Combinatorial Analysis, Probability, and Applications

The program in Combinatorial Analysis, Probability, and Applications is designed to equip students with the theoretical foundations and methodological tools necessary for the rigorous analysis of complex phenomena, whether deterministic or random. It encompasses a coherent set of techniques from combinatorics (such as arrangements, permutations, combinations, and the inclusion-exclusion principle) as well as core elements of probability theory (probability spaces, conditional probabilities, independence, Bayes’ theorem, random variables, classical distributions, expectation, and variance). These concepts have diverse applications in fields such as games of chance, system reliability, queueing theory, finance, cryptography, and simulation methods. Moreover, they play a central role in artificial intelligence, particularly in uncertainty modeling, machine learning, Bayesian networks, data generation, decision-making under uncertainty, and the statistical evaluation of algorithmic performance