Finite Cyclic Groups Part 1

Finite cyclic groups are finite groups which are generated by a single element.
They capture the patterns in rotational symmetries.
In this video we discuss the intuition behind them and why they obey the axioms of group theory.
We then look at the first few examples from C2 to C4.

[@Gismho]

Excellent exposition as usual!!! Thank you for taking the time to explain every item/concept from first principles .... and your repetition ensures comprehension.

[@gerdkukemilk5663]

Best explanation I have found on this topic, amazing videos, thank you so much.

[@pratapbasak146]

Excellent!!!!!!!!!!!!!!

[@trxx3922]

Fantastic, thank you!

[@michelef406]

Is there any way to send you some money to say thank you for these lectures?

[@StevieBaskin]

@23:00 Isn't it clearer to say n-σ(360/n) so that we can see that it's really just a matter of finding the permutation that will rotate the circle the rest of the way? It's only n-1 because σ is equal to 1.
Otherwise great tutorial. Thank you.

[@deadfish3789]

These videos are interesting. Do you discuss any uses of it at any point?

[@navjotsingh2251]

Hugh Jones it’s also heavily used in cryptography, google most likely uses results from group theory to protect their applications like TH-cam!

[@absolutezero6190]

Navjot Singh yeah crypto uses a ton of number theory and group theory

[@vulicuba8079]

Is the order of Cn n or (n+1)? Order n does not seem to count the identity to rotation.

[@DavidJohnston_deadhat]

Rotation by n = the identity. So the order of Cn is n.

[@inayatullahsheikh5569]

if video is short it would be better.If u repeat ur talk again and again,it becomes boring.There is also a little noise which looks bad.

[@navjotsingh2251]

Danush S well said. Inayat at shut up.

[@g-abeshawel9603]

how come on earth you say this one of the best explanation what I see in this course ever please don't write such things, in any case, because things are done perfectly

[@Anteater23]

G-Abe Shawel ?

[@abublahinocuckbloho4539]

how many fucking times do you need to repeat that the set of cyclic permutations is a set of rotations of a disc

[@ptyxs]

I vastly prefer a didactic video with many repetitions but which I completely understand at each and every moment than a dense one where I am constantly asking myself wheter I really understood what was just said. This video is for me absolutely perfect as a pedagogical tool.