoring. We explore the double angles for sine, cosine and tangent
From playlist Double Angle Formulas
Examples With Cosets -- Abstract Algebra Examples 9
âSupport the channelâ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn đą Discord: https://discord.gg/Ta6PTGtKBm âmy other channelsâ Main Channel: https://www.youtube.
From playlist Abstract Algebra
Hankyung Ko: A singular Coxeter presentation
SMRI Algebra and Geometry Online Hankyung Ko (Uppsala University) Abstract: A Coxeter system is a presentation of a group by generators and a specific form of relations, namely the braid relations and the reflection relations. The Coxeter presentation leads to, among others, a similar pre
From playlist SMRI Algebra and Geometry Online
Cosets -- Abstract Algebra video 9
âSupport the channelâ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn đą Discord: https://discord.gg/Ta6PTGtKBm âmy other channelsâ Main Channel: https://www.youtube.
From playlist Abstract Algebra
Hypergroup definition and five key examples | Diffusion Symmetry 4 | N J Wildberger
We state a precise definition of a finite commutative hypergroup, and then give five important classes of examples, 1) the class hypergroup of a finite (non-commutative) group G 2) the character hypergroup of a finite (non-commutative) group G 3) the hypergroup associated to a distance-tr
From playlist Diffusion Symmetry: A bridge between mathematics and physics
Abstract Algebra | Lagrange's Theorem
We prove some general results, culminating in a proof of Lagrange's Theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Visual Group Theory, Lecture 5.2: The orbit-stabilizer theorem
Visual Group Theory, Lecture 5.2: The orbit-stabilizer theorem Suppose a group G acts on a set S. The orbit of s in S is the collection of states (in S) reachable from s. The stablizer of s is the set of elements (in G) that fix s. The orbit-stabilizer theorem says that |G|=|Orb(s)|*|Stab
From playlist Visual Group Theory
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
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 4
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist Ăcole d'ĂtĂ© 2022 - Cohomology Geometry and Explicit Number Theory
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 class April 13, 2021
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/ma
From playlist Super Lo-fi in class videos
Other Forms of the Cosine Double-Angle Formula
Watch more videos on http://www.brightstorm.com/math/precalculus SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook âș ht
From playlist Precalculus