Thank you for making KZbin a better place to pass time.
@SalDin_6 жыл бұрын
literally have an abstract algebra exam tomorrow. videos are undoubtedly a great help!
@mksarav756 жыл бұрын
Thank you to the entire team who worked hard to produce this great video series.
@mortervolk66766 жыл бұрын
I can't believe you guys have covered so much info in less than 10 minutes! That's really great, Socratica. Keep up the good work. (From Syria with love!)
@scipionedelferro4 жыл бұрын
This is the most packed video of the series, content-wise. So many interesting and fascinating stuff mentioned, too quickly! It would be fantastic to have more videos on simple finite groups. You guys are the best!
@PunmasterSTP3 жыл бұрын
That zooming-in and Monster group music! So suddenly intense, just like the rate of my learning after finding Socratica several days ago!
@raunitsingh6762 жыл бұрын
I can only imagine how much time and effort and knowledge is required to put out a video like this.
@raunitsingh6763 жыл бұрын
It's so sad that they have stopped making videos, now who will teach me more of such awesome things
@kennedyada11175 жыл бұрын
Man, I have an exam tomorrow and I was looking for slow easy to understand videos with examples that drive the points home, but you're just as fast as my lecturer assuming that I already knew everything about math when I was born.
@eleazaralmazan40896 жыл бұрын
Thank you so much Socratica! You make mathematics very intriguing!
@adeelali84175 жыл бұрын
This is where my journey with your series ends, you have been a great help! This video in particular is very comprehensive! :D Thank you thank you thank you!
@Socratica4 жыл бұрын
We're so glad you found our videos helpful! Thank you so much for watching. Please share with anyone you think we could help! 💜🦉
@daca83956 жыл бұрын
"releace a video every hour" Nooo, I will witerally spand my life watching your videos...
@janko47656 жыл бұрын
So, I am learning quantum mechanics and the abstract algebra is like a language you're using to talk about it. Although these lectures don't cover representations of groups and Lie's groups which are also needed for my quantum mechanics classes, I must say I'm in love! The concepts you're covering seem like they come in a natural way one after another and you want to know everything about every single concept. They don't seem just like a random topics you need to understand as fast as you can! The enthusiasm and the sort of an adventurous vibe I'm getting from the way you're talking is making me feel like I'm watching a movie! Thank you!!
@jaimelima24203 жыл бұрын
I am afraid to going to sleep today and have bad dreams because of this monster group. Thanks making us understand these concepts.
@kamyarghandi99956 жыл бұрын
Would love for this series to eventually get to an explanation of what E8 is and why it is considered such a beautiful mathematical object.
@rajendralekhwar41315 жыл бұрын
First of all thanks for your all videos.. I don’t get time to comment, on every video, but let me tel u , Your explanation is just awesome ..👍👍keep it up 👍👍 Please every time keep trying to make abstract mathematics as a layman language subject as long as possible I know it’s hard to do every time , but that’s the only way we can convert maximum individuals to love higher mathematics ...❤️
@herbertpalines34434 жыл бұрын
This is a nice introduction to finite simple groups! Thank you, Socratica!
@derciferreira25239 ай бұрын
You resumed 300 years of mathematics in just 8:52 minutes. Thank you.
@noellundstrom74476 жыл бұрын
I love seeing you go a little deeper into abstract algebra, nice job you earned a donation!
@Socratica6 жыл бұрын
We're so glad you are enjoying our videos! Your donation is SO appreciated. It will help us make more of these videos!! Thanks so much for your kind words and support.
@arpanbhattacharjee4706 жыл бұрын
Wonderful presentation!!! The videos are a great resource to understand the basics as well as some of the advanced concepts of Abstract Algebra neatly, quickly and efficiently... I'm a researcher in Applied Mathematics and the videos helped me a lot to revise my algebra concepts in a gist... Thanks a lot... Waiting for more topics on Advanced Mathematics to come...
@rodneytopor18469 ай бұрын
Nice summary. I think it would be helpful to elaborate the correspondence between prime numbers and simple groups as follows: Every finite group (positive integer) can be expressed as a product of a unique set of simple groups (prime numbers) by the Jordan-Hoelder Theorem (Fundamental Theorem of Arithmetic). But a given set of simple groups can be multiplied in different ways to give different product groups (the extension problem you mentioned), whereas a given set of prime numbers can be multiplied in only one way to give a unique composite number. I guess the reason for this is that arithmetic multiplication is commutative but group multiplication is not.
@Grassmpl3 жыл бұрын
This lady knows so much. How about a video on cohomology groups?
