Group Homomorphisms - Abstract Algebra

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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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This video was made possible by our VIP Patrons on Patreon!
Thank you for supporting our work this year. Because of you, we are able to continue making the highest quality math videos, free for the world.
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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
www.jmilne.org/math/CourseNote...
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
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Опубликовано:

25 дек 2019

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Комментарии : 310

@Socratica 7 месяцев назад

If you'd like to learn more, we have a free course on Group Theory! www.socratica.com/courses/group-theory

@yutopia7 4 года назад

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!

@Dusk425 2 года назад

We are in the same boat

@hegelscat9423 2 года назад

Some people cant do algebra but can do analysis, and some people can do analysis and not algebra, and then there is those fortunate enough that can do both. But teachers influence that a lot. I have been lucky enough to have a great algebra teacher. I've notice among the faculty at my school that their preference is influenced by undergraduate professors.

@dialecticalmonist3405 2 года назад

I never understood math. But when I started learning about Group Theory / Category Theory, it finally began to make sense to me. All that algebra nonsense started to actually mean something.

@yutopia7 2 года назад

@@dialecticalmonist3405 I genuinely envy you. I wish I had your brain.

@yutopia7 2 года назад

@@dialecticalmonist3405 I genuinely envy you. I wish I had your brain.

@yassineaghlaoui1906 4 года назад

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!

@dialecticalmonist3405 2 года назад

"Passing the test" is not isomorphic to understanding the material.

@atrophysicist 5 месяцев назад

Moroccain here too, also came to learn about algebraic structures to pass the bac exam and i can tell you that our teacher didn't do a good job of explaning it either so im glad i found this series.

@Cpt.Zenobia 4 года назад

I found this channel while searching something in Number Theory for my cryptography class, but now I really got into pure mathematics and started studying it as a hobby & implementing what ever I can because of this channel. Keep up the good work.

@kemsekov6331 2 года назад

This is the best of "Watch while eat. Think for day" thing ever! Your content give me joy incomparable to anything else!

@Ray-jg5dj 4 года назад

You talk really well. Perfect intonation and really satisfying. It makes the information easier to remember and prevent people from getting bored. Great !

@John-lf3xf 4 года назад

This brand you have built is very impressive. You’re brilliant!

@facepalm4e 4 года назад

So glad to see you guys are still making these videos! Such a good way to explain Homomorphisms!

@KazimirQ7G 4 года назад

Thank you! I'm really glad you guys are back, despite the campaign to continue Python videos, it's good to see you're not restricted to that.

@MrGiuse72 Год назад

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

@Socratica 4 года назад

We're so glad you're watching Socratica! You can subscribe for more great STEM videos here: bit.ly/SocraticaSubscribe Our Abstract Algebra playlist is here: bit.ly/AbstractAlgPlaylist

@JoaoVictor-wx5lz 4 года назад

Volta com o socrática português, o Brasil precisa de um incentivo para ter uma boa educação e seu conteúdo nos ajuda a ser estudantes melhores

@dariuszg9991 4 года назад

Your videos about SQL are super cool and funny!

@kamranabdulkhaev1767 4 года назад

Dear Socratica, Your videos are great, but I have difficulties in understanding the order of the playlist. Some videos starts with Abstarct Algebra in braces, some ends with this words and some even doesn't have them. Moreover the content (topic) sometimes jumps from one video to another. Is the playlist in a right order?

@johnsun2580 4 года назад

This video is much more understandable and beginner friendly than the Stanford lecture I've struggled to follow. Thank you!!

@PunmasterSTP 3 года назад

I think subscribing can definitely STEM any tides of ignorance!

@MusicalInquisit 4 года назад

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

@RalphDratman 4 года назад

This works perfectly for my speed of comprehension and level of knowledge about groups. Thank you!

@annushekhar6042 2 года назад

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

@ramumaha2779 3 года назад

i love how u explain the each concept and include those awesome background music to emphasis the important points.

@michaelturkson9378 Год назад

yes yes, the background music

@edt8597 4 года назад

Merry Christmas 🦌⛄🎄🎅 Thanks for all the useful stuff you posted this year👍

@Socratica 4 года назад

You are so welcome - thank you for watching!! 💜🦉

@Or0203 3 года назад

Found my new favorite math channel. Thanks a lot

@MadanKumar-xg6xy 8 месяцев назад

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

@louis6331 2 года назад

That was the most beautiful example of isomorphism. I didn't understand it until I heard it on TED Talk and I said what is isomorphic. That's when I found this channel. And it was so much easier to understand then any other thing that concerns any other thing that concerns algebra. I was never good at it. But this made me understand it in a whole new light. Thank you. Keep up the good work. This was the most mind-blowing and understandable way of explaining what I did not know. Thanks again.

