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What direction ought a math grad student take?

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Hi everyone. I was hoping for a little advice. I'm a math grad student so this post is a little beyond the "what maths do I need" posts that I see, as I've done graduate linear, numerical, graph theory, etc. I need to pick a specific direction/adviser and I'd like it to be relevant to machine learning. My choice is between algorithms and functional analysis (the functional analysis prof was great to talk to when I was working through the SVM algorithm). Any thoughts?

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