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
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)
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
Simple Groups - Abstract Algebra
Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order
From playlist Abstract Algebra
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 1.6: The formal definition of a group
Visual Group Theory, Lecture 1.6: The formal definition of a group At last, after five lectures of building up our intuition of groups and numerous examples, we are ready to present the formal definition of a group. We conclude by proving several basic properties that are not built into t
From playlist Visual Group Theory
Group Theory: The Simple Group of Order 168 - Part 1
We present two realizations of the simple group of order 168. In part 1, we count the number of matrices in PSL(2,Z/7) and SL(3,Z/2).
From playlist *** The Good Stuff ***
Chapter 5: Quotient groups | Essence of Group Theory
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory! In fac
From playlist Essence of Group Theory
Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou
From playlist MathHistory: A course in the History of Mathematics
Olivier Wittenberg - On the cycle class map for zero-cycles over local fields
Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo avec Olivier Wittenberg (ENS et CNRS) The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field
From playlist Conférences Paris Pékin Tokyo
Richard Taylor Harvard University; Distinguished Visiting Professor, School of Mathematics March 17, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Complex geometry of Teichmuller domains (Lecture 2) by Harish Seshadri
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Perfect points on abelian varieties in positive characteristic. - Rössler - Workshop 2 - CEB T2 2019
Damian Rössler (University of Oxford) / 24.06.2019 Perfect points on abelian varieties in positive characteristic. Let K be the function field over a smooth curve over a perfect field of characteristic p 0. Let Kperf be the maximal purely inseparable extension of K. Let A be an abelian
From playlist 2019 - T2 - Reinventing rational points
Amos Nevo: Representation theory, effective ergodic theorems, and applications - Lecture 2
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 Dynamical Systems and Ordinary Differential Equations
Not every voting system generates impossibility: Score Voting and Impossibility
Not every voting system generates impossibility in the sense of Arrow's Impossibility theorem. That is there are voting systems that have the Weak Pareto, Independence of Irrelevant Alternatives, and Non-Dictatorial properties simultaneously. In particular we look at the relationship betwe
From playlist The New CHALKboard
[BOURBAKI 2017] 21/10/2017 - 4/4 - Serge CANTAT
Progrès récents concernant le programme de Zimmer [d'après A. Brown, D. Fisher, et S. Hurtado] ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://tw
From playlist BOURBAKI - 2017
Emanuel Milman: Functional Inequalities on sub-Riemannian manifolds via QCD
We are interested in obtaining Poincar ́e and log-Sobolev inequalities on domains in sub-Riemannian manifolds (equipped with their natural sub-Riemannian metric and volume measure). It is well-known that strictly sub-Riemannian manifolds do not satisfy any type of Curvature-Dimension condi
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Singular moduli spaces and Nakajima quiver varieties - Giulia Saccà
Giulia Saccà Member, School of Mathematics October 28, 2014 The aim of this talk is to study a class of singularities of moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non generic polarization, with r
From playlist Mathematics
[BOURBAKI 2017] 11/03/2017 - 3/4 - Patrick MASSOT
Patrick MASSOT — Flexibilité en géométrie de contact en grande dimension [d'après Borman, Eliashberg et Murphy] Les structures de contact sont des champs d'hyperplans apparaissant naturellement au bord de variétés symplectiques ou holomorphes et dont l'attrait provient d'un subtil mélang
From playlist BOURBAKI - 2017
GT23. Composition and Classification
Abstract Algebra: We use composition series as another technique for studying finite groups, which leads to the notion of solvable groups and puts the focus on simple groups. From there, we survey the classification of finite simple groups and the Monster group.
From playlist Abstract Algebra