@DiegoMathemagician 4 года назад

Best Christmas gift

@kyle-silver 4 года назад

The best Christmas present!

@bryanchambers1964 4 года назад

Thanks Patreon. It has been a dream of mine to teach myself Galois theory. Your quick vids give me some momentum for that.

@wellfederal 4 года назад

Hi! I have a degree in physics, but unfortunately I don't work in the field. Your channel is inspiring. CONGRATULATIONS!! I am Brazilian and would love to see more videos on Socrática Português. In Brazil, whose STEM education is deficient, its channel is sorely missed. Congratulations again !!

@mohanbhattrai2752 3 года назад

Your all videos are excellent . you are the export on abstract algebra .I salute you on your knowledge.

@stevejohnson1685 4 года назад

Very nice video! A friend just wrote a paper on group theory, with mappings from R to R. I read through it, and had some thoughts about it (I'm not an abstract algabraicist), which were confirmed in this video. Happy! Another commenter asked for more on Haskell; I'd request the same, particularly with the connections to the mathematical underpinnings you're so good at explaining. Thanks again for your carefully scripted and clearly elucidated concepts!

@chaitanyatuckley4666 13 дней назад

Finished the entire playlist. It was wonderful.

@Socratica 13 дней назад

Thank you for sticking with us!! 💜🦉

@aaronnorman9755 2 года назад

I am amazed by your ability to move information through my thick skull, thank you very much!!!

@Vfdking 4 года назад

You (people) make me gratuitous. Thnx for nice videos on my phone, helping with intuition.

@FuqYoMarmar 4 года назад

Thank you very much. Well explained and easy to follow.

@hammademuhammad3266 2 года назад

Thanks Socratica you are very helpful and assisting teacher of mathematics you have made my many question simple for me

@MBAVD5 4 года назад

wow this is so useful to understand mapping between groups...thank you for these videos...happy holidays

@fredericoapuleio9583 4 года назад

Eu adorei o vídeo. Gostaria de ver mais. Parabéns pelo excelente trabalho. Eu não sabia que vcs prosseguiam fazendo vídeos. E o fato de ser de matemática é melhor ainda. Sugiro uma série em problem solving. Grande abraço!

@uniquechannel3086 4 года назад

The table explanation gave me more reality perspective and helped to understand the formula

@Djn77645 2 года назад

I had so many aha moments watching your videos (10 days before my exam) cheers from France 🤙

@cristiandavid706 3 года назад

Thank you for videos like this!

@wjshood 4 года назад

Its weird but I've forgotten all my analysis, but I remember this stuff perfectly. I love algebra everything just makes so much sense

@merdenbryant8872 2 года назад

Great presentation. Thank you!

@Jabber_Wock 4 года назад

Great 👍 thank you for an excellent update. And a very happy Holiday Season to you, friends and family.

@distrologic2925 4 года назад

Math is awesome. Especially algebra, which is like a language for mathematics. I wish more people could speak it.

@bazislapper6283 4 года назад

Thanks from MSU . Greate material, it was very important for me to know this now.

@Silentgluttony 4 года назад

what an awesome introduction into abstract algebra

@markell1172 4 года назад

Those deep concepts compacted in one video cool

@charlieng3347 8 месяцев назад

Your channel is just awesome

@davidkeelyng6746 4 года назад

Parabéns pelo conteúdo, pela aula, só dê um pouco a mais de atenção ao Socrática Português por favor, continue postando vídeos com maior frequência! Abraço.

@jeremylaughery2555 3 года назад

It's mathemagical! Great work!

@mr.qadeer1122 2 года назад

what a awesome teaching method i ever got.

@ayushdwivedi3519 3 года назад

I'm fond of your way of teaching. It's wonderful and it has let me to love abstract algebra. Can you please make video on automorphism and inner automorphism.

@Gunth0r 4 года назад

Oh boy, and I thought this was just a python channel. I know what I'm binge watching this week.

@sebastianparamera2424 4 года назад

Very well explained.

@user-zh8vh7pk1l 3 года назад

Thank you very much, for the clear explanations

@TheTessatje123 Год назад

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

@shubh1606 4 года назад

I dont have any exam related to group theory in future and its 1 january 2:30 am and i am still watching this video because i love group theory nice explanation,Happy new year

@tareksaad1393 2 года назад

came across this video a year ago, then landed back here again... am in a Bitcoin rabbit hole, and am looking for something just dont know what it is... but its somewhere here ... just wanted u to know i love ur videos ... u made me love math again ... appareciate math... and be like a kid trying to figure how the rabbit came out of the hat! peace!

@JohnDoe-oo9ll 2 года назад

Man this is fire

@romywilliamson4981 4 года назад

Please do more advanced topics with modules! And also PIDs, EDs, UFDs etc. You're so good at explaining this kind of thing but it doesn't go far enough for my Rings and Modules course and I'm finding it really hard to get an intuition for a lot of the concepts involved.

