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
Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
The projective line can be given a Euclidean structure, just as the affine line can, but it is a bit more complicated. The algebraic structure of this projective line supports some symmetries. Symmetry in mathematics is often most efficiently encoded with the idea of a group--a technical t
From playlist Math Foundations
Isometry groups of the projective line (II) | Rational Geometry Math Foundations 139 | NJ Wildberger
In this video we show that the algebraic approach to the metrical structure of the projective line, including the group of isometries including rotations and reflections, can all be defined and studied over a finite field. This is quite a remarkable fact. It leads us to think that perhaps
From playlist Math Foundations
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
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
Isometry groups in planar geometry | WildTrig: Intro to Rational Trigonometry | N J Wildberger
In this video we look at isometry groups in three planar geometries, the Euclidean (blue) geometry, and two relativistic geometries (red and green). These geometries arise from particular dot products, or symmetric bilinear forms. To simplify the discussion, we first introduce grounded is
From playlist WildTrig: Intro to Rational Trigonometry
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
Parallel session 4 by Jens Heber
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
Lie Groups and Lie Algebras: Lesson 9 - The Classical Groups Part VII
Lie Groups and Lie Algebras: Lesson 9 - The Classical Groups Part VII First, we review the idea of volume-preserving transformations and metric preserving transformations. Then we begin our examination of the canonical structure of certain metrics. That is, we look at how certain types of
From playlist Lie Groups and Lie Algebras
Symmetric spaces (Lecture – 02) by Pralay Chatterjee
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Crossed Products and Coding Theory by Yuval Ginosar
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Atomistically inspired origami
Oxford Mathematics Public Lectures - Richard James - Atomistically inspired origami The World population is growing at about 80 million per year. As time goes by, there is necessarily less space per person. Perhaps this is why the scientific community seems to be obsessed with folding t
From playlist Oxford Mathematics Public Lectures
Kevin Whyte, Lecture 2: Infinite Groups in Geometric Topology, Part 2
31st Workshop in Geometric Topology, University of Wisconsin-Milwaukee, June 13, 2014
From playlist Kevin Whyte: 31st Workshop in Geometric Topology
Examples of non-positively curved groups - Kim Ruane
Women and Mathematics Title: Examples of non-positively curved groups Speaker: Kim Ruane Affiliation: Tufts University Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
A Natural Proof of the First Isomorphism Theorem (Group Theory)
The first isomorphism theorem is one of the most important theorems in group theory, but the standard proof may seem artificial, like every step of the proof is set up knowing that we're trying to create an isomorphism. In this video, we show an alternate proof with no such tricks using th
From playlist Group Theory
Symmetric spaces (Lecture – 01) by Pralay Chatterjee
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Abstract Algebra | Group Isomorphisms
We give the definition of an isomorphism between groups and provide some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Grigori Avramidi: Topology of ends of finite volume, non positively curved manifolds
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" The structure of ends of nonpositively curved, locally symmetric manifolds is very well understood. In this talk, I will explain features of the locally symmetric
From playlist HIM Lectures: Junior Trimester Program "Topology"
Abstract Algebra: An abelian group G has order p^2, where p is a prime number. Show that G is isomorphic to either a cyclic group of order p^2 or a product of cyclic groups of order p. We emphasize that the isomorphic property usually requires construction of an isomorphism.
From playlist Abstract Algebra