[Assess students' understanding of pointwise versus uniform convergence for sequences of functions on real intervals, including tests (e.g., Weierstrass M-test, uniform Cauchy), construction of counterexamples, and the precise consequences for preservation or failure of continuity, termwise integration (Riemann/Lebesgue), and termwise differentiation. Problems will require proofs, verification of hypotheses for standard theorems, and analysis of examples where interchange of limit with integral or derivative is invalid.]