@michaelren48453 жыл бұрын
I cannot believe I have followed from episode 1 to 22 and intend to keep going. You explain these abstract and difficult ideas in a much clear way than my any of my professor. Thank you so much! [I might find a small typo in episode 22 for Simple Groups at 03:04 in the second line (title not included) "Quotient groups are simple: (N_1/1), (N_1/N_2), (N_3/N_2)..." Is it intended to be (N_2/N_1)?]
@huttarl Жыл бұрын
I wondered about that (N_1/N_2) as well. Glad it's not just me.
@ruiyingwu8936 жыл бұрын
I am pretty new at group theory, so I did some 'research' (aka me typing it onto Google ) ... |A_13|= 13!/2= 3 113 510 400 Thats... a lot of subscribers you are asking for...
@randomdude91355 жыл бұрын
T series has surpassed both pewds and Music to become no 1. But even they've got apprx 107M subs.
@jonmolina9485 жыл бұрын
You could've simply taken the cardinality of S_13, 13!, and divided that by 2. The cardinality of even permutations in S_n is always the same as the number of odd (If n >= 2). You can prove it by defining a bijection between the two sets.
@RalphDratman6 жыл бұрын
This is a wonderful presentation -- thank you! What exactly is Socratica?
@Socratica6 жыл бұрын
Thank you for your kind comment! We're a small team of educators who make videos for KZbin! You can read more about us here: www.patreon.com/socratica
@HikingWithRiley5 жыл бұрын
Slide at 6:27, “intervertible” is written, “invertible” was spoken
@saurabhsingh-ow7ue4 жыл бұрын
well this 8 mins video is the best investment of my life till now....thank you madam.....
@Socratica4 жыл бұрын
That is so nice of you to say, thank you! We're so glad we could help. 💜🦉
@ashwanirao73544 жыл бұрын
Your way of explanation is wonderful
@AHeil19636 ай бұрын
There is a typo at 3:10: (N1/N2) should probably be (N2/N1). Congratulations and many thanks for the excellent video!
@kresimir19656 жыл бұрын
I got goosebumps when I saw Monster group :O And the music was whaaat
@priyanka-samal.5 ай бұрын
Thank you in these 9 min video u explained a lot and in a simple way
@ahmedengineer57786 жыл бұрын
I like your enthusiam ..... you sure have passion for the subject you are discussing ..... but I think that you need to add more examples .... and more important real life applications ..... the problem that makes alot of people hate math is that they feel it is irrelivant to thier every day life ..... one of the merets of educational videos on youtube is the appility to show people how science really affects thier life
@bobsagget92124 жыл бұрын
I study business but I really like these videos
@alvaroquispe-unsa10 ай бұрын
Thanks for the video series, although I don't speal English, there are so useful for me. My best greetings from Arequipa - Peru
@upendraagnihotri26864 жыл бұрын
Thanks for making me understand a bit in the ocean. I am struggling very hard to get the essence of it.
@luyombojonathan66889 ай бұрын
Thank you alot for these series
@cameronspalding97923 жыл бұрын
@8:23 The number she’s aiming for is half of 13 factorial which is 3.1 *10^9
@My_oxytocin2 жыл бұрын
Love your indetails information on group.❤️❤️❤️
@christianorlandosilvaforer34515 жыл бұрын
wow at least i came to this video.. finally i can understand why pol eq. of 5 or more grade have not a general formula as solution!!! thank you socratica team!
@RurczakKurczak3 жыл бұрын
3:04 can we take N1/N2, where N2 is bigger than N1? I think not, since N2 has to be a normal subgroup of N1 to be able to take a quotient group.
@giorapeniakov31532 жыл бұрын
seems like a mistake?
@filipve736 жыл бұрын
1) Time will tell ?? (abstract) Perhaps there is a group between the "Happy Family" and the "Pariahs" 2) For patreon support do you accept also Bitcoins ?
@Socratica6 жыл бұрын
1) People are researching ways to unify the sporadic groups. I'll need to check on the latest research to see what progress has been made. 2) We *do* accept bitcoins! :) You can find our address on our "About" page: kzbin.infoabout Thank you so much for considering supporting us!!
@FranFerioli4 жыл бұрын
The gist of Galois theory in under 10 min! The groups might be simple, but this video is certainly not. Outstanding work, as usual Socratica...
@oldPrince222 жыл бұрын
To be honest, this video has a much higher requirements for the audience. Hence is not that consistent with the previous videos about abstract algebra. And the topics covered in this video is seldom used for a beginner of abstract algebra.
@NH-zh8mp2 жыл бұрын
Bravo, I love this video, it’s so fascinating and helpful
@fengzm7 ай бұрын
|A13| is approximately 3 billion. Way to go, Socratica!😃
@ChaudharyAteeq4406 жыл бұрын
Great...Please upload more videos on abstract Algebra...also in linear algebra and real Analysis
@paramanandadas13194 жыл бұрын
At 3:05 there is a mistake. I think that is not N1/N2 but N2/N1
@davidpal13786 жыл бұрын
I like your videos on abstract algebra , but can you make videos on real sequences. Like bounced and unbound sequences , least upper bound greatest lower bound , infima , Suprema etc. if you do so then , It would be a great help .
