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Recently in search of tests for uniformity of multidimensional distributions I luckily stumbled upon something called 'geometric discrepancy theory'. It seems to be a very powerful and elegant subject which interconnects algebraic geometry, number theory, statistics, stochastic integration and computational complexity. It sounds a lot like something I'd like to study, however there are some questions:

What prerequisites should I have?

How well should I know core algebraic geometry? My knowledge are limited by Cox, which, I suspect, is not enough. Moreover, what over advanced topics will be useful to know beforehand?

What are recommended texts?

By now I found this interesting book "Applied Algebra and Number Theory" by collective of authors, however it's unclear if it suited for first reading on subject. If you studied this subjects before, what sources do you consider particularly useful. Personally, I prefer books with geometric presentation and multitude of problems and exercises to work through.

I'm grateful for any help.

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You should certainly read Matousek's book "Geometric Discrepancy - An Illustrated Guide", which is very accessible. Another good introduction is Chazelle's "The Discrepancy Method: Randomness and Complexity".

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