Develop convexity, conjugate duality, