Assess students' ability to define pointwise versus uniform convergence, state equivalent criteria (e.g., sup-norm convergence), construct examples and counterexamples, and analyze consequences for continuity, integration, and differentiation — including proving preservation of continuity under uniform convergence, justifying interchange of limit and integral, and stating conditions for term-by-term differentiation (uniform convergence of derivatives or related hypotheses). Tasks may include short proofs, constructions, and computations.