Simple Groups - Abstract Algebra

Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order, alternating groups An (n bigger than 4), groups of Lie type, and the 26 sporadic groups, including the Monster Group.

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

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[bckzilla]

Thank you for making Youtube a better place to pass time.

[SalDin_]

literally have an abstract algebra exam tomorrow. videos are undoubtedly a great help!

[mksarav]

Thank you to the entire team who worked hard to produce this great video series.

[mortervolk]

I can't believe you guys have covered so much info in less than 10 minutes! That's really great, Socratica. Keep up the good work. (From Syria with love!)

[scipionedelferro]

This is the most packed video of the series, content-wise. So many interesting and fascinating stuff mentioned, too quickly! It would be fantastic to have more videos on simple finite groups. You guys are the best!

[raunitsingh]

I can only imagine how much time and effort and knowledge is required to put out a video like this.

[PunmasterSTP]

That zooming-in and Monster group music! So suddenly intense, just like the rate of my learning after finding Socratica several days ago!

[kennedyada]

Man, I have an exam tomorrow and I was looking for slow easy to understand videos with examples that drive the points home, but you're just as fast as my lecturer assuming that I already knew everything about math when I was born.

[raunitsingh]

It's so sad that they have stopped making videos, now who will teach me more of such awesome things

[derciferreira]

You resumed 300 years of mathematics in just 8:52 minutes. Thank you.

[daca]

"releace a video every hour" Nooo, I will witerally spand my life watching your videos...

[eleazaralmazan]

Thank you so much Socratica! You make mathematics very intriguing!

[adeelali]

This is where my journey with your series ends, you have been a great help! This video in particular is very comprehensive! :D Thank you thank you thank you!

[jaimelima]

I am afraid to going to sleep today and have bad dreams because of this monster group. Thanks making us understand these concepts.

[Grassmpl]

This lady knows so much. How about a video on cohomology groups?

[saurabhsingh-owue]

well this 8 mins video is the best investment of my life till now....thank you

[ruiyingwu]

I am pretty new at group theory, so I did some 'research' (aka me typing it onto Google ) ... |A_13|= 13!/2= 3 113 510 400

Thats... a lot of subscribers you are asking for...

[janko]

So, I am learning quantum mechanics and the abstract algebra is like a language you're using to talk about it. Although these lectures don't cover representations of groups and Lie's groups which are also needed for my quantum mechanics classes, I must say I'm in love! The concepts you're covering seem like they come in a natural way one after another and you want to know everything about every single concept. They don't seem just like a random topics you need to understand as fast as you can! The enthusiasm and the sort of an adventurous vibe I'm getting from the way you're talking is making me feel like I'm watching a movie! Thank you!!

[rajendralekhwar]

First of all thanks for your all videos..
I don’t get time to comment, on every video, but let me tel u,
Your explanation is just awesome ..👍👍keep it up 👍👍
Please every time keep trying to make abstract mathematics as a layman language subject as long as possible
I know it’s hard to do every time, but that’s the only way we can convert maximum individuals to love higher mathematics ...❤️

[kamyarghandi]

Would love for this series to eventually get to an explanation of what E8 is and why it is considered such a beautiful mathematical object.