Assess graduate students' ability to evaluate and compare Tikhonov, total variation (TV), and sparsity‑promoting regularization for linear and nonlinear ill‑posed inverse problems in Hilbert spaces. Topics tested: theoretical foundations (existence, stability, source conditions, convergence rates), parameter choice methods (discrepancy principle, L‑curve, cross‑validation), algorithmic implementations (proximal methods, ADMM, iterative regularization), discretization effects, and practical trade‑offs (edge preservation vs. smoothing, bias, computational cost). Require derivations, convergence proofs for representative models, and reasoned choices for given problem scenarios and noise regimes.