Probability theory has long provided a rigorous framework for quantifying uncertainty, yet its extension to infinite sets introduces profound conceptual challenges and opportunities. Contemporary ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, Chernoff bounds and large deviations, martingales, ...