@ChanawerebiChanawerebi7 ай бұрын
hello! why do we get R^(n^2) ? why is n^2 a dimension?
@gauravsinha60606 жыл бұрын
I love this channel. Thanks for the great video.
@SSJProgramming3 жыл бұрын
Great video, But slightly misleading at 5:14 There is no general formula for degree 5 and higher *** IF *** you consider only using BASIC operations like +,-,*,/, roots, powers, exp(x), log(x), sin(x), cos(x) etc. Its a common misunderstanding that this hold for ALL types of multivalued functions you can consider. And in fact, there are GENERAL solutions for degree 5 and higher. Using elliptic functions, or jacobi theta functions, some others I can't even recall, hypergeometric etc.
@CSAN336 жыл бұрын
These are actually really nice videos, I'm impressed!
@woahdaggies6 жыл бұрын
Please do a video on the Monster!
@moaadmaaroufiii20573 жыл бұрын
amazing work!! keep up
@gharsepadhonasantoshkumarj91543 жыл бұрын
Great lecture
@himanshugarg60625 жыл бұрын
Is this connected to M theory in physics (because Monster group) and 26 dimensions that were needed before modern string theory allowed for 10 (before moving on to 11)..? P.S.: Very pop sciency.. I know..
@bat_man10892 жыл бұрын
Thank you teacher 😊
@gylje-99056 жыл бұрын
I am just amazed! I only can thank you..
@孙林可3 жыл бұрын
I've heard that there is only ONE mathematician alive now who understands the whole 10000 pages of simple groups. S a d.
@dekippiesip4 ай бұрын
And his name is?
@mohdfarhan85626 жыл бұрын
Plz give video's on some examples on abstract algebra like inverse , order of an element..etc.
@Socratica3 жыл бұрын
Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra
@himanshugarg60625 жыл бұрын
Stick to one of the names : like factor group or quotient group.. And similarly in other situations.. Maybe show an asterisk comment at the bottom of the video.. I'm a fan.. Trying to help..
@ashishpathak294710 ай бұрын
At 7:27 the instructor mentions that monster group contains 20/26 sporadic groups as either subgroups or quotient groups. But as monster group is a simple group, then it shouldn't have any normal subgroups right? And hence we shouldn't be able to form any quotient groups? Can someone please comment on what I'm missing here.
@MuffinsAPlenty8 ай бұрын
I looked it up. Apparently the happy family are all _subquotients_ of the Monster Group. Given a group G, a group K is a _subquotient_ of G if K is isomorphic to a quotient of a subgroup of G. In other words, K is a subquotient of G if there is some subgroup H ≤ G and some normal subgroup N ⊴ H so that K ≅ H/N. This does not contradict the simplicity of the monster group because H will not be normal in G there. This is not a failure on your part, though, because the video didn't say this.
@Jung8506 жыл бұрын
This is really awesome! Great work. 😍🤗🤗
@mueezadam84384 жыл бұрын
A masterclass presentation.
@basudebmondal9542 жыл бұрын
Group is very interesting chapter in abstract algebra
@guru66446 жыл бұрын
Very clear explain... Thanks.
@noraalbogami5866 жыл бұрын
unique presentation information ... thanks a lot ..
@vaishaliitkan74436 жыл бұрын
Nice explanation
@MarvellousMartha4 жыл бұрын
you say "remember manifolds?" but i am not able to find a video of yours covering manifolds. which one is it? thx
@sebastiananaya256 жыл бұрын
Hola Muy buenos videos, excelente calidad Me gustaría que volvieran en español
@thavibu5 жыл бұрын
Interesting that two of the concepts in the video are named after 19th century Norwegian mathematicians, Abel and Lie
@whalingwithishmael77515 жыл бұрын
Can you do a video on the monster group? John Conway thinks that he’s going to go to his grave without having learned why it’s there and that would be tragic
@alfredbeadman71143 жыл бұрын
Would love that. Want to learn more about it!
@anyachan5674 жыл бұрын
Briliant work!
@tharagleb6 жыл бұрын
Order of A13 is 3,113,510,400
@rylieweaver1516 Жыл бұрын
At 1:01, it should say that N is normal if gNg^-1 is a subset of N, not equal
@MuffinsAPlenty Жыл бұрын
Let G be a group and N be a subgroup of G. 1) gNg^-1 is a subset of N for all g in G 2) gNg^-1 = N for all g in G Statements 1 and 2 are equivalent. So either can be used as the definition.
