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I am interested in Big Data and related jobs after graduation from Math PhD/Masters, what topics and fields of Mathematics should a student learn that are most relevant to Big Data?

Currently, I know Algebraic Topology (Persistent Homology) would be one relevant topic, are there any other areas of Math that would be useful in Big Data?

Thanks and best regards.

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closed as primarily opinion-based by Daniel W. Farlow, muaddib, Claude Leibovici, Michael Galuza, apnorton Aug 10 '15 at 4:40

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ What sort of Big Data problems are you thinking of trying to handle? The only thing which is definitely in common here would be programming/probability/statistics. But if there is some richer structure of interest, then many other ways of analyzing that structure could prove useful. $\endgroup$ – Ian Jul 29 '15 at 10:59
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    $\begingroup$ I would definitely throw statistics and numerical linear algebra into the hat of options $\endgroup$ – KyleW Jul 29 '15 at 13:25
  • $\begingroup$ What is the meaning of "Big Data"? $\endgroup$ – Lehs Jul 29 '15 at 21:10
  • $\begingroup$ A part of the question is discussed in the recent Why does topology rarely come up outside of topology? $\endgroup$ – Laurent Duval Apr 2 '16 at 21:52
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Big Data is a very broad definition. If want to work in data-mining or machine learning my list would start with these

  1. Statistics/Measure theory
  2. Optimisation (in general and especially convex optimisation)
  3. Funcional Analysis
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  • $\begingroup$ Thanks! How would Measure Theory and Functional Analysis help? $\endgroup$ – yoyostein Jul 31 '15 at 8:26
  • $\begingroup$ To some extent, almost all math might be useful, and no one can predict the future path of big data analysis, now extremely chaotic and entering its 'know it all' teenage years. But there is a reason I did not specifically mention these two areas in my Answer. $\endgroup$ – BruceET Jul 31 '15 at 18:23
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I agree with programming/computation, probability/statistics, and linear algebra from Comments. Also, Optimization from Answer. Would add group theory.

Find out what computer languages are currently in greatest use as the time graduation gets near, especially for managing and parsing large datasets; learn the basics of all. Unless the landscape changes fundamentally by then, currency in computer languages will be necessary to get past the first interview. You may not do vast amounts of programming yourself, but you'll need to collaborate every day with people who do.

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Save for basic statistics and probabilities (i.e. on finite sets), let me disappoint you: well-done precalculus should be enough.

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