Group concept mapping

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

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 Group Theory?

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

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 1: Introduction

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 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

Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory

An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerges very apparently when counting the total number of symmetries in some tricky but easy way. This video series continues to develop your intuition towards some fundamental concepts and results in Grou

From playlist Essence of Group Theory

GT1. Definition of Group

Abstract Algebra: We introduce the notion of a group and describe basic properties. Examples given include familiar abelian groups and the symmetric groups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.o

From playlist Abstract Algebra

GT2. Definition of Subgroup

Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-

From playlist Abstract Algebra

Paolo Antonini: The Baum-Connes conjecture localized at the unit element of a discrete group

Talk by Paolo Antonic in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar on June 3, 2020.

From playlist Global Noncommutative Geometry Seminar (Americas)

AMMI 2022 Course "Geometric Deep Learning" - Lecture 11 (Beyond Groups) - Petar Veličković

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 11: Category Theory • Set category • Functors • Natural

From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)

Étienne Ghys: A guided tour of the seventh dimension

Abstract: One of the most amazing discoveries of John Milnor is an exotic sphere in dimension 7. For the layman, a sphere of dimension 7 may not only look exotic but even esoteric... It took a long time for mathematicians to gradually accept the existence of geometries in dimensions higher

From playlist Abel Lectures

Category Theory: The Beginner’s Introduction (Lesson 1 Video 1)

Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed

From playlist Category Theory: The Beginner’s Introduction

4. System Architecture and Concept Generation

MIT 16.842 Fundamentals of Systems Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/16-842F15 Instructor: Olivier de Weck This lecture focused on the phase of system architecture and concept generation in a design process and introduced different methods and tools. Lic

From playlist MIT 16.842 Fundamentals of Systems Engineering, Fall 2015

AMMI 2022 Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract groups • Symmetry groups • Gro

From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)

Stable Homotopy Seminar, 9: Infinite Loop Spaces, and Homotopy Colimits

The fibrant spectra are the Ω-spectra, and we can give an elegant explicit description of the fibrant replacement. The "infinite loop space" functor, which is the derived right adjoint to the suspension spectrum, is then given by taking the 0th space of an equivalent Ω-spectrum. This allow

From playlist Stable Homotopy Seminar

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

Shadows of Computation - Lecture 3 - The gap between equivalent concepts

Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In the third lecture Will sp

From playlist Shadows of Computation

Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory

Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in u

From playlist Essence of Group Theory

Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos. The next simplest topology ha

From playlist Toposes online