Group Homomorphisms - Abstract Algebra
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- Опубліковано 25 гру 2019
- 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
amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
www.jmilne.org/math/CourseNote...
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If you'd like to learn more, we have a free course on Group Theory! www.socratica.com/courses/group-theory
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!
We are in the same boat
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.
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.
@@dialecticalmonist3405 I genuinely envy you. I wish I had your brain.
@@dialecticalmonist3405 I genuinely envy you. I wish I had your brain.
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!
"Passing the test" is not isomorphic to understanding the material.
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.
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Such a good way to explain Homomorphisms!
This brand you have built is very impressive. You’re brilliant!
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
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
Your videos about SQL are super cool and funny!
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?
This video is much more understandable and beginner friendly than the Stanford lecture I've struggled to follow. Thank you!!
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This works perfectly for my speed of comprehension and level of knowledge about groups. Thank you!
Merry Christmas 🦌⛄🎄🎅
Thanks for all the useful stuff you posted this year👍
You are so welcome - thank you for watching!! 💜🦉
Did you know we have an Abstract Algebra newsletter? You can sign up here! snu.socratica.com/abstract-algebra
Wonderful
One of the best video explaining the motivation behind homomorphism in Group Theory. Thanks a lot.
The best Christmas present!
i love how u explain the each concept and include those awesome background music to emphasis the important points.
yes yes, the background music
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.
Best Christmas gift
I couldn't tolerate other channel's one hour video on group so I came here.....Thank you Socratica!
Found my new favorite math channel. Thanks a lot
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!
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Finished the entire playlist. It was wonderful.
Thank you for sticking with us!! 💜🦉
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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!
wow this is so useful to understand mapping between groups...thank you for these videos...happy holidays
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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.
The table explanation gave me more reality perspective and helped to understand the formula
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Very well explained.
The notation on 7:43 clearifies a lot , because often the group operations of different groups have the same symbol.🙏
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Long time no see
Hello hello! Thanks for watching! 💜🦉
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Thank you very much, for the clear explanations
Thank you so much!!!
Uma sugestão. Poderiam fazer vídeos sobre como alguns grandes matemáticos pensaram para chegar a essas conclusões(nesse caso específico, teoria dos grupos).
I came to UA-cam to look for philosophy answers and ended up here but this was pretty interesting to watch!
Fantastic presentation.
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
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.
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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.
Groups! Again! YES!!!!!
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Kind of mind blowing seeing this for the 1st time
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One is not simply 'done' with abstract algebra.
Mindblowing👍
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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.
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Hello to our Socratica Friends in Pakistan! 💜🦉
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.
So nice
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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' ?
I love it when the No! flies in forcefully after she poses the question 😂
Thanks!
Thank you so much for your kind contribution! Much appreciated!! 💜🦉
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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.
Thanks.
Explain was good
brilliant
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Helpful
Great tutorials!! Oh Yeah