Group Homomorphisms - Abstract Algebra

A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another.

Homomorphisms will be used through abstract algebra. You will study homomorphisms between groups, rings, fields, modules, vector spaces, and more.

Correction note: at 6:10 -i in the second table should be outlined in purple. Thank you to viewer Power Max for catching this!

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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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[yutopia]

I always loved math and I still do. Everything upto calc 3 was easy for me. I even went to college as a math major. Unfortunately, once I took abstract algebra everything fell apart and my last 3 years in college turned into a living hell. I read the textbooks and nothing made sense to me. My professors didn’t do a good job explaining the concepts either. I really wish I had a teacher like you. Better late than never!

[yassineaghlaoui]

Absolutely the TEACHER OF THE YEAR. Far better than our teacher who just tells us to memorize the definition of an homomorphism without knowing the intuition behind it. Thank you so much. I really appreciate the great work you're doing. Keep doing so!
Cheers from Morocco!

[Cpt.Zenobia]

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[kemsekov]

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[ProfessorDBehrman]

She speaks very clearly. Thanks for giving this introduction to the homomorphism.

[MusicalInquisit]

Every time I watch these videos, I always feel that I am doing something epic (thanks to the music).

Watching this is epic.

[kaebynj.quintero]

I came to YouTube to look for philosophy answers and ended up here but this was pretty interesting to watch!

[MrGiuse]

I praise you attitude of briefly clarifying the scopes, heuristically describing the motivations of definitions and theorems . THANK YOU

[annushekhar]

I couldn't tolerate other channel's one hour video on group so I came you Socratica!

[TheTessatje]

The notation on 7:43 clearifies a lot, because often the group operations of different groups have the same symbol.🙏

[MadanKumar-xgxy]

One of the best video explaining the motivation behind homomorphism in Group Theory. Thanks a lot.

[distrologic]

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[wellfederal]

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[Junnabeaverchewy]

😓 where was this video last semester?! I'm done with Abstract Algebra but i still love watching these videos!

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[desativa]

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