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
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
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 Homomorphisms - Abstract Algebra
A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be
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)
Gregory Margulis: Kolmogorov-Sinai entropy and homogeneous dynamics
Abstract: Homogeneous dynamics is another name for flows on homogeneous spaces. It was realized during last the 30–40 years that such dynamics have many applications to certain problems in number theory and Diophantine approximation. In my talk I will describe some of these applications a
From playlist Gregory Margulis
302.3A: Review of Homomorphisms
A visit to the homomorphism "zoo," including definitions of mono-, epi-, iso-, endo-, and automorphisms.
From playlist Modern Algebra - Chapter 17 (group homomorphisms)
Yakov Sinai - The Abel Prize interview 2014
00:15 beginnings, family influences 00:55 no Olympiad success 02:00 mathematical talent 02:30 schooling (WWII, USSR) 04:20 teachers 05:35 Moscow State University (Mekh mat) 07:40 mathematics vs. mechanics 08:52 Dynkin 10:13 Kolmogorov 10:35 Gel'fand 12:31 Rokhlin, Abramov 17:25 Dynamical s
From playlist The Abel Prize Interviews
PMSP - Random-like behavior in deterministic systems - Benjamin Weiss
Benjamin Weiss Einstein Institute of Math, Hebrew University June 16, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
Lewis Bowen - Classification of Bernoulli shifts
November 20, 2015 - Princeton University Bernoulli shifts over amenable groups are classified by entropy (this is due to Kolmogorov and Ornstein for Z and Ornstein-Weiss in general). A fundamental property is that entropy never increases under a factor map. This property is violated for no
From playlist Minerva Mini Course - Lewis Bowen
Michel Broué: Building Cathedrals and breaking down Reinforced Concrete Walls
This lecture was held at The University of Oslo, May 21, 2008 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2008 1. Abel Laureate John Thompson: “Dirichlet series and SL(2,Z)" 2. Abel Laureate Jacques Tits: “Alg
From playlist Abel Lectures
Andreï Kolmogorov: un grand mathématicien au coeur d'un siècle tourmenté
Conférence grand public au CIRM Luminy Andreï Kolmogorov est un mathématicien russe (1903-1987) qui a apporté des contributions frappantes en théorie des probabilités, théorie ergodique, turbulence, mécanique classique, logique mathématique, topologie, théorie algorithmique de l'informati
From playlist OUTREACH - GRAND PUBLIC
Surjective homomorphisms in abstract algebra
We have looked at homomorphisms before: https://www.youtube.com/watch?v=uTIvIFmVEAg&list=PLsu0TcgLDUiI2VH4ubaKNLxp8O5DN9pF3&index=33 https://www.youtube.com/watch?v=NuYczPkUZGY&list=PLsu0TcgLDUiI2VH4ubaKNLxp8O5DN9pF3&index=34 https://www.youtube.com/watch?v=3Oo0O1vVPoQ&list=PLsu0TcgLDUiI2V
From playlist Abstract algebra
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s
From playlist Abstract Algebra
Randomness and Kolmogorov Complexity
What does it mean for something to be "random"? We might have an intuitive idea for what randomness looks like, but can we be a bit more precise about our definition for what we would consider to be random? It turns out there are multiple definitions for what's random and what isn't, but a
From playlist Spanning Tree's Most Recent
Dissipation and singularities - Dubrulle - Workshop 1 - CEB T3 2019
Dubrulle (Service de Physique de l’Etat Condensé, CNRS, CEA Saclay, Université Paris-Saclay) / 11.10.2019 Dissipation and singularities Turbulent flows are characterized by a self-similar energy spectrum, signature of fluid movements at all scales. This organization has been describ
From playlist 2019 - T3 - The Mathematics of Climate and the Environment
Nicola Garofalo: Hypoelliptic operators and analysis on Carnot-Carathéodory spaces
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Bourbaki - 16/01/2016 - 1/4 - Damien GABORIAU
Damien GABORIAU — Entropie sofique [d'après L. Bowen, D. Kerr et H. Li] L’entropie fut introduite en systèmes dynamiques par A. Kolmogorov. Initialement focalisée sur les itérations d’une transformation préservant une mesure finie, la notion fut peu à peu généralisée, jusqu’à embrasser l
From playlist Bourbaki - 16 janvier 2016
Homomorphisms in abstract algebra examples
Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th
From playlist Abstract algebra