Like and share this video series if you think this video series is useful or just enjoy these videos in general. Also, don't forget to subscribe with notifications on!
i dont mean to be off topic but does someone know of a way to log back into an instagram account? I was dumb forgot my password. I would love any tricks you can offer me
@Alejandro Gianni i really appreciate your reply. I got to the site through google and I'm trying it out now. Looks like it's gonna take quite some time so I will get back to you later when my account password hopefully is recovered.
I'm currently not at the stage where these (group theory) videos will help me very much (just started discrete math very recently). However, knowing the quality of your videos I'm sure that they'll help me a lot when I decide to learn this beautiful subject. Don't ever stop making these! I'm sure your channel will blow up soon.
this series is so good!! I'm so glad I stumbled upon it. it looks like the UA-cam algorithm is starting to recommend to more people, I hope that translates to more people appreciating your fantastic content :)
Talking about technical aspects of your videos - I think your way of articulation/pronunciation/separation of the words and the speed of your talk is just optimal. And perfectly relevant to the Purpose. Thank you for your videos. And best wishes.
The slide you have at 11:18 is so helpful in summarizing the contents of the theorem. Extremely helpful in studying for an abstract algebra exam. Thank you so much!
Thank you for making this video. I had trouble understanding Abstract Algebra in undergrad, and now that I’m in grad school I am struggling even more because I couldn’t understand homomorphism and isomorphism. I kept looking for videos with visuals and I’m glad I came across this video, it really helped me understand. I will be sharing it with my friends.
Thanks for doing this series! Loved it. I've been self studying group theory (which means I'm learning proofs of the theorems along with intuitions) and these videos were helpful. I often find that proofs are not difficult to do when you have a solid intuition of the concept.
Hey I know it's been six months, but I was just curious how your self-study has been going. I'm also studying a bit myself, just off and on from time to time...
@@PunmasterSTP Amazing honestly. But that's always been the case for me, for some reason. I do better on my own than with the help of teachers probably because I like to take my time and not cram everything in an hour lecture. I ace all my exams if that's anything to go by? So yeah, self study, totally recommended 10/10.
We nurture great enthusiasm for the idea! We wouldn't mind some more on properties of specific types of groups either. This topic is so important, but so dryly explained elsewhere, that we are surely thirst for your juicy intuitions. Thanks a lot! Also, the more examples the better
Thanks so much for the compliment! I did say that I would put an end to the series in the last chapter of the video series though... I will try to see if there is any more demand to the continuation of this video series!
Thanks a lot for making these videos, they are actually making me understand the subject matter unlike my uni classes. I hope you get the recognition you truly deserve.
I took two courses in abstract algebra in Uni, one from a a famous group theorist. I am a visual learner, so pure math was always a challenge, but providing visual descriptions of symmetries and how they related to various subgroups (right, left, normal, etc.) was always lacking. These video are great, and can provide valuable context to a rigorous study of the topic. Nice work, and keep going. Posterity will, in my opinion, treat your efforts kindly.
Well ! I do not understand the video but i know that it will be intresting and informative for me when i will move in higher classes. Never stop uploading such videos . Earlier I thought symmetries are not intresting but your content changed my ideas.
Due to popular demand, I have actually extended this series to chapter 7 and a little summary of the entire video series; but I did put a stop there... I might do an "Intermediate group theory" series as opposed to "Essence" in the future, but only if I can find a good way to visualize the other group theory concepts. I am still making a lot of interesting mathematics videos, even though my upload schedule isn't too consistent. I try to upload at least monthly, but honestly there is no guarantee on this.
It 'd be interesting if you show an application of group theory where it's really essential for the proof. Some problem that could not or hardly be solved in a strait forward way
You asked about what the viewers might be interested in knowing about. I would be interested in knowing how GROUP THEORY has been used to solve real world problems. In Physics they use the rotation matrices and various subgroups for Maxwell's equations U(1), QED - SU(2) and QCD. Well that is nice but it does not seem like they have done anything other than a very accurate description of all the possibilities. This is useful overall. Was it used to determine all the possible Path Integrals in QED? Can GROUP THEORY be used to describe wave interactions? There are phases, phase velocity and group velocity. It seems like this would be perfect for GROUP THEORY. Is there computer software you can use to put in what you know about a system in regard to the groups? And this software will tell you more based upon what you already know. It seems like GROUP THEORY would be perfect for the quantum. Because everything is a linear combination of the quantum. Is it being used in that manner. And there seems on first glance to be a correlation between Calculus, integrals and group theory. Because when you integrate, you really need to know what groups to integrate by. For volume the group is area and so forth. But how powerful could this be?
Thanks so much for the appreciation! I am definitely not doing UA-cam full time, so I can only upload occasionally, but hopefully each upload is a good one!
