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
Equivalence Relations Definition and Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.
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
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
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
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Set Theory (Part 6): Equivalence Relations and Classes
Please feel free to leave comments/questions on the video and practice problems below! In this video, I set up equivalence relations and the canonical mapping. The idea of equivalence relation will return when we construct higher-level number systems, e.g.integers, from the natural number
From playlist Set Theory by Mathoma
Put all three properties of binary relations together and you have an equivalence relation.
From playlist Abstract algebra
Linear algebra: Prove the Sherman-Morrison formula for computing a matrix inverse
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Victor Panaretos: The extrapolation of correlation
CONFERENCE Recording during the thematic meeting : "Adaptive and High-Dimensional Spatio-Temporal Methods for Forecasting " the September 29, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks
From playlist Analysis and its Applications
Geordie Williamson: Geometric Representation Theory and the Geometric Satake Equivalence
MSI Virtual Colloquium: Geometric Representation Theory and the Geometric Satake Equivalence Geordie Williamson (University of Sydney) During this colloquium Geordie will explain in very broad terms, what the Langlands correspondence is and why people care about it. He will then explain i
From playlist Geordie Williamson: Representation theory and the Geometric Satake
Noether’s Theorem in Classical Dynamics : Continuous Symmetries by N. Mukunda
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
Deep Learning Lecture 7.3 - TICA, TCCA and time-autoencoders
Learning Slow Manifolds with Markovian methods: - time-lagged canonical correlation analysis (TCCA) - time-lagged independent component analysis (TICA) - time-autoencoders
From playlist Deep Learning Lecture
Resonances for Normally Hyperbolic Trapped Sets - Semyon Dyatlov
Semyon Dyatlov University of California April 2, 2013 Resonances are complex analogs of eigenvalues for Laplacians on noncompact manifolds, arising in long time resonance expansions of linear waves. We prove a Weyl type asymptotic formula for the number of resonances in a strip, provided t
From playlist Mathematics
Deep Learning Lecture 7.4 - VAMPnet
Learning Slow Manifolds with Markovian methods - variational approach for Markov processes (VAMP) - VAMPnet
From playlist Deep Learning Lecture
Marie Kerjean: Differential linear logic extended to differential operators
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual
From playlist Logic and Foundations
Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 3)
Due to technical problems the blackboard is not visible. The lecture was held within the framework of the Hausdorff Trimester Program Mathematics of Signal Processing. In Gabor analysis one studies the construction and properties of series expansions of functions with respect to a set of
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
The inverse of a matrix -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
Alexander Figotin : Overdamping in gyroscopic systems composed of high-loss and lossless components
Abstract: Using a Lagrangian framework, we study overdamping phenomena in gyroscopic systems composed of two components, one of which is highly lossy and the other is lossless. The losses are accounted for by a Rayleigh dissipative function. We prove that selective overdamping is a generic
From playlist Mathematical Physics