PhD Courses in Denmark

This course provides a rigorous but accessible foundation in the mathematical and probabilistic tools used throughout PhD-level quantitative coursework. It is designed for PhD students in economics, econometrics, finance, business intelligence, operations research, and related quantitative fields, and it prepares students for later technical courses without duplicating the advanced theory covered there.

The course deliberately prioritizes depth, pacing, and reusable reasoning patterns over breadth. The central themes are mathematical language and proof habits; deterministic limits and convergence; approximation of functions; projection and least-squares geometry; compactness, existence, and basic optimization; probability and conditional expectation; and stochastic convergence. 

The course also introduces deterministic ideas that prepare students for more advanced econometric theory. In particular, students study pointwise and uniform convergence of functions, the supremum norm, equicontinuity, compactness, and the Weierstrass theorem. These topics provide useful intuition for later courses where uniform laws of large numbers, stochastic equicontinuity, and extremum-estimator arguments are developed formally.