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For my CS degree I have had most of the "standard" mathematical background:

  • Calculus: differential, integral, complex numbers
  • Algebra: pretty much the concepts up until fields.
  • Number Theory: XGCD and related stuff, mostly for crypto.
  • Linear Algebra: up until eigenvectors/eigenvalues
  • Statistics: probabilities, testing
  • Logic: propositional, predicate, modal, hybrid.

My main interests in the CS area are security, cryptography and artificial intelligence. I was wondering if there are any suggestions for mathematical topics that could be interesting for these areas, particularly for AI as it is not my main field of study at the moment.

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  • $\begingroup$ See my answer for a related question on cstheory. Short answer: Learn ALL the math! $\endgroup$ – JeffE Jul 8 '13 at 0:30
  • $\begingroup$ not sure what "linear algebra up until eigenvectors" is but learn as much linear algebra as you can. or rather, what @JeffE said $\endgroup$ – Sasho Nikolov Jul 8 '13 at 4:05
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For the field of A.I. and machine learning, I would recommend you to explore and learn more about these topics:

  • Statistics
  • Probability
  • Stochastic processes
  • Bayesian Data Analysis
  • Convex Optimization
  • Graph Theory

With your math background, you could easily pick any good machine learning book and learn the required math that you don't have as you go. Kevin Murphy's new book, Machine Learning: A Probabilistic Perspective, covers most of these topics and it serves as a good introductory textbook to machine learning.

I personally learned a lot from Dephne Koller's book, Probabilistic Graphical Models. It also covers most of the previously mentioned topics, but, as the book's name suggests, it focuses on graphical models.

Although both of these books have enough math to keep you busy for a while, you might find "The Elements of Statistical Learning", by Hastie et al. more useful if you want to focus more on the mathematical part of the machine learning.

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AI is 99% statistics these days. Learn about probability, and how it intersects with graph theory (bayes nets, etc.).

As for cryptography, if you've got number theory, the only real thing I can think of to extend this is group/field theory. In particular, learn about eliptic curves, but I doubt you'd find a math class that taught that that wasn't specifically a crypto class.

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    $\begingroup$ I've already had elliptic curves fortunately, very interesting subject. More advanced statistics is a good suggestion though. $\endgroup$ – Mythio Jul 6 '13 at 19:30

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