# Which math fields should I learn further for a specific approach to AIs?

I finished learning “How to Prove It: A Structured Approach, 2nd Edition” by Daniel J. Velleman a while ago.

It taught me propositional logic and first order logic for proof techniques. I was taught how to solve basic math problems. However, I didn't feel that I learned enough formal logic.

I'm learning an approach to AI based on language/semiotics and turing ordinals, and I have a feeling that formal logic might be important, but I'm not sure.

If there is particularly not a useful math field for that approach, I plan to learn linear algebra, calculus, probability, and statistics in order because those fields are necessary for computer science, machine learning, and many other disciplines. I'm not sure about discrete mathematics, yet.

• They all help, but combinatorial optimisation probably the most. – Alec Teal Oct 9 '15 at 11:14

I don't claim to be an expert on the subject of AI, but this is my experience so far with Computer Science:

Discrete math is absolutely crucial. The reason it is crucial is that in calculus, our "bread and butter" and main definition is the definition of a limit. However, in a computer we can't define limit. We can't define infinity.

In calculus, we know that for any $\epsilon >0 , a$ there is some number $b$ such that $b=a+\epsilon$. In a computer however this is simply not true. The numbers have "holes" between them, a computer is strictly a discrete machine, not continuous. This leads to many problems and interesting discussions that we are addressing in Discrete Math.

Linear Algebra, Probability and Formal Languages and Proposition Logic are also extremely important as you stated.

Regarding the less important subjects:

1) Differential Equations. A very important subject on its own, not widely used in the sense of AI and robotics to my information. It is more used to solve problems in physics.

2) Complex Analysis. Again, very important by its own right, not very relevant to AI and computer science.

3) Measure Theory and Topology, again, not relevant.

To sum up, if I were you, I'd focus more on subjects that are purely computer science subjects. Such as Formal Logic, Automata, Graph theory, Combinatorics, Study of algorithms and their runtime analysis.

• I learned an informal subset of formal mathematical logic in “How to Prove It: A Structured Approach, 2nd Edition” by Daniel J. Velleman. Do I need to learn formal mathematical logic properly? – crocket Oct 9 '15 at 11:34