Properties of groups | Outlines of mathematics and logic | Group theory

List of group theory topics

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).

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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

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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

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Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics

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From playlist Visual Group Theory

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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

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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

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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

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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

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Abstract Algebra and Group Theory | Nathan Dalaklis

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From playlist The First CHALKboard

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Evolution for Everyone - "A Sociological Breakthrough"

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From playlist Terry Lectures

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GAP - 1 by Alexander Hulpke

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From playlist Group Theory and Computational Methods

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Group theory 31: Free groups

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

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Moduli Spaces of Principal 2-group Bundles and a Categorification of the Freed.. by Emily Cliff

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From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)

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From playlist 2021 - IMT4307 - Serious Games

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From playlist Math talks

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A (somewhat) new paradigm for mathematics and physics | Diffusion Symmetry 1 | N J Wildberger

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From playlist Diffusion Symmetry: A bridge between mathematics and physics

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On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari

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From playlist Group Algebras, Representations And Computation

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Mathematical Knowledge Management software survey (paper review)

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From playlist Reviews

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Groups and subgroups

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From playlist Basics: Group Theory

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Introduction to text analysis in python

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