Abstract Algebra 9.3: Factor Groups

[@justinpearce6707]

Hello Patrick. These videos don't have crazy view but they are easily the best abstract algebra 1 videos on this platform. I cannot thank you enough for these video lectures. You have managed to very quickly convey this information in a way that is extremely easy to understand. It is a shame that these videos are not getting thousands of views considering how incredible they are. Thank you again for taking the time to make these, they are exceptional.

[@patrickjones1510]

Thank you for the kind words. They mean a lot to me. Honestly, I'm surprised the videos have gotten as many views as they have. I made them when I got roped into teaching an abstract algebra course after the previous professor bailed at the last minute. The course was scheduled to be online (which I think is a horrible way to teach any course with this much theory), and I didn't have the option of changing it. I figured that if I had to create videos anyway, I may as well make them available for anyone that was willing to watch.

[@ClumpypooCP]

I really like the way youre teaching this. Not sure why, but it works for me. Thanks!

[@TheTessatje123]

Really great video!! Writing down the factor/quotient group in a table, makes it much easier to understand than how it's normally introduced! One question: Why is {R90, R270}=R270K 8:43? And similarly, {H, V}=VK 9:09?

[@patrickjones1510]

Remember that R270*K is the set which consists of each element of K multiplied by R270. K in the example is {R0,R180}, and R270*R0=R270, R270*R180=R90. The other one is similar, you just need to remember how the group operation works.

[@TheTessatje123]

@@patrickjones1510 Of course! Thanks for your quick response 🙂

[@francisellec.largado6409]

hello, can I ask if the quotient group is the same as the factor group?

[@patrickjones1510]

Yes, those are just two terms for the same thing.

[@yBazo82]

this is very good, thanks

[@TrucNguyen-co2pt]

The video is so good and easy to understand.Thank you! it would be better if you continue the video without breaking them into different parts or having a link to the next part somewhere....

[@patrickjones1510]

I'm glad you found the video helpful. I am no longer teaching an abstract algebra course, so I'm very unlikely to do any further work on these videos. However, there is a playlist which has all the videos in order, so that might help with your sequencing.

[@EpicOfficialUNNES]

Why we do 0+H not 0xH?

[@patrickjones1510]

It is typical to use the symbol of the group operation. Since our group operation on the integers is addition, we just use the same notation.

[@EpicOfficialUNNES]

@@patrickjones1510 is only addition?

[@EpicOfficialUNNES]

Or we can use other operation

[@patrickjones1510]

@@EpicOfficialUNNES Multiplication is not a group operation on the integers, since it lacks inverses.

[@EpicOfficialUNNES]

@@patrickjones1510 what is group operation on integers?

[@aryankumarprasad1574]

Subbed

[@dineshprajapat9039]

Sirr plzz aap Hindi m smja do na...