Abstract Algebra: The definition of a Group

Learn the definition of a group - one of the most fundamental ideas from abstract algebra.

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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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[KirbyTheKirb]

I don't understand how this channel never popped up in my recommended. I watch a lot of math, 3blue1brown, Numberphile and other math/physics related channels. The YouTube algorithm really screwed me by waiting this long to introduce this channel.

[Lotus-Son]

Super concise and entertaining video that doesn't lose the integrity of the content. I will try and recommend this video over others for those learning.

[Khazam]

I like how simple the script is and how the video is to the point.

[smartinminutes]

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[dgross]

wow, i absolutely loved how she was droppin them math knowledge bombs, similar to the feeling i get when reading, Euler! wouldn't be surprised if this lady was a free Mason, err sumn. I feel inspired to pick up abstract algebra now! Thank you! SUBSCRIBED!

[mohubeduabram]

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[imranaalam]

Because it has a patreon page. Meaning no ads for google usually.

[viniciusrocha]

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[VasiliyZemlyanov]

Great video, thanks!
Hope to see more math videos.

[jvzx]

I have a question. When you say there are only two operations in arithmetic, isn't multiplication also addition in disguise? I mean, isn't it just a series of additions of the same number? If addition and multiplication are indeed different, why is expoonentiation not included as a third operation(a series of multiplications just like multiplication is a series of additions)? I hope you can clarify this to me, please!

[AmitKuMunda]

it would be nice to have a verified tick mark on your channel... carry on

[saksham]

What is the meaning of abstract in abstract algebra
You said element is more abstract than number what does it mean. Plz help

[Grassmpl]

Can there ever be a nonabelian group where every subgroup is normal?

[ineverchangemyplayericon]

6 years later and this awesome playlist got in my recomended.

[Socratica]

Haha thanks for your nice comment! We're so glad you like it - please share it with your friends. And your neighbors. And everyone you know! :)

[iamcreasy]

You did it in 3 min what my instructor couldn't do in 3 weeks.

[RagMama]

Excellent lesson! Your explanations are clear and understandable. Plus I love your relaxed presentation and humor!
Rick

[sanjursan]

Just perfect.  Math could not be expressed any better. More, and in more depth please.

[sharathkumar]

The first few comments on this video are a nice display of one of the things that makes STEM fields harder for women.

[WestOfEarth]

I appreciate your Feynman-esque approach of disassembling jargon. I'm convinced that more people would understand, and perhaps even enjoy, advanced math and physics but for the jargon.