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
This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)
From playlist Summer of Math Exposition Youtube Videos
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)
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
This is lecture 1 of an online mathematics course on group theory. This lecture defines groups and gives a few examples of them.
From playlist Group theory
Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
Visual Group Theory, Lecture 1.4: Group presentations
Visual Group Theory, Lecture 1.4: Group presentations We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a
From playlist Visual Group Theory
An Introduction To Group Theory
I hope you enjoyed this brief introduction to group theory and abstract algebra. If you'd like to learn more about undergraduate maths and physics make sure to subscribe!
From playlist All Videos
Lie Groups and Lie Algebras: Lesson 42 Group Theory Review #1
Lie Groups and Lie Algebras: Lesson 42 Group Theory Review #1\ In order to push on with Lie Group Theory, it is reasonable to do a good review of group theory itself. This is the first lecture of such a review. A link to the Group Explorer: https://nathancarter.github.io/group-explorer/
From playlist Lie Groups and Lie Algebras
Problems in the theory of automorphic forms: 45 years later - Robert Langlands
Topic: Problems in the theory of automorphic forms: 45 years later Part I Speaker: Robert Langlands Date: 2014
From playlist Mathematics
Lie Groups and Lie Algebras: Lesson 43 Group Theory Review #2 (improved video quality)
Lie Groups and Lie Algebras: Lesson 43 Group Theory Review #2 In this lecture we examine a great way of becoming familiar with the smaller groups: the subgroup lattice. We use this to remind ourselves about normal subgroups, cyclic subgroups, and the center of a group. Errata!: The norma
From playlist Lie Groups and Lie Algebras
Martin Bridson - Profinite isomorphism problems.
Martin Bridson (University of Oxford, England)
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Robert Langlands, Problems in the theory of automorphic forms: 45 years later (1/3) [2014]
For an Oxford conference last week, (https://www.maths.nottingham.ac.uk/personal/ibf/files/S&C-schedule.html) Langlands contributed a one-hour video talk, filmed in his office. One hour was not enough, so hours two and three are also available, as well as a separate text 9https://publicati
From playlist Number Theory
Frédéric Patras - Substitutions in non-commutative multivariate power series
We describe a group law on formal power series in non-commuting variables in- duced by their interpretation as linear forms on a Hopf algebra of sentences. We study the corresponding structures and show how they can be used to recast in a group theoretic form various identities and transfo
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022
Robert Langlands - The Abel Prize interview 2018
00:17 The esthetics and beauty of mathematics 05:13 Creative moments and revelations: are numbers beautiful or are they satisficing 07:55 Langlands background from British Columbia and “lack of academic ambition” 10:30 Langlands on why he chose mathematics after all and science interest 1
From playlist The Abel Prize Interviews
p- groups - 1 by Heiko Dietrich
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
Lecture 1: Invitation to topos theory
This talk introduces the motivating question for this semester of the Curry-Howard seminar, which is how to organise mathematical knowledge using topoi. The approach sketched out in the talk is via first-order theories, their associated classifying topoi, and adjoint pairs of functors betw
From playlist Topos theory seminar
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
The process of forgetting | Revision for Psychology A-Level or IB
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. Study (daily and weekly) planners https://www.prim
From playlist AQA A-Level Psychology | Revision Playlist