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What mathematics can be interesting for these CS areas?
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Problem
For my CS degree I have had most of the "standard" mathematical background:
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.
- 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.
Solution
For the field of A.I. and machine learning, I would recommend you to explore and learn more about these topics:
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.
- 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.
Context
StackExchange Computer Science Q#13114, answer score: 10
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