Same is dual to different. The normal subgroup is dual to homomorphism (factor group) synthesizes the kernel. The image (co-domain) is a copy, equivalent or dual to the factor group (domain) - the 1st isomorphism theorem. Isomorphism (absolute sameness) is dual to homomorphism (relative sameness or difference). Injective is dual to surjective synthesizes bijective or isomorphism. Similarity, equivalence = duality! Isomorphism represents the orthogonal complement or the dual of the kernel. Homo is dual to hetero.
But what should e the value of phi to prove the second isomorphism from the first one? And how do we do it? It would be great if someone could throw some light on this, any hit would work, PLEASE.
Is there any reason that you permanently emphasis words you are saying? I mean you don't need to give yourself too much pressure. SSSSSSubgroup --> Subgroup ROOOOOOTATIONNNN -> Rotation Loosen up a little!
As a non native English speaker, thanks a lot for the clarity in those difficult words. They have, after all, just been introduced by your videos to us viewers.
Like and share this video series if you think this video series is useful or just enjoy these videos in general. Also, don't forget to subscribe with notifications on!
i dont mean to be off topic but does someone know of a way to log back into an instagram account?
I was dumb forgot my password. I would love any tricks you can offer me
@Calvin Briggs instablaster :)
@Alejandro Gianni i really appreciate your reply. I got to the site through google and I'm trying it out now.
Looks like it's gonna take quite some time so I will get back to you later when my account password hopefully is recovered.
@Alejandro Gianni It worked and I now got access to my account again. I'm so happy!
Thanks so much, you saved my account!
@Calvin Briggs Glad I could help xD
Bored you said? These lectures are diamonds!
Thanks so much for the appreciation!
Putting the mathematical rigor/jargon click into place with such enlightening expositions is so satiating,thank you.
I'm currently not at the stage where these (group theory) videos will help me very much (just started discrete math very recently). However, knowing the quality of your videos I'm sure that they'll help me a lot when I decide to learn this beautiful subject. Don't ever stop making these! I'm sure your channel will blow up soon.
I just came across your comment and I was curious. How did discrete math go, and did you end up taking group theory?
I just started watching this series now, but I just came here to say that I'm not bored at all!!! Your videos are great :)
Glad you like them!
I've had a really tough time understanding the isomorphism theorem in my group theory course, and this video helped a lot. Thank you for making it.
this series is so good!! I'm so glad I stumbled upon it. it looks like the UA-cam algorithm is starting to recommend to more people, I hope that translates to more people appreciating your fantastic content :)
Glad you like the content!
Talking about technical aspects of your videos - I think your way of articulation/pronunciation/separation of the words and the speed of your talk is just optimal. And perfectly relevant to the Purpose. Thank you for your videos. And best wishes.
Thanks so much!
Thank you!!
It makes me a little bit sad how many views this has. But people will realize sooner or later!
Sure!you are right.
The slide you have at 11:18 is so helpful in summarizing the contents of the theorem. Extremely helpful in studying for an abstract algebra exam. Thank you so much!
Thank you for making this video. I had trouble understanding Abstract Algebra in undergrad, and now that I’m in grad school I am struggling even more because I couldn’t understand homomorphism and isomorphism. I kept looking for videos with visuals and I’m glad I came across this video, it really helped me understand. I will be sharing it with my friends.
Wow, thank you for the kind words! Glad that it helps!
Hey I just came across your comment and was curious. How is grad school going, or did you already graduate?
@@PunmasterSTP I graduated this May! And I ended up with an A in Abstract Algebra :)
@@BrendaGarcia-gq1sv I’m very glad to hear it!
Thanks for doing this series! Loved it. I've been self studying group theory (which means I'm learning proofs of the theorems along with intuitions) and these videos were helpful. I often find that proofs are not difficult to do when you have a solid intuition of the concept.
Yes! That's the purpose of this video series!
@@mathemaniac Can you recommend me a book/notes for group theory that centers around intuition?
Hey I know it's been six months, but I was just curious how your self-study has been going. I'm also studying a bit myself, just off and on from time to time...
@@PunmasterSTP Amazing honestly. But that's always been the case for me, for some reason. I do better on my own than with the help of teachers probably because I like to take my time and not cram everything in an hour lecture. I ace all my exams if that's anything to go by? So yeah, self study, totally recommended 10/10.
@@pepepepe5802 That’s wonderful to hear! I never took abstract algebra, but I’ve been fascinated to learn about it.
We nurture great enthusiasm for the idea! We wouldn't mind some more on properties of specific types of groups either. This topic is so important, but so dryly explained elsewhere, that we are surely thirst for your juicy intuitions. Thanks a lot! Also, the more examples the better
Thanks so much for the compliment! I did say that I would put an end to the series in the last chapter of the video series though... I will try to see if there is any more demand to the continuation of this video series!
