Hi Mary! You could write about the Stirling numbers and their relation to different functions. I believe the Stirling numbers of the first kind can be written as a sum of different polygamma functions which is pretty cool, the math is quite advanced though. They can also be represented as a relatively long sum, which is quite hard to simplify.

the Stirling numbers of the second kind are very related to the Berlounni numbers and the binomial coefficients.

There’s plently of relatively unexplored mathematics involved, such as the R-Stirling numbers and the like.

If you are really into combinatorics you could discuss how the application of different operators to some simple combinatoric identity manipulates the numbers given. Such as (n+1,k)= (n,k-1)+k(n,k) is equal to k! times {n+1,k} = k{n,k-1}+ k{n,k} but it is not (k!)^2 times [n+1,k] = k^2[n,k-1] + k[n,k].

In two of your videos you prove i^i = e^(-Pi/2) and the ith root of i, I^(1/i) = e^(Pi/2). When I multiply i^i by i^(1/i) I get i. But when I multiple the representations e^(-Pi/2) and e^(Pi/2) I get e. So, does i = e? Where have I gone wrong?

Ok, Mary. I will think about what can I suggest.

Hi Mary! You could write about the Stirling numbers and their relation to different functions. I believe the Stirling numbers of the first kind can be written as a sum of different polygamma functions which is pretty cool, the math is quite advanced though. They can also be represented as a relatively long sum, which is quite hard to simplify.

the Stirling numbers of the second kind are very related to the Berlounni numbers and the binomial coefficients.

There’s plently of relatively unexplored mathematics involved, such as the R-Stirling numbers and the like.

If you are really into combinatorics you could discuss how the application of different operators to some simple combinatoric identity manipulates the numbers given. Such as (n+1,k)= (n,k-1)+k(n,k) is equal to k! times {n+1,k} = k{n,k-1}+ k{n,k} but it is not (k!)^2 times [n+1,k] = k^2[n,k-1] + k[n,k].

Peculiar stuff, it may be worth checking out!

Cheers