I want to thank Socratica .I'm from India🇮🇳 and by your abstract algebra video I completed my graduation which I failed last year so thank you so much❤❤❤❤😊😊😊
I don't usually comment on TH-cam videos, but damn this channel is the only thing helping me pass my third year abstract math class and I am so thankful that it exists. A sincere thank you from South Africa!!!
The comments would be Ideal if they were devoid of puns. One could however Factor out the puns and see what is Left. Would that be Right? If so then it would be Double Sided, and puns in a Class of their own.
i just finished watching all abstract algebra videos they are amazing!!! Please keep going with the content this type of learning is sooo efficient and I actually learn something
Hey socratica, I will literally watch Liliana teach any math and science overview from real analysis to topology to electromagnetism. I do not care. This channel has helped us immensely even without a whiteboard and I fear you're not taking advantage of our admiration
Socratica is by far my favorite YoutTube channel so far. Ironically, I have found this channel not a week ago, but couldn't believe the quality of delivery. Specially this lady who teachs Abstract Algebra is just incredible. Hail maths!
Hey socratic, I will literally watch Liliana teach any math and science overview from real analysis to topology to electromagnetism. I do not care. This channel has helped me immensely even without a whiteboard
I’m sure I’d have had to see the absorption property explained like this once upon a time but this was a really neat reminder of why an ideal has to satisfy it!
We're so glad you're learning with us! We love making these videos. And thank you for so kindly supporting our channel-it means we can keep making more! 💜🦉
Wait, at 8:17, earlier you said that a ring does not require a multiplicative identity "1", but now you say that since ideal may not have a multiplicative identity "1" so ideal is not a subring. You contradict yourself.
8:1111:27 I think all ideals are the subrings even ideals are more than subrings because subrings contain their own element multiplication but ideal contain all multiplication of their element with any ring element. And it's not necessary for subring to contain the multiplicative identity 1 which is you telling that it is missing in an ideal then it is not subring example set of even number is the subring of the ring of the set of integer
Serious comment. How deep are you going to go with ideals? You did a segment on modules some time ago. Please show the connection between modules and ideals. Let R be a ring with identity, 1, and let I be an ideal containing 1. What can be said about I? Are there proper ideals that may, as a set contain other ideals but are not contained in any proper ideals? That is, are there always maximal ideals? Let R be a commutative ring with identity. What do the quotient rings of maximal ideals look like? I could go on but I think that I am a bit far down the rabbit hole already. Thank for your work --- This is a great channel.
And also, what happens if we try to mod out by a left ideal? A right ideal? What algebraic structure do we obtain? Socratica is doing such a great job with algebra. I took algebra years ago but I still love watching these videos presented so beautifully. :)
Many of your other videos are helpful because they are relevant to me and I gain a greater understanding. This video, I barely understand a single word, but it's somehow so very meditative to listen to.
The way I see it that an ideal is generated by an element you want to act as 0. Notice that the definition of an ideal is basically the definition of 0: 0 + 0 = 0 (I is a subgroup of the additive group) and 0 * r = 0 (xr is in I for all r in the ring and x in I)
Hola hace poco vi uno de tus videos sobre las estrellas de neutrones, pero lo vi en un canal tuyo en español lo abandonaste hace 5 años cosa que no note hasta que me suscribi, quise ver mas de tus videos en este canal en español y me encontre con el video de un anuncio en el cual indicabas que volverias, creo animarte a que vuelvas en especial con los temas de astronomia y fisica, veo que aqui en tu canal de español no te ha ido muy bien que digamos pero he visto otros canales en español que les a ido muy bien y han crecido mucho hasta tener millones de suscriptores, te animo a que cumplas con lo dicho y vuelvas a tu canal en español saludos desde colombia.
This may sound strange but is abstract algebra actually complete ?.If You treat a every number as already being 4d with 360 twist.(Hopf Vibration)Euler's identity is a realistic equation for a 1D number line. In Hopf Fib ration A Ring will always be a Field relative to another number ?.
it would be useful to add that ideals are in fact subrings if one keeps with the idea of a ring not needing an identity, I guess tough that rings with identity were more popular then too
I noticed in defining the properties of Ideals, there is the terms iy and xi -- it appears there's an order to how 'i' is multiplied -- I believe I understand this is due to Rings not being Albien under multiplication. But what does this look like beyond definitions? What would be an example? Thanks.
First, you need to think about a Ring that ia not abelian. The easiest example should be the 2×2 matrices, e.g. in the real numbers. Then you can think about the right ideal with zeros in the Second row. If you try multiplying any matrices with other in the given ideal, you should notice that the order makes a difference 😁 Hope i was able to help & my english skills were not too bad 😂 Edit: you can get a left ideal the same way by taking the 2×2 matrices with zeros in the second column It will also work with the first row or the first column, basically works the same way 😁
1:05 Tiny mistake here. When the regular less than or equal sign is used, it doesn't imply that the subgroup is NOT normal. At least that is how I was taught in my course.
Th other five partitions of Z are the can only be wriiten compactly ,as 1.z, 2.Z, 3.Z, 4.z and 5.z ie as normal subgroups by the definition of normal subgroups of Z she just gave.
Another example: The set 3Z formed by multiplying each integer by 3 forms an ideal. The quotient ring Z/3Z has three elements: 0 + 3Z = {0, ±3, ±6, ±9,…} 1 + 3Z = {…, −8, −5, −2, 1, 4, 7,…} 2 + 3Z = {…, −7, −4, −1, 2, 5, 8,…}
Do you give your patreons an insight into your video production and editing process? Would love to become your patreon if you tell how you guys edit vids :)
That's not something we've done before, but we have considered creating a new channel to share with everyone the lessons we've learned on making videos and running a TH-cam channel. Maybe we should do a poll to see how much interest there would be in this idea?
Hello I have great appreciation and reverence for your channel and it's prominence A need you to make a Video on 1. Temperatures below absolute zero 2. Gravitational waves property. If they travel at light speed, do they have other similar properties like reflection, refraction, diffraction, doppler shift polarization. What is their wavelength range? does special relativity apply to it? 3. Collapsing an air bubble with sound underneath a liquid surface 4. Square waves
@@andrerangel1029 ela é apenas uma apresentadora do canal, o dono é um cara, tem o canal em espanhol que parou faz uns 2 ou 3 anos de postar videos, faz 8 ou 6 anos que ela apresenta os 3 canais e talvez esteja esgotada e decidiram manter ela apresentando apenas esse canal, já que é o maior.
Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra
What is the name of background music that you used ? Please tell me !!!! 🤗🤗🤗
I want to thank Socratica .I'm from India🇮🇳 and by your abstract algebra video I completed my graduation which I failed last year so thank you so much❤❤❤❤😊😊😊
Congratulations!! You should be very proud about your hard work. Thank you for telling us - it really inspires us to make more videos!! 💜🦉
Love the way she presents concepts.
Well, definitely better than my teacher did.
She’s just an actor, but I agree, the writing is amazing in these videos. Very good compared to other lectures I’ve been seeing!
I don't usually comment on TH-cam videos, but damn this channel is the only thing helping me pass my third year abstract math class and I am so thankful that it exists. A sincere thank you from South Africa!!!
OMG this 12 minutes video is like a sonata, I am completely into it. Such a pleasure in my mind to enjoy mathematics. Math is beautiful, thank you.
I wish I discovered this channel at the beginning of the semester! Great explanations!!
Bro this is me for real
This.Series.Is.Genius !!!!
A big thanks to all the patreons. Such educational videos are a gift. 💯
The comments would be Ideal if they were devoid of puns. One could however Factor out the puns and see what is Left. Would that be Right? If so then it would be Double Sided, and puns in a Class of their own.
Niiice.... ;-)
i just finished watching all abstract algebra videos they are amazing!!! Please keep going with the content this type of learning is sooo efficient and I actually learn something
Hey socratica, I will literally watch Liliana teach any math and science overview from real analysis to topology to electromagnetism. I do not care. This channel has helped us immensely even without a whiteboard and I fear you're not taking advantage of our admiration
Socratica is by far my favorite YoutTube channel so far. Ironically, I have found this channel not a week ago, but couldn't believe the quality of delivery. Specially this lady who teachs Abstract Algebra is just incredible. Hail maths!
Thanks!
Oh my goodness, thank you for your kind contribution, Socratica Friend! It really goes a long way helping us make more of these videos. 💜🦉
Professor didn't explain why an ideal is called ideal. Thanks a lot for clear and precise explanation!
We're so glad we could help - thanks for letting us know!! 💜🦉
Amazing, wonderful, the clearest and most useful explanation ever. THANKS!!! Giving some money right now!!!
These videos are joy personified
These keep popping up in my recommended. I don't understand much of it but it's still pretty interesting
Hey socratic, I will literally watch Liliana teach any math and science overview from real analysis to topology to electromagnetism. I do not care. This channel has helped me immensely even without a whiteboard
I’m sure I’d have had to see the absorption property explained like this once upon a time but this was a really neat reminder of why an ideal has to satisfy it!
Wow love it thank you for saving me.. I truly finds it difficult to understand this
Abstract algebra before.
"There are many ways you can motivate the concept of an Ideal in abstract Algebra" Ma'am YOU're motivating me to learn that concept
These videos are incredible, would be great to see a topology series !
Nah they would just be homeomorphic to these videos.
ok, so to recap (correct me, if i am wrong):
assume:
(G,+,·) is a ring
Thank you these are dream topics I have been yearning to learn since a teenager. Thanks.
We're so glad you're learning with us! We love making these videos. And thank you for so kindly supporting our channel-it means we can keep making more! 💜🦉
Your abstract algebra videos are amazing!!! Keep making videos!!!
One word for this video: PERFECT
super happy to see these videos are being developed further!! hoping to see a video on the Sylow theorems and ring homomorphisms soon!
I've watched this video at least 8 times during the last 48 hours I'm losing it
Best math-pun-turned-into-sponsorship-message I've ever seen...
I finally got what ideals mean! Can't thank you enough!!😭💕
This is so wonderful to hear! Thank you for telling us!! 💜🦉
Thank you! This is the best explanation of ring ideals I've found!
Love the way she teaches.
Omg I just understood everything...you made it easy ...Thank you!
Just loved the way how you make concepts so easy and do relate the things ❤
i am early..but this video is very good... previous i had no interest in algebra..but due to you videos i like reading algebra
Awesome, but I hope some more videos are coming on prime ideals, maximal ideals, principal ideals and the isomorphism theorems.
Also varieties and schemes.
Me too waiting for
This make so much sense and meaning and really do understand what your saying and mean. Thank you for all the video
I was extremely waiting for your videos on the topic of Abstract Algebra please upload Daily videos
Daily videos? Do you think making a video takes a couple of minutes?
heehee thanks for that - if only! 💜🦉
@@Socratica welcome @Socratica 😇
@@gucker OK i know its too much difficult
I'm sorry @Socratica
We're so happy you're enjoying the videos!! But yes, it does take us a lot of work. More are coming! 💜🦉
A wonderful explanation I've never seen in any text (Gallian included.)
These videos are incredible resources
you snapped in this one 😍
Come here to find definition but got whole think clear really ❤️❤️❤️
Months of waiting.... Finally!!!!
I request you to share some lectures according to Algebric topology.
You can learn it yourself. That's a very fundamental group. Lol.
Great videos, saviour for students in the pandemic
love your videos, just a tip: you could ask small questions to test the insight of the viewer and his understanding of what you said
you are an ideal teacher
I love abstract algebra because of her ideal presentation.
