Test students' understanding of definitions and theorems about uniform convergence of sequences of functions on intervals or metric spaces, including uniform Cauchy criteria, examples and counterexamples, and the consequences for preservation of continuity, term-by-term integration, and differentiation. Ask for short proofs and applications: show when uniform convergence preserves continuity, justify interchange of limit and integral, apply sufficient conditions for differentiating under the limit (e.g., uniform convergence of derivatives plus convergence at a point), and construct sequences that fail these properties without uniformity.