Properties of groups | Outlines of mathematics and logic | Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography. (Wikipedia).
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
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
Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics
Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics Groups are always lurking where symmetry arises. In this lecture, we explore many beautiful examples of groups that arise from natural symmetries in science, art, and mathematics. This includes shapes of molecules,
From playlist Visual 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
Group theory | Math History | NJ Wildberger
Here we give an introduction to the historical development of group theory, hopefully accessible even to those who have not studied group theory before, showing how in the 19th century the subject evolved from its origins in number theory and algebra to embracing a good part of geometry.
From playlist MathHistory: A course in the History of Mathematics
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
Researchers Use Group Theory to Speed Up Algorithms — Introduction to Groups
This is the most information-dense introduction to group theory you'll see on this website. If you're a computer scientist like me and have always wondered what group theory is useful for and why it even exists and furthermore don't want to bother spending hours learning the basics, this i
From playlist Summer of Math Exposition 2 videos
Abstract Algebra and Group Theory | Nathan Dalaklis
What kinds of things do algebraists study? Well, a group is an example of such a mathematical object that is both important to algebraists and one that pops up in all different fields of mathematics. Here I give an intro to the basics of Group Theory. Namely, the group axioms, Abelian grou
From playlist The First CHALKboard
Evolution for Everyone - "A Sociological Breakthrough"
Dwight H. Terry Lectureship January 18, 2005 A Sociological Breakthrough David Sloan Wilson is Professor of Biological Sciences with a joint appointment in Anthropology at Binghamton University (State University of New York). He is also director of EvoS, a program founded in 2003 th
From playlist Terry Lectures
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
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
Moduli Spaces of Principal 2-group Bundles and a Categorification of the Freed.. by Emily Cliff
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
04 - Topic Selection & Overview of Psychological Models
Initial discussion of topic selections and group formation (to be completed for next week) Introduction to psychological theories as relevant for Serious Games
From playlist 2021 - IMT4307 - Serious Games
This is an experimental video where I give answers to the (mostly) mathematical questions asked by viewers.
From playlist Math talks
A (somewhat) new paradigm for mathematics and physics | Diffusion Symmetry 1 | N J Wildberger
The current understanding of symmetry in mathematics and physics is through group theory. However in the last 120 years, a new strand of thought has gradually appeared in a number of disciplines, from as varied as character theory, strongly regular graphs, von Neumann algebras, Hecke algeb
From playlist Diffusion Symmetry: A bridge between mathematics and physics
On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari
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
Mathematical Knowledge Management software survey (paper review)
In this video I talk about the paper "The Space of Mathematical Software Systems — A Survey of Paradigmatic Systems" found here: https://arxiv.org/abs/2002.04955 My notes on the text and all links shown on in the video can be found here: https://gist.github.com/Nikolaj-K/87371836d1dd1abfba
From playlist Reviews
Jacob explains the fundamental concepts in group theory of what groups and subgroups are, and highlights a few examples of groups you may already know. Abelian groups are named in honor of Niels Henrik Abel (https://en.wikipedia.org/wiki/Niels_Henrik_Abel), who pioneered the subject of
From playlist Basics: Group Theory
Introduction to text analysis in python
Speaker: Austin van Loon (SICSS-Princeton 19; Ph.D. student in Sociology at Stanford University) Description: The increased availability of machine-readable text provides a unique opportunity for social scientists, granting us unprecedented access to many aspects of both historical and co
From playlist All Videos