@rylieweaver1516 Жыл бұрын
@@MuffinsAPlenty How do you know that the statements are equal?
@MuffinsAPlenty Жыл бұрын
@@rylieweaver1516 You can prove it! Statement 2 implies statement 1 without really any work. So most of the work goes into showing statement 1 implies statement 2. So suppose statement 1 is true: gNg^-1 is a subset of N for all g in G. Now fix an arbitrary g in G, and we will want to prove that gNg^-1 = N. To show two sets are equal, we can show they are subsets of each other. By statement 1 (which we are assuming), gNg^-1 is a subset of N. So all we have to do is show that N is a subset of gNg^-1. To do that, we should take an arbitrary element n of N. We want to find an element m of N so that n = gmg^-1. Can we do this? I think this is a good exercise for you to try on your own, but you are welcome to comment back again asking for the rest of the details, and I can provide them.
@IjazKhan-fm4si3 жыл бұрын
Great Socratica❤❤❤
@AkiraNakamoto Жыл бұрын
3:05 There is a typo/error. N2/N1, not N1/N2. The latter doesn't make sense.
@Drtsaga4 жыл бұрын
Hi guys! Can anyone explain how the monster group can contain quotient groups? I thought that in order for a group to contain a quotient groups, it needs to contain normal subgroups. (simple groups do not contain normal subgroups, and the monster is a simple group) Thank you.
@MuffinsAPlenty4 жыл бұрын
I looked it up. Apparently the happy family are all _subquotients_ of the Monster Group. Given a group G, a group K is a _subquotient_ of G if K is isomorphic to a quotient of a subgroup of G. In other words, K is a subquotient of G if there is some subgroup H ≤ G and some normal subgroup N ⊴ H so that K ≅ H/N.
@qaziarshad9393 жыл бұрын
Hausdorff Space and T2 space is also T3 space ? is it Right?
@ladmondraxngfuskiii94266 жыл бұрын
视频讲的很清楚,获益匪浅!
@eliasgarciaclaro61366 жыл бұрын
Este canal es increíblemente bueno
@chindinaresh73055 жыл бұрын
Vf
@mohdfarhan85626 жыл бұрын
It's well undertaken video
@MrMojo04176 жыл бұрын
Let H be a subgroup of G. You can make cosets of any H within G. But cosets only quality as factor groups if H = N. Is this correct?
@MrMojo04176 жыл бұрын
This video was packed with information!
@information29496 жыл бұрын
Ma'am plz make one vedio on P group, sylow p-subgroups and related theorem
@Henry-yr2hn4 жыл бұрын
A13 is a huge group !
@spotlight90276 жыл бұрын
I need your lectures about real analysis and topology
@giorapeniakov31532 жыл бұрын
A factor group is also known as a quotient group
@aniketchandak74266 жыл бұрын
Please upload video on Riemann integral...
@christopherrippel29586 жыл бұрын
I was watching your videos in December to prepare myself for my Abstract Algebra course that started in early January. I come to find out that he is one of the few professors that started the course with category theory and threw me for a loop. Is there any channel on You Tube that you would recommend to supplement my studies?
@mohitsaini21143 жыл бұрын
Nice
@1337w0n3 жыл бұрын
7:33 How is it that the monster group contains any of the other members of the happy family as quotient groups? I'm under the impression that simple groups can't have quotient groups.
@MuffinsAPlenty2 жыл бұрын
I looked it up. Apparently the happy family are all _subquotients_ of the Monster Group. Given a group G, a group K is a _subquotient_ of G if K is isomorphic to a quotient of a subgroup of G. In other words, K is a subquotient of G if there is some subgroup H ≤ G and some normal subgroup N ⊴ H so that K ≅ H/N. This does not contradict the simplicity of the monster group because H will not be normal in G there.
@mehdinadjafikhah73144 жыл бұрын
S_n is not simple for any n>1 because A_n is a normal subgroup with index 2 of it! But, A_n is simple for n>4.
@AzrgExplorers4 жыл бұрын
Wait, how can the monster group have quotients if it's simple? Don't quotient groups and normal subgroups go together?
@governmentday35115 жыл бұрын
thank you
@House_ssb6 жыл бұрын
More about calculus please
@bhavyaanbarasan79195 жыл бұрын
Hi mam Can u please do a video on decomposition of graph
@muhammadafzaalkhan92776 жыл бұрын
at which author of abstract algebra book i select for himself to read.
@manuelroman8156 жыл бұрын
Muy buenos sus videos pero si colocan los subtitulos para que el publico en español pueda seguir disfrutando de sus videos seria genial!
@yenmejos31626 жыл бұрын
hi, can you also make videos about non-cyclic groups :)