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I'm mainly a CS major, but I also want to learn more advanced mathematics. I see lot of cross over between CS and applied math, same can't be said about pure math.

Definition of 'advanced': Something a pure math major learns during and after late undergraduate years.

What are the fields that combines advanced mathematical topics with computer science?

Theoretical computer science and computational group theory are good examples.

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    There are lots of interesting answers to this question, but I don't know what is meant by CS in this context. Is it programming? Theory of computation? Formal Languages? Analysis of algorithms? Something else really cool that I forgot to mention?2010-08-09
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    The more theoretical part of CS, what you said except programming are what I was thinking. Other possibility are database theory, artificial intelligence and networks.2010-08-09
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    [Modern computer algebra](http://cosec.bit.uni-bonn.de/science/mca/).2012-08-24

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