(Abstract Algebra 1) Definition of Cosets
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- Опубліковано 9 сер 2017
- This video introduces a relation which will be used to define the cosets of a group. First, the relation is shown to be an equivalence relation, then the equivalence classes are described, and finally the definition of cosets is given.
I've spent the last several weeks watching the videos in this Abstract Algebra 1 playlist, but now it has ended. I realize that life happens, and you may have other things that have taken up your life (work, family, studies, etc., and I hope you are still among the living, considering how many left due to COVID-19). But if you ever have a chance to continue this playlist or to begin an Abstract Algebra 2 playlist, I'll want to pick up where we left off. By the way, I am a few days short of my 70th birthday and took Abstract Algebra half a lifetime ago, at age 35. I decided I needed a refresher, so I happened upon this playlist.
Holy moly! 70 year old? That's really cool that you study at this age, huge respect!
I have watched the entire playlist, and they are the best abstract algebra videos I have ever found. Thank you so much! You have saved my course!!!
I must say I really like your way of first going through the intuition of proofs with natural language and then going into the formal part - I used to often skip proofs because many times they would be too burdensome for me to understand. But the way you explain them makes it natural and easy to understand. Thank you!
Watched the entire playlist, was very lucid and concise. Thanks a lot!
Actually you r amazing teaching...please do more videos in Abstract Algebra
Thanks to you I will pass my exam tomorrow!!
Your videos are really great!! Your style of teaching makes it easy to understand. Thanks...
I couldn't have recieved a better notification today. Thank you so much for making a new video!!! Im taking my final at the beginning of september after attempting to self study abstract algebra and your videos have been HEAVEN SENT!
WHEN I do well, it'll be mostly thanks to you!!
Wow, thank you for the wonderful comment! I'm really glad to hear that my videos have been helping you study. I hope the exam goes well!
Outstanding video lecture. Excellent for self study.
Your explanation is great ! Hope you make more videos like that ! Thanks !
u are a excellent teacher! thank you for your effort!
This is the best video i have encountered for Abstract Algebra. Sir can u do more videos on Isomorphism, Homomorphism, sylows, Ring and Integral domain, langrange theorem and other part of Abstract Algebra
Really nice video... Thanks a lot
Sir your all videos are very helpful.
Thank you so much! Well explained.
Oh Sir...thank you so much for this...Just like Sal Khan saved my last 4 courses... you're going to save my course this time ☺👍👌
No problem! I'm glad I could help!
Thanks, that was nice. My book and videos I've watched so far didn't have this step in this video, and it was quite nice to see cosets as equivalent classes.
I agree, I think it makes sense to think about them this way.
I'm trying to self learn Abstract Algebra from your videos and Gallian book. So far, your videos have helped me a lot than any other books or videos. Keep up the good work, I'd say!
Thank you! I plan on making more videos soon.
I highly suggest you check out Charles Pinter's A Book of Abstract Algebra. It's the best introduction to abstract algebra I have ever seen and it is Dover publication so you can get it for like $15 or so.
The book is really intuitive, the explanations and insights are fantastic, however the rigor is also present, which means that you won't miss on anything. The problems are really cool and the book covers a pretty standard undergrad level abstract algebra course. Hope this helps! Note that often with math books titles can be incredibly decieving, meaning that Dummit and Foote for example is a massive behemoth compared to pretty much any other undergrad algebra book lmao.
Berserker i just want to learn abstract algebra for cryptography. Will these videos on youtube along with the book you recommended be enough to understand current cryptographic methods that use groups?
Thanks sir. Really helpful vedio
I really appreciate your hard work. But could you please make videos after this topic like quotient group homomorphism and isomorphism
Thank you so much...this is nice.but I request you..plz make more video on group theory.
all love for the greatest
your videos are very helpful.
can i please ask if you have videos for mathematical analysis?
very nice video..please upload isomorphism and homomorphism
tariq khawaja
Excellent video lectures. Thank you.
Do you also have videos for Abstract Algebra II? I could not find them. If you have please give me the link address. Thank you
nice video
will you make more videos?
thanks mate
Extremely disappointed in myself for missing such a thorough introduction to cosets!
Hello, I liked your lecture very much. abstract algebra is a lesson that I did not understand at all, but I understood it very well with you, but I was very sorry that your videos were up to the cosets part. How can I access the continuation?
YESS!!!! Cosets, i have seen your playlist on abstract algebra. are you planning on adding homomorphism, rings, fields?
I do plan on adding those topics. And I have more to say about cosets, as well!
where did you go:(
@@learnifyable Will we ever see these... you've been such a help!!
9:52 should "a" also be in H?
Excellent series, I hope the author is doing well somewhere and will continue later on 😥
love your video!!!!!
For your symmetric definition aren't you assuming commutativity when you go from the third line to the fourth?
No, let (AiB)i = C such that
(AiB)C = e
(AiB)(BiA)
(Ai)(BBi)(A)
(Ai)e(A)
(Ai)(A) = e
He’s not assuming commutativity. 3:20 if you look here you see he has actually applied the operation as he’s not taking the inverse of Ai in the line you reference
Hi, what book do you use as reference?
I think he uses Seymour Lipschutz Set theory's Book..
examples please
Later videos bro
Hi,, how is this possible (a^-1b)^-1= b^-1(a^-1)^-1 ?
Try multiplying them and you will see that you get the identity, which by definition the inverse. We called it the "socks and shoes theorem." Normally you put on your socks and then your shoes. So the inverse process is to take off your shoes and then your socks, not the other.
Explicitly (inverse(a) * b) * (inverse(b) * a) = inverse(a) * (b * inverse(b)) * a
= inverse(a) * identity * a
= inverse(a) * a = identity.
@@mrnogot4251 it also works for when you put your shoes on first, and then your socks. Although your socks wear out faster.
WAIT. NO. COME BACK. I HAVE A 58 D:
stil dont get it, took you a long time before getting to cosets imo...
bro u stopped makin em videos when it started to get hard af. thats sad