This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
AlgTopReview4: Free abelian groups and non-commutative groups
Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such
From playlist Algebraic Topology
Group Theory for Physicists (Definitions with Examples)
In this video, we cover the most basic points that a physicist should know about group theory. Along the way, we'll give you lots of examples that illustrate each step. 00:00 Introduction 00:11 Definition of a Group 00:59 (1) Closure 01:34 (2) Associativity 02:02 (3) Identity Element 03:
From playlist Mathematical Physics
This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.
From playlist Group theory
Visual Group Theory, Lecture 6.6: The fundamental theorem of Galois theory
Visual Group Theory, Lecture 6.6: The fundamental theorem of Galois theory The fundamental theorem of Galois theory guarantees a remarkable correspondence between the subfield lattice of a polynomial and the subgroup lattice of its Galois group. After illustrating this with a detailed exa
From playlist Visual Group Theory
Group Theory: The Center of a Group G is a Subgroup of G Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof
From playlist Abstract Algebra
Algorithms for groups of homeomorphisms - Susan Hermiller
Women and Mathematics Title: Algorithms for groups of homeomorphisms Speaker: Susan Hermiller Affiliation: University of Nebraska Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Approximations of groups, subquotients of infinite direct products and equations... - Lev Glebsky
Stability and Testability Topic: Approximations of groups, subquotients of infinite direct products and equations over groups Speaker: Lev Glebsky Affiliation: Universidad Autónoma de San Luis Potosí Date: November 25 2020 For more video please visit http://video.ias.edu Glebsky-2020-11-
From playlist Stability and Testability
This lecture is part of an online graduate course on Galois theory. We discuss Abel's theorem, that says a general quintic equation cannot be solved by radicals. We do this by showing that if a polynomial can be solved by radicals over a field of characteristic 0 then its roots lie in a s
From playlist Galois theory
Galois Groups Revisited - Chapter 25
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 25
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
15 - Algorithmic aspects of the Galois theory in recent times
Orateur(s) : M. Singer Public : Tous Date : vendredi 28 octobre Lieu : Institut Henri Poincaré
From playlist Colloque Evariste Galois
Andrew Wiles: Fermat's Last theorem: abelian and non-abelian approaches
The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel P
From playlist Sir Andrew J. Wiles
Definition of a Group and Examples of Groups
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Group and Examples of Groups
From playlist Abstract Algebra
A recap of what we've been doing up until Spring Break, plus what we're going to do for the rest of the semester.
From playlist Modern Algebra