Assess students' ability to analyze local and global convergence properties of Newton and quasi-Newton methods for nonlinear systems: derive local convergence rates (quadratic, superlinear) and required regularity conditions (Jacobian nonsingularity, Lipschitz continuity, Kantorovich-type hypotheses); evaluate globalization strategies (line search, trust-region, merit functions) and their conditions for global convergence; compare BFGS/SR1 update behavior and the Dennis–Moré condition for superlinear convergence of quasi-Newton methods; and apply these criteria to diagnose convergence or failure on given example systems and algorithm variants.