@selvapeter2370 3 года назад

Fantastic presentation.

@Icenri 4 года назад

Groups! Again! YES!!!!!

@Icenri 4 года назад

Also, first time I catch a video with 0 views 🤭

@Socratica 4 года назад

@@Icenri WOW first viewer!! 💜🦉

@ViniciusSilva-vc4jt 4 года назад

Uma sugestão. Poderiam fazer vídeos sobre como alguns grandes matemáticos pensaram para chegar a essas conclusões(nesse caso específico, teoria dos grupos).

@moularaoul643 3 года назад

Thank you so much!!!

@IamInloveWithEther 4 года назад

These are very helpful!!

@ajinruben4184 3 года назад

thank you so much.It helped me a lot. And saved my time.

@kaebynj.quintero2993 2 года назад

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

@othmanabdalamohamedadanabd1978 3 года назад

I proud to watch your lecture🙏🏼🙏🏼❤❤

@Socratica 2 года назад

Did you know we have an Abstract Algebra newsletter? You can sign up here! snu.socratica.com/abstract-algebra

@MadanKumar-xg6xy 8 месяцев назад

Wonderful

@shukhratergashov7609 Год назад

Thanks so much !

@chimachan6652 2 года назад

i can just say : you r the best keep going

@anujarora0 4 года назад

Long time no see

@Socratica 4 года назад

Hello hello! Thanks for watching! 💜🦉

@yousify 4 года назад

Nice Nice Nice! I liked the sound engineering in the video and the way you speak!! I liked most the 9:40 "mag ... ic"!

@MateusSantos-zx2cz 4 года назад

Olá, moça do Socratica. Vocês não irão mais postar vídeos no Socratica português? Por favor, não nos deixem, adoramos as suas aulas e você; esse seu jeito incrível de falar e com ótimos conteúdos.

@evansjahja711 4 года назад

Thank you for making me interested in the weird sides of math

@sugongshow 2 года назад

You're awesome! Thank you for allowing me as a part of your "group". :) Keep up the great work.

@sugongshow 2 года назад

By the way, in honor of Women's History Month, I am going to do a presentation on women in math. With that, I am going to try to give you a plug. Again, thank you for all that you do.

@Socratica 2 года назад

That's very kind of you. Good luck in your presentation!! 💜🦉

@sugongshow 2 года назад

@@Socratica , thank you very much. It went well even though I had a very short 10 minutes.

@Junnabeaverchewy 4 года назад

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

@ooos2989 4 года назад

One is not simply 'done' with abstract algebra.

@isaacstamper7798 4 года назад

This is so nice

@hemantyadav6637 4 года назад

Mindblowing👍

@c27Blay 3 года назад

Lifesaver!

@ravishanker785 3 года назад

great work

@muzamilhussain9908 6 месяцев назад

what excellent way you have

@luiskretzschmar7557 6 месяцев назад

wow this is very nice!!! keep it up

@bradleymorgan8223 2 года назад

you have compressed 3 lectures worth of monotonous droning into 10 minutes, very impressive!

@craigruchman7007 3 года назад

Kind of mind blowing seeing this for the 1st time

@acquireknowledge8327 2 года назад

You are Owsome brilliant mind blowing teacher... watching from Pakistan 🇵🇰

@Socratica 2 года назад

Hello to our Socratica Friends in Pakistan! 💜🦉

@lucaolmastroni6270 3 года назад

Thanks, very nice videos. Do you plan to create some videos to give an overview of 'Representation theory' ? Same question for 'group action on a set' ?

@clementboutaric3952 4 года назад

That was very good.

@tee21.21 Год назад

Sooo good 🎉

@drlangattx3dotnet 4 года назад

thank you very much.

@dscmtr686 4 года назад

Great videos! Maybe some graph theory?

@SubhomoyHaldar 4 года назад

Even though my semester on Modern Algebra is over, I'm still watching this. Thanks for helping out with the A!

@rambo3rd471 4 года назад

Same!

@drlangattx3dotnet 3 года назад

thank you

@victorrodrigues1407 4 года назад

Olá, tudo bem? Eu ainda não visitei toda a biblioteca do canal, mas já gostaria de fazer uma sugestão: um vídeo sobre idiomas e oratória. Que tal? Tenho certeza de que seria um tema muito bem vindo, pois é só olhar os top comments do socrática em qualquer uma das três línguas nas quais o conteúdo é disponibilizado para perceber que a maneira de falar da Liliane é muito admirada pelos inscritos, mais até, feliz ou infelizmente, que o conteúdo de alguns vídeos em si. Agradeço pelo ótimo trabalho que compartilham e peço desculpas pelo comentário em português.