#monoids #grouptheory #subgroup #abstractalgebra
Where does the block structure of groups come from? And how does it secretly encode information about prime numbers, parallel lines, and orientation? In this video, you will get a deep explanation about subgroups, quotient groups, block structure and more, without using any formulas. We look at many examples of concepts that emerge magically from the technical details.
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The links for this video:
[M3M] www.math3ma.com/blog/whats-a-...
www.math3ma.com/blog/whats-a-...
This is Tai-Danae Bradley's blog from which I quoted in the video. It combines nice visuals with great exposition. It's really worth a read.
[VIS] • Visual Group Theory, L...
A long and very detailed series about group theory. If you plan to study higher math, this one is a must-watch. It will take time, but you will learn most of the details you need.
0:00 Introduction
1:54 Subgroups
3:03 Representatives & cosets
11:03 Lagrange theorem
12:35 Prime numbers
13:28 Internal block structure
14:26 The quotient group
18:45 Parallel lines
21:52 Orientation
24:14 Getting new concepts for free
This video is published under a CC Attribution license
( creativecommons.org/licenses/... )
1 июл 2024