Assess students' ability to compare Newton's method, the secant method, and quasi-Newton methods for solving nonlinear systems, focusing on convergence order and rates, local/global convergence and stability, Jacobian and inverse approximations, computational cost per iteration and overall efficiency (function/Jacobian/evaluation counts), sensitivity to initial guesses and ill-conditioning, and practical trade-offs in implementation such as line search, damping, and common update formulas (BFGS, DFP). Include tasks that require theoretical justification of convergence behavior, complexity estimates, and interpretation of numerical experiment results across representative test problems.