Thanks a lot for making these videos, they are actually making me understand the subject matter unlike my uni classes. I hope you get the recognition you truly deserve.
I took two courses in abstract algebra in Uni, one from a a famous group theorist. I am a visual learner, so pure math was always a challenge, but providing visual descriptions of symmetries and how they related to various subgroups (right, left, normal, etc.) was always lacking. These video are great, and can provide valuable context to a rigorous study of the topic. Nice work, and keep going. Posterity will, in my opinion, treat your efforts kindly.
Thanks so much for the appreciation!
I was just curious; who was the famous group theorist?
Honestly this content is unreal. Thank you for helping me with Math 113!
Glad to help!
I'm just curious; did you take any more math classes after 113, and if so, which ones?
Well ! I do not understand the video but i know that it will be intresting and informative for me when i will move in higher classes. Never stop uploading such videos . Earlier I thought symmetries are not intresting but your content changed my ideas.
Hey I was just curious if you ended up taking a group theory (or similar) class.
Keep this going!
Loving this series, if you keep posting more i'll be sure to follow
Due to popular demand, I have actually extended this series to chapter 7 and a little summary of the entire video series; but I did put a stop there... I might do an "Intermediate group theory" series as opposed to "Essence" in the future, but only if I can find a good way to visualize the other group theory concepts.
I am still making a lot of interesting mathematics videos, even though my upload schedule isn't too consistent. I try to upload at least monthly, but honestly there is no guarantee on this.
Sad to see so less views....i know that u will lead...keep up the great content.
The visuals of your videos are so helpful. Thank you for making them!
Im french and I understand this better than my french lessons , nice video + 1 subscriber
Awesome! Glad that this video helps!
Homomorphism? More like "Hurry up, this is incredible, isn't it?" Your videos are so good, and I can't wait to watch the rest!
Your videos are excellent! Definitely not bored
Glad you like them!
I am LOVING this series :D
It 'd be interesting if you show an application of group theory where it's really essential for the proof. Some problem that could not or hardly be solved in a strait forward way
You asked about what the viewers might be interested in knowing about. I would be interested in knowing how GROUP THEORY has been used to solve real world problems. In Physics they use the rotation matrices and various subgroups for Maxwell's equations U(1), QED - SU(2) and QCD. Well that is nice but it does not seem like they have done anything other than a very accurate description of all the possibilities. This is useful overall. Was it used to determine all the possible Path Integrals in QED? Can GROUP THEORY be used to describe wave interactions? There are phases, phase velocity and group velocity. It seems like this would be perfect for GROUP THEORY. Is there computer software you can use to put in what you know about a system in regard to the groups? And this software will tell you more based upon what you already know. It seems like GROUP THEORY would be perfect for the quantum. Because everything is a linear combination of the quantum. Is it being used in that manner. And there seems on first glance to be a correlation between Calculus, integrals and group theory. Because when you integrate, you really need to know what groups to integrate by. For volume the group is area and so forth. But how powerful could this be?
Plz keep uploading more videos..
Good explainaton.
Thanks so much for the appreciation! I am definitely not doing UA-cam full time, so I can only upload occasionally, but hopefully each upload is a good one!
Thank you! Very elegantly explained! You've got yourself a new sub, I'm sure many more will follow with time!
Awesome, thank you!
Super clear explanations, though I'm gonna rewatch the video several times to make sure I get everything right
Very very very good experience, thank you.
Thanks for the compliment!
I'd love to see something about Lie Groups and Lie Algebras
Thank you!
Hopefully this helps!
9:06
0:16
Awesome, extremely helpful
please introduce more applications 🙏
Same is dual to different.
The normal subgroup is dual to homomorphism (factor group) synthesizes the kernel.
The image (co-domain) is a copy, equivalent or dual to the factor group (domain) - the 1st isomorphism theorem.
Isomorphism (absolute sameness) is dual to homomorphism (relative sameness or difference).
Injective is dual to surjective synthesizes bijective or isomorphism.
Similarity, equivalence = duality!
Isomorphism represents the orthogonal complement or the dual of the kernel.
Homo is dual to hetero.
this was amazing
But what should e the value of phi to prove the second isomorphism from the first one? And how do we do it? It would be great if someone could throw some light on this, any hit would work, PLEASE.
11:00
doesn’t an isomorphism also have to be onto?
WHAT ABOUT COLORBLIND PEOPLE??!!! REEEEEEEEEEE
bullshit, if they're isomorphic, they're the same.
Is there any reason that you permanently emphasis words you are saying? I mean you don't need to give yourself too much pressure.
SSSSSSubgroup --> Subgroup
ROOOOOOTATIONNNN -> Rotation
Loosen up a little!
Maybe it is subconscious. Will improve this in later videos :)
As a non native English speaker, thanks a lot for the clarity in those difficult words. They have, after all, just been introduced by your videos to us viewers.
Homosexual