Student Seeks Foundational Abstractions Linking Analysis And Probability

A prospective MSc student starting a Mathematics & Data Science program (real analysis, probability, PDEs, measure theory, functional analysis, machine learning) asks which core abstractions—limits, convergence, operators, and measure-theoretic probability—recurringly connect physics, PDEs, and numerical methods. They request a small set of foundational ideas that clarify stability, modeling, and the mathematical structure behind computational approaches.