i have been sweeping through books and manuals the entire day and you are the only person i found on the internet who explained it thoroughly. thanks for everything.
Sir m from Pakistan and really impressed by your knowledge and teaching method... My all concepts are clear now about isomorphism theorems.. I Salute u I didn't understand before when my teacher taught me who took his doctorate degree from germany
Thank you so much for all those videos, l found you channel at least 20 hours before and up to now l have seen more than 50 of them. Related to this one, l have a question on the first part of the proof. At the part on 4:50 l not understanding why we can change the order of them. Honesty too much appreciation.
I thank you for the number theory course that you have raised the lessons well understood and explained, but I have a question for you can upload lessons on Legazander and Jacoby and the Eiler function and a squared residual with examples of questions on the subject?
I have a whole playlist on quadratic residues and the Legendre symbol: ua-cam.com/play/PL22w63XsKjqwn36stOtD07VMfcCT-HRLc.html I also have some videos on Euler's totient function starting with: ua-cam.com/video/F240HAeioB8/v-deo.html It should be pretty easy to find the rest from there.
Thank you for the perfect logical proof.But in my opinion how to understand the theroy is more important.If we really understand what the theorem is really saying,the proof is just formal writing.So I really want to know how did mathematicians come up with this theorem and what does it really means.Thank you for your proof.And English is my second language,maybe I can't indicated well.So wish you can forgive and point out my mistakes.
I think i have 2 questions Did you ever tell why we got (H intersect N) normal to H for free by the last proof? If so, was it given in the end in terms of the kernel og phi? I think i might be confused but isnt (H intersect N) normal to H because for every element q in (H intersect N), hqh^{-1} will be in H because it is essentially just a multiplication of elements in H? When showing surjectivity of phi you write im(phi)=HN/N. Didnt we just show that HN/N is contained in im(phi) without the reverse inclusion? Thank you so much for these videos, it has been my goal for some time to learn the theorems of isomorphisms for groups and your videos have really helped.
I know this is a bit late but answering questions perhaps benefits my own learning as much as it hopefully benefits others. For your first question, we don't prove that (H intersect N) is normal in H directly. If we consider hqh^{-1} then yes, we can see that this expression must be in H but we can't know for sure that it is also in N. We have to show that (H intersect N) is normal in H a different way. We show it by proving that ker(phi) = (H intersect N), which Michael did in the video. There is a standard result about homomorphisms that shows that the kernel of a homomorphism is always a normal subgroup of the domain, no matter what the two groups are or what the map is, as long as that map is a homomorphism. Since the map Michael constructed in the video here is indeed a homomorphism, then its kernel (namely, H intersect N) is normal in H since H is the domain of the homomorphism. For your second question, the reverse inclusion is implied because phi is well-defined. We know that phi(h) = hN with hN being in HN/N no matter what h we pick from H. Even if this wasn't explicitly spoken about, it can be deduced fairly quickly by inspection which is perhaps why Michael didn't mention it.
I know im randomly asking but does someone know of a method to log back into an instagram account? I somehow forgot my password. I would love any help you can offer me.
@Connor Lorenzo I really appreciate your reply. I got to the site on google and Im in the hacking process now. Looks like it's gonna take quite some time so I will reply here later when my account password hopefully is recovered.
the more I learn about abstract algebra, the more I appreciate mathematics.. What a beautiful proof
i have been sweeping through books and manuals the entire day and you are the only person i found on the internet who explained it thoroughly. thanks for everything.
Sir m from Pakistan and really impressed by your knowledge and teaching method... My all concepts are clear now about isomorphism theorems.. I Salute u I didn't understand before when my teacher taught me who took his doctorate degree from germany
Thank you very much. Unmatched clarity on this difficult topic at least for me
great video series
my baby likes it
Excellent! Very neat proof
I appreciate that the wide back
Good job man ! may Allah show you the right way !!
thanks for helping us to be protected by god! Allah may bless YOU too, Mr.!
Where do I find the one hour long video of examples for the first isomorphism theorem that you mention at the beginning of the video?
Enjoy: ua-cam.com/video/BE8lhcGfSiI/v-deo.html
@@MichaelPennMath Great! Thank you.
Thank you so much for all those videos, l found you channel at least 20 hours before and up to now l have seen more than 50 of them. Related to this one, l have a question on the first part of the proof.
At the part on 4:50 l not understanding why we can change the order of them.
Honesty too much appreciation.
since N is a normal subgroup of G (gn1=n2g for some n1, n2 in N) and H is a subgroup of G
Is there another video of yours that explains why we need to check if the phi is surjective? 10:41
It's because to apply the First Isomorphism Theorem, HN/N has to equal the image of phi :)
I thank you for the number theory course that you have raised the lessons well understood and explained, but I have a question for you can upload lessons on Legazander and Jacoby and the Eiler function and a squared residual with examples of questions on the subject?
I have a whole playlist on quadratic residues and the Legendre symbol: ua-cam.com/play/PL22w63XsKjqwn36stOtD07VMfcCT-HRLc.html
I also have some videos on Euler's totient function starting with: ua-cam.com/video/F240HAeioB8/v-deo.html
It should be pretty easy to find the rest from there.
Thank you for the perfect logical proof.But in my opinion how to understand the theroy is more important.If we really understand what the theorem is really saying,the proof is just formal writing.So I really want to know how did mathematicians come up with this theorem and what does it really means.Thank you for your proof.And English is my second language,maybe I can't indicated well.So wish you can forgive and point out my mistakes.
I think i have 2 questions
Did you ever tell why we got (H intersect N) normal to H for free by the last proof? If so, was it given in the end in terms of the kernel og phi?
I think i might be confused but isnt (H intersect N) normal to H because for every element q in (H intersect N), hqh^{-1} will be in H because it is essentially just a multiplication of elements in H?
When showing surjectivity of phi you write im(phi)=HN/N. Didnt we just show that HN/N is contained in im(phi) without the reverse inclusion?
Thank you so much for these videos, it has been my goal for some time to learn the theorems of isomorphisms for groups and your videos have really helped.
I know this is a bit late but answering questions perhaps benefits my own learning as much as it hopefully benefits others.
For your first question, we don't prove that (H intersect N) is normal in H directly. If we consider hqh^{-1} then yes, we can see that this expression must be in H but we can't know for sure that it is also in N. We have to show that (H intersect N) is normal in H a different way. We show it by proving that ker(phi) = (H intersect N), which Michael did in the video. There is a standard result about homomorphisms that shows that the kernel of a homomorphism is always a normal subgroup of the domain, no matter what the two groups are or what the map is, as long as that map is a homomorphism. Since the map Michael constructed in the video here is indeed a homomorphism, then its kernel (namely, H intersect N) is normal in H since H is the domain of the homomorphism.
For your second question, the reverse inclusion is implied because phi is well-defined. We know that phi(h) = hN with hN being in HN/N no matter what h we pick from H. Even if this wasn't explicitly spoken about, it can be deduced fairly quickly by inspection which is perhaps why Michael didn't mention it.
Thank you so much, I got your lesson!
I know im randomly asking but does someone know of a method to log back into an instagram account?
I somehow forgot my password. I would love any help you can offer me.
@Angel Lee instablaster ;)
@Connor Lorenzo I really appreciate your reply. I got to the site on google and Im in the hacking process now.
Looks like it's gonna take quite some time so I will reply here later when my account password hopefully is recovered.
@Connor Lorenzo It did the trick and I now got access to my account again. I'm so happy:D
Thank you so much you really help me out :D
@Angel Lee you are welcome :)
Plzz can you solve imo 2015 problem 2 😊