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I'm studying math (just started) and I like programming as well (just started this too), is there a career or a branch of research including deep aspect of this two aspects? Is there someone among you who is doing this perhaps?

The sensation I have is that there's much more "application" (improving skills in coding) than "pure research" (and when there is it's often about computability and limit of computability). I'm sure I'm wrong about this but that's quite all i can see now.

Can you suggest me a book that can introduce me to the mathematical aspects of artificial intelligence? I would prefer text with examples and exercises.

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I do text mining and machine learning. It has a great deal of all of the three things you mentioned –  mathguy Aug 17 '12 at 11:32

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Artificial Intelligence is a broad field. To get to the mathematical foundation of the field you will have to dive deeper than most introductory books will go - so for the sake of simplicity I will assume that you are not interested in aspects like general decision making, planing and pathfinding (all of which will be covered in basic AI books - but without much mathematical background).

If you want to combine the both fields Math and AI, you best bet is (in my opinion) with Genetic Algorithms or Neural Networks. I can only name two books that might be to your liking - hopefully someone else will add more.

An Introduction to Genetic Algorithms by Melanie Mitchell is certainly basic enough for you to read right away. As an introductory book it will not go into too much detail with calculations (or even omit them, including the results, alltogether), but the books skims a lot of interesting topics that might give you a feel of what can be done with proper mathematics in the field of Genetic Algorithms. Also it mentions some aspects like evolutionary activity that I have yet to see in another book. It contains a lot of exercises, half of which are thought exercises and half of which are programming exercises though, so not too much math there...

Spiking Neuron Models by Wulfram Gerstner and Werner Kistler on the other hand is a rather advanced book ("for advanced undergraduate or graduate students"). It covers the modeling of networks of neurons which communicate by a series of spikes instead of a scalar intensity as it is done in most practical AI uses. As such it is much closer to the real world counterpart of actual braincells and indeed starts with the Hodgkin-Huxley model of the neuron, that has been derived from the behaviour of the neurons of a squid. There is plenty of math in this book, hence the difficulty to study it though. It is an very interesting introduction to somewhat recent developments in the field - but you need at least basic knowledge in differential equation theory and should be comfortable with more advanced mathematical notations / concepts (partial differentiation, dirac-delta, big-O-notation etc.).

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