Yeah she's good at the generators and the relations.
thanks a load this cleared up a lot for me
Wait, at 8:17, earlier you said that a ring does not require a multiplicative identity "1", but now you say that since ideal may not have a multiplicative identity "1" so ideal is not a subring. You contradict yourself.
Yes! this made me so confused, every ideal is subring but the converse isn't true.
what the fuck 1 minute into the video and she already made me understand factor groups and normal subgroups
عاشت ايدك على هذا الشرح الاكثر من رائع💙
Liliana, sou sua fã! Diva em tudo que faz!
Cant wait for this series to reach Galois theory!
8:11 11:27 I think all ideals are the subrings even ideals are more than subrings because subrings contain their own element multiplication but ideal contain all multiplication of their element with any ring element. And it's not necessary for subring to contain the multiplicative identity 1 which is you telling that it is missing in an ideal then it is not subring example set of even number is the subring of the ring of the set of integer
Your presentations are wonderful. I wish I had your videos when I was in college.
You probably had to learn off of typewriter manuscripts.
@@Grassmpl No, just chalk boards. :-)
I love your lectures
Serious comment. How deep are you going to go with ideals?
You did a segment on modules some time ago. Please show the connection between modules and ideals.
Let R be a ring with identity, 1, and let I be an ideal containing 1. What can be said about I?
Are there proper ideals that may, as a set contain other ideals but are not contained in any proper ideals? That is, are there always maximal ideals?
Let R be a commutative ring with identity. What do the quotient rings of maximal ideals look like?
I could go on but I think that I am a bit far down the rabbit hole already.
Thank for your work --- This is a great channel.
And also, what happens if we try to mod out by a left ideal? A right ideal? What algebraic structure do we obtain? Socratica is doing such a great job with algebra. I took algebra years ago but I still love watching these videos presented so beautifully. :)
@@tracyh5751 Let A be a ring with I a left ideal. Then A/I is left A-module.
I think you know this stuff already. Ideals and quotient are also modules. Maximal ideal always exist due to Zorns Lemma.
more videos please!!. thank you so much
You are awesome. I would love to see a similar video series on category theory concepts.
The universal properties just get tensor and tensor.
Many of your other videos are helpful because they are relevant to me and I gain a greater understanding. This video, I barely understand a single word, but it's somehow so very meditative to listen to.
Great job explaining
The way I see it that an ideal is generated by an element you want to act as 0. Notice that the definition of an ideal is basically the definition of 0: 0 + 0 = 0 (I is a subgroup of the additive group) and 0 * r = 0 (xr is in I for all r in the ring and x in I)
Hola hace poco vi uno de tus videos sobre las estrellas de neutrones, pero lo vi en un canal tuyo en español lo abandonaste hace 5 años cosa que no note hasta que me suscribi, quise ver mas de tus videos en este canal en español y me encontre con el video de un anuncio en el cual indicabas que volverias, creo animarte a que vuelvas en especial con los temas de astronomia y fisica, veo que aqui en tu canal de español no te ha ido muy bien que digamos pero he visto otros canales en español que les a ido muy bien y han crecido mucho hasta tener millones de suscriptores, te animo a que cumplas con lo dicho y vuelvas a tu canal en español saludos desde colombia.
Great concept.
Hi Socratica, thanks for the videos. But Why don't you think to prepare a MOOC about Groups & Galois Theory on a site like Coursera, or Udemy?
Wonderful presentation
Thank you very much ma'am 👍👍. We are like your teaching ideas.
Thank you Michael Harrison for the lectures.
Wish my classes could be this simple and clear so I don't have to sit through 90 mins.
Thanks for this video. I like your slide, please can indicate me the type of the beamer presentation are you using?
This girl's skills are next level. The math and the visuals.
Thank you so much for such a nice lectures. Would you plz upload short lectures on finite fields, Galois theory, elliptic curves, algebraic curves
This may sound strange but is abstract algebra actually complete ?.If You treat a every number as already being 4d with 360 twist.(Hopf Vibration)Euler's identity is a realistic equation for a 1D number line. In Hopf Fib ration A Ring will always be a Field relative to another number ?.
