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I'm not even from Berkeley and this must be one of the best math courses I've hadThank you!
I love how you describe some things as rather something "stupid" as thou is what builds the beauty of mathematics.
There is a slight mistake at 24:23. Both for the equality at the bottom of the page and also for the product of the two parentheses to come out 1, the denominator should be 2^(a+1) instead of 2^(a-1).Thank you for the great content!
thanks! could you help me understand why b = 1 implies we can't have any other primes dividing it?
@@1manasharmabecause that would make the sum of the divisors even greater, but with a power of 2 and one other prime the sum is already 2n.
Super explanation..thank you sir
It would be nice if Ramanujan had given some kind of motivation for his "observations" (other than thoughts of his Devi, of course).
Probably this interests you, from another Fields medalist, Prof. Timothy Gowers, czcams.com/video/PHkYqPX3Je4/video.html
Thanks!
divisors(10) * divisors(6) = divisors(60)provided 10 and 6 are relatively primeuseful :)d(power N of prime) = N + 1
Thanks
Somebody needs to develop a crypto that is mined by doing calculations in number theory.
yeeeeeeeeeeeeeee
I would like to remind that, even if it's not so widely used, the pronunciation of μ is mi(pronounced like "me") not mu, same for ni
I'm not even from Berkeley and this must be one of the best math courses I've had
Thank you!
I love how you describe some things as rather something "stupid" as thou is what builds the beauty of mathematics.
There is a slight mistake at 24:23. Both for the equality at the bottom of the page and also for the product of the two parentheses to come out 1, the denominator should be 2^(a+1) instead of 2^(a-1).
Thank you for the great content!
thanks! could you help me understand why b = 1 implies we can't have any other primes dividing it?
@@1manasharmabecause that would make the sum of the divisors even greater, but with a power of 2 and one other prime the sum is already 2n.
Super explanation..thank you sir
It would be nice if Ramanujan had given some kind of motivation for his "observations" (other than thoughts of his Devi, of course).
Probably this interests you, from another Fields medalist, Prof. Timothy Gowers, czcams.com/video/PHkYqPX3Je4/video.html
Thanks!
divisors(10) * divisors(6) = divisors(60)
provided 10 and 6 are relatively prime
useful :)
d(power N of prime) = N + 1
Thanks
Somebody needs to develop a crypto that is mined by doing calculations in number theory.
yeeeeeeeeeeeeeee
I would like to remind that, even if it's not so widely used, the pronunciation of μ is mi(pronounced like "me") not mu, same for ni