What are the mathematical prerequisites to be able to study general artificial intelligence (AI) or strong AI?
Let's start with the basics:
- Calculus (Derivatives, Integrals, and Series - get comfortable with summation and product notations). Multi-variable Calculus (Gradients, Directional Derivatives, Vectors)
http://tutorial.math.lamar.edu/ (go to content in top left corner - work your way through Calculus 1, 2, 3.
Linear Algebra (this is a big one , co-variance matrices, matrix algebra, matrix inverses, Ax=b (linear systems of equations), eigenvalues, eigenvectors, etc. ) - http://cs229.stanford.edu/section/cs229-linalg.pdf
Probability Theory and Statistics (distributions like Beta,Bernoulli, Dirichlet, Gaussian, Multivariate Gaussian (seriously know your linear algebra), Poisson, know expectations, know moments, know sufficient statistics, know exponential families, likelihood vs probability, pmf vs pdf, random variables, stochastic processes - Markov Chains especially and again know your linear algebra).
A little bit about information theory (KL divergence).
Discrete Mathematics (know combinatorics, and get familiar with set theory and at least the common notations of math symbols - generally speaking, when reading something pertaining to AI I personally find that most of the battle is trying to understand what the notations or symbols are saying)
Then if you seriously want to get into the fundamentals, I suggest taking a class in Probabilistic Graphical Models. There is an excellent course on Coursera with Professor Daphne Koller (there 3 courses take all three).
https://www.coursera.org/learn/probabilistic-graphical-models-3-learning/home/welcome <- this is one of the courses
Most of the answers are oriented towards statistical/probabilistic models. For more 'classic' AI I would say you would need some knowledge of predicate calculus. This is the more symbolic planning approach to AI problem solving.
You could argue it's a bit 'old school', but still relevant for certain aspects of AI.
I always recommend starting with game theory, combinatorial game theory, and algorithmic combinatorial game theory, (but I'm potentially biased;)
Combinatorics is a given--discrete mathematics is heavily utilized in computer science, and, with the advent of Combinatorial Game Theory (CGT), ability to determine if a given choice can be deemed optimal ("perfect play"). CGT arises out of traditional Game Theory, which we sometimes term "economic game theory" to make the distinction. Out of Game Theory also arises subfields such as Evolutionary Game Theory, which is important in AI.
These fields relate to rationality, which is the basis for optimized decision making. Decision making algorithms seems to be the fundamental distinction of what constitutes an Artificial Intelligence.
All problems, from a fundamental standpoint, can be regarded either as puzzles--non-competitive context--or games--competitive context. This distinction is based on whether there is a single agent (puzzles) or multiple agents (games.)