Abstract Algebra: Motivation for the definition of a group

The definition of a group is very abstract. We motivate this definition with a simple, concrete example from basic 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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[deepakmecheri]

Yes! This channel is pure gold. Professors often don't explain stuff at this level

[Lmanyakaa]

4am in the morning and that abstract algebra pun made me burst out a loud laugh haha.. splendid.

[yelircaasi]

I like the way she explains things. It's hard to be thorough without "talking down" or "dumbing it down, " but I think she nails it.

[jpnesseth]

Thank you SO SO SO much for this!

I shouldn't admit this, but...
...I went through entire courses on Galois Theory & Lie Algebras...
...all without ever really realising this most basic fact.

The curiosity was there, of course...but...I just assumed it was an artefact of abstraction.

Instead, ends up it was the very method itself,
Shamelessly waving it's self-styled raison d'être in front of our faces.

This should have been obvious from the start!


Always appreciate a (not-so-)subtle reminder to look up from the granular minutia on occasion,
and take step back to appreciate what all of this is actually for.

Seriously;
Thank you a million, million ways.

[merbstimeline]

Ive been in Abstract Algebra class getting confuse every day untill i meet you Socratica. You are pretty Good. I give you five Star. Thank you so much.

[mksarav]

Very very well done video. I have no words to express the joy.

[vasdgod]

I am a student and have no job but want to donate to this beautiful channel. But have no money, I am sure after I get job I will dinate to this channel.

[sanjursan]

This is very well done on so many levels.  Thank you so much.

[souvikdebroy]

This channel is like a gold mine for Physics and Math students like me! Thank you very much!

[vecter]

Astounding beauty in the simplicity and power of this group definition. Thank you for demonstrating the motivation for these axioms with such clarity.

[abhishekojha]

Thank you i haven't learnt this much from my whole 2nd year. You and your team are just AWESOME. 👍👍
God bless you🌷

[maunil]

You make so nice videos. Keep making. Thanks for keeping students like me interested in maths.

[alejrandom]

This is deep, I know the basics of group theory and how it relates to subsets of matrices and rubiks cubes, but I never noticed it's relation to the solvability of equations. This is so simple yet so crazy. Thanks for being on youtube ♡

[yongmrchen]

Being able to teach abstract subjects like mathematics while smiling is a talent.

[lexflow]

Whoever that narator is she is the best orator of math i have ever seen in my life. So enthralling

[uttiyapaul]

You are a wonderful teacher....I have seen nobody ( I mean it) explaining such complex things so simply....

[akashgola]

Fast + knowledge + that smile in end 💯

[gk-qfhv]

The "impossible easy"!
What a great way of putting it!
THANKS

[raunitsingh]

Elon musk should also give a donation to this channel, khan academy is great but man this channel is on another level

[CaPsNoII]

thank you so much .... you made it easy .. and i wish if i had a teacher like you in my college ..