Is there an order in which we should watch your videos in order to become familiar with these concepts? EDIT: Never mind. I found it.
Fantastic expositor....
it would be useful to add that ideals are in fact subrings if one keeps with the idea of a ring not needing an identity, I guess tough that rings with identity were more popular then too
Thank You Ma'am🙏
I noticed in defining the properties of Ideals, there is the terms iy and xi -- it appears there's an order to how 'i' is multiplied -- I believe I understand this is due to Rings not being Albien under multiplication. But what does this look like beyond definitions? What would be an example? Thanks.
First, you need to think about a Ring that ia not abelian. The easiest example should be the 2×2 matrices, e.g. in the real numbers. Then you can think about the right ideal with zeros in the Second row.
If you try multiplying any matrices with other in the given ideal, you should notice that the order makes a difference 😁
Hope i was able to help & my english skills were not too bad 😂
Edit: you can get a left ideal the same way by taking the 2×2 matrices with zeros in the second column
It will also work with the first row or the first column, basically works the same way 😁
This is still here!!!!??? I haven't been on this channel in 4 years!!!
U teach very activel I IAM impressed
A very good expression. Could you tell me your software to make this video? Thanks so much!
Why do you think we need (x+I)(y+I)=xy+I but (x+I).(y+I) is not equal to another expression?
what an explanation! wow
1:05 Tiny mistake here. When the regular less than or equal sign is used, it doesn't imply that the subgroup is NOT normal. At least that is how I was taught in my course.
True. Obviously she mean "not necessarily" normal. We can all forgive her for that it's all cool.
Thank you! 🙏
Th other five partitions of Z are the can only be wriiten compactly ,as 1.z, 2.Z, 3.Z, 4.z and 5.z ie as normal subgroups by the definition of normal subgroups of Z she just gave.
Another example:
The set 3Z formed by multiplying each integer by 3 forms an ideal.
The quotient ring Z/3Z has three elements:
0 + 3Z = {0, ±3, ±6, ±9,…}
1 + 3Z = {…, −8, −5, −2, 1, 4, 7,…}
2 + 3Z = {…, −7, −4, −1, 2, 5, 8,…}
8:18 Brilliant! 😂
Could you please tell us about Categories? Quite difficult theme for understanding:(
It take a while to understand. The universal properties just get tensor and tensor.
Do you give your patreons an insight into your video production and editing process? Would love to become your patreon if you tell how you guys edit vids :)
That's not something we've done before, but we have considered creating a new channel to share with everyone the lessons we've learned on making videos and running a TH-cam channel. Maybe we should do a poll to see how much interest there would be in this idea?
@@Socratica , that'd be great. I really just want to know about your vid creation and editing process. :)
Well done.
please provide full lecturing of abstract algebra.
Good stuff
Hello
I have great appreciation and reverence for your channel and it's prominence
A need you to make a Video on
1. Temperatures below absolute zero
2. Gravitational waves property. If they travel at light speed, do they have other similar properties like reflection, refraction, diffraction, doppler shift polarization. What is their wavelength range?
does special relativity apply to it?
3. Collapsing an air bubble with sound underneath a liquid surface
4. Square waves
Seria bom se você fizesse uma versão em português também.
Já existem Socrática português.
Mas ela parou de colocar vídeos lá??? pq???
@@andrerangel1029 ela é apenas uma apresentadora do canal, o dono é um cara, tem o canal em espanhol que parou faz uns 2 ou 3 anos de postar videos, faz 8 ou 6 anos que ela apresenta os 3 canais e talvez esteja esgotada e decidiram manter ela apresentando apenas esse canal, já que é o maior.
What is the solution ideal Z15
Please reply because I have exam 😭
Qué penita verte por acá, de seguro vas a triunfar como no lo hiciste en socrática en español.....
Hello, can I communicate with this teacher?
thanks big sis
10:59 Why are ideals not called normal subrings
A lot of subatomic geometry was involved in bringing this person into being.