Mathematical Foundation of Artificial Intelligence Algorithms 4010-PAI-30

During the course, students will become familiar with the following topics:
Linear algebra, in particular: definitions of algebra, vectors, matrices and special types of matrices, representing a system of linear equations as a matrix problem and methods of solving it, techniques of diagonalization and matrix inversion, as well as the definition of the eigenvalue problem.
Calculus, in particular: the definition of isomorphism, definitions of the derivative and integral and their properties, the gradient, Jacobian and Hessian matrices, partial derivatives, and critical points of single- and multivariable functions.
Analytical geometry and gradients, in particular: vector spaces, bases of vectors, orthogonality and normality of bases, vector projections, function spaces, as well as scalar and vector products.
Probability and its distributions, in particular: definitions of probability spaces, events, random variables, major probability distributions, density functions and distribution functions, basic concepts of descriptive statistics, independence of random variables, and key theorems of statistics.
Fundamentals of statistics, in particular: construction and analysis of plots, estimators, confidence intervals, hypothesis testing, Monte Carlo simulations, and Bayesian methods.
The classes will consist of a lecture part and computational exercises.