Representations of Finite Groups | A few more common examples.
ฝัง
- เผยแพร่เมื่อ 4 ก.ค. 2020
- We present a few more common examples of representations of finite groups. These include cyclic groups, dihedral groups, the quaternions, and the symmetric group.
Please Subscribe: th-cam.com/users/michaelpennma...
Personal Website: www.michael-penn.net
Randolph College Math: www.randolphcollege.edu/mathem...
Randolph College Math and Science on Facebook: / randolph.science
Research Gate profile: www.researchgate.net/profile/...
Google Scholar profile: scholar.google.com/citations?...
If you are going to use an ad-blocker, considering using brave and tipping me BAT!
brave.com/sdp793
Books I like:
Abstract Algebra:
Judson(online): abstract.ups.edu/
Judson(print): amzn.to/2Xg92wD
Dummit and Foote: amzn.to/2zYOrok
Gallian: amzn.to/2zg4YEo
Artin: amzn.to/2LQ8l7C
Differential Forms:
Bachman: amzn.to/2z9wljH
Number Theory:
Crisman(online): math.gordon.edu/ntic/
Strayer: amzn.to/3bXwLah
Andrews: amzn.to/2zWlOZ0
Analysis:
Abbot: amzn.to/3cwYtuF
How to think about Analysis: amzn.to/2AIhwVm
Calculus:
OpenStax(online): openstax.org/subjects/math
OpenStax Vol 1: amzn.to/2zlreN8
OpenStax Vol 2: amzn.to/2TtwoxH
OpenStax Vol 3: amzn.to/3bPJ3Bn
I used to be a speedcuber (i. e. A person who tries to solve the Rubik's cube as fast as possible) and it helped me a lot to develop an intuition for discrete group theory. Some concepts like permutation, conjugation and cyclic subgroups are actually useful to solve the cube.
In this case, the elements of the group are the combinations of face turns together with the operation of composing transformations. Each element of the group can be viewed as a certain scramble or as a certain (very large) square matrix in a matrix representation.
Hoping this series will make a comeback
Will you eventually discuss irreducible representations and character tables?
I love your representation theory vids! Since it is really hard for undergraduates to study rep. theory, I really hope you would like to upload more vids on this area.
very nice video! i see the Pauli matrices in your representation of the quaternions :D as a physicist i would love to see you doing a video on Lie groups and their representations :)
It's been 2 years wheres the continuation video ? 🥺
I hope you continue with this series! :)
Awesome video and very clear/clean examples! Thank you!
Thanks so much for this videos sir. I tend to love your topic/course series videos. Am learning much from them. Thanks once more
I have a nice number theory problem for you Mr Michael
The problem:
Find all integers (a,b,c,d) such that
1
You are the best! Thank you so much for so clear explanation
Thank you for this video i like your explanation. Can you share more video in representation groupe theory, example , Schur's lemma and Maschke's theorem
Your videos are amazing I wish i knew about u thr moment u started this channel ❤️ keep moving forward also feel free to add ads in ur videos i don't mind them on the contrary
Thanks. It would be nice if you can teach how to get 4-dimensional real representation of Q8.
Fascinating.
Hi guys . Is this video a part of other videos that talks about it because i don’t really understand what is going on . So ask to send men the playlist. And thx you for that .
Please more videos on group representations.
I have a very similar topic in abstract algebra! Good one!
can you do a video on boolean algebra ?
20:56
cool!
What are C(k), could you please define? I am a stat major and had only one abstract algebra course
By C (k), he means "C, the complex numbers (or k, an arbitrary field)."
Pls suggest a best abstract algebra text
As an undergrad, I used Topics in Algebra by Herstein. In grad school, I used Algebra by Artin. YMMV
++
Help me solve the problem:
Given a sharp angle xOy, M is a fixed point in the angle xOy, through M construct the line d cut Ox, Oy at A, B such that: AB is the smallest
Please help me : let function f(x) continuity in (0,1) and integral of f(x)=integral of xf(x) with x:0->1, froof exist c €(0,1) : cf(c^2)=1010 integal f(x) with x:0->c^2. I don't know much about English.