Group Isomorphisms in Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Isomorphisms in Abstract Algebra - Definition of a group isomorphism and isomorphic groups - Example of proving a function is an Isomorphism, showing the group of real numbers under addition is isomorphic to the group of posit
From playlist Abstract Algebra
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Group automorphisms in abstract algebra
Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem
From playlist Abstract algebra
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Introduction to additive combinatorics lecture 5.8 --- Freiman homomorphisms and isomorphisms.
The notion of a Freiman homomorphism and the closely related notion of a Freiman isomorphism are fundamental concepts in additive combinatorics. Here I explain what they are and prove a lemma that states that a subset A of F_p^N such that kA - kA is not too large is "k-isomorphic" to a sub
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Second Isomorphism Theorem for Groups Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Second Isomorphism Theorem for Groups Proof. If G is a group and H and K are subgroups of G, and K is normal in G, we prove that H/(H n K) is isomorphic to HK/K.
From playlist Abstract Algebra
Almgren's isomorphism theorem and parametric isoperimetric inequalities - Yevgeny Liokumovich
Variational Methods in Geometry Seminar Topic: Almgren's isomorphism theorem and parametric isoperimetric inequalities Speaker: Yevgeny Liokumovich Affiliation: Massachusetts Institute of Technology; Member, School of Mathematics Date: November 20, 2018 For more video please visit http:/
From playlist Variational Methods in Geometry
C. De Lellis - Center manifolds and regularity of area-minimizing currents (Part 4)
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are ar
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
C. De Lellis - Center manifolds and regularity of area-minimizing currents (Part 5)
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are ar
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
C. De Lellis - Center manifolds and regularity of area-minimizing currents (Part 3)
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are ar
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
C. De Lellis - Center manifolds and regularity of area-minimizing currents (Part 2)
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are ar
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
Abstract Algebra: In analogy with bijections for sets, we define isomorphisms for groups. We note various properties of group isomorphisms and a method for constructing isomorphisms from onto homomorphisms. We also show that isomorphism is an equivalence relation on the class of groups.
From playlist Abstract Algebra
Now that we know what quotient groups, a kernel, and normal subgroups are, we can look at the first isomorphism theorem. It states that the quotient group created by the kernel of a homomorphism is isomorphic to the (second) group in the homomorphism.
From playlist Abstract algebra
C. De Lellis - Center manifolds and regularity of area-minimizing currents (Part 1)
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are ar
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
Abstract Algebra | Properties of isomorphisms.
We prove some important properties of isomorphisms. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Camillo De Lellis: De Giorgi and Almgren in a simple setting (part III)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: The course aims at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi’s celebrated epsi
From playlist Winter School on "Interfaces in Geometry and Fluids"
Camillo De Lellis: De Giorgi and Almgren in a simple setting (part II)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: The course aims at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi’s celebrated epsi
From playlist Winter School on "Interfaces in Geometry and Fluids"
Camillo De Lellis De Giorgi and Almgren in a simple setting (part IV)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: The course aims at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi’s celebrated epsi
From playlist Winter School on "Interfaces in Geometry and Fluids"
Camillo De Lellis: De Giorgi and Almgren in a simple setting (part I)
The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: The course aims at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi’s celebrated eps
From playlist Winter School on "Interfaces in Geometry and Fluids"
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about t
From playlist Essence of Group Theory