by Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman serves as a critical bridge between standard undergraduate mathematical economics and the advanced, abstract mathematics required for modern research. It provides the rigorous real and functional analysis foundations needed to understand high-level texts like Stokey and Lucas's Recursive Methods in Economic Dynamics Core Objectives and Approach
This piece is not a substitute for a full-year real analysis course for math majors. We do not prove the Heine–Borel theorem for its own sake, nor do we obsess over pathological counterexamples that never appear in economics. by Dean Corbae, Maxwell B
We assume you have taken intermediate calculus and basic probability. You may not have written a proof before. That is fine. The first chapter gently introduces logical notation, quantifiers ((\forall, \exists)), and proof techniques (direct, contrapositive, induction). You will learn to read and write a simple epsilon argument—not to become a pure mathematician, but to understand why, for example, a utility function can be approximated by a sequence of polynomials (Stone–Weierstrass) or why OLS coefficients converge in probability (Slutsky’s theorem requires pointwise convergence of random functions). We do not prove the Heine–Borel theorem for