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Personal Statement Accuracy

I was wondering if there were any graduates or students who have experience with probability theory and combinatorics who could help me: I've written part of my personal statement referring to 'Game, set and math' by Ian Stewart and then went on to discuss a particular part of the book however for obvious reasons I don't know if what I've written is strictly true. I understood the book on the surface but not thoroughly. I wanted to convey how different branches of maths can be used in conjunction with each other as that is how it appeared in the book and from my current knowledge but I can't be sure and would like confirmation or correction if possible.

I would paste the part here but that would risk plagiarism so if you can help could you either reply to the thread or PM me. Thanks a lot.