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mary livesong
Jun 7, 2019

Bachelor thesis

Hello ,I have to write a bachelor thesis next year ,I need some suggestions on a good subject. I was thinking about Fibonacci 's numbers!

What do you think?Any other suggestions or advises 😊

2 comments
Mr k
Jun 8, 2019

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

Jet
Jun 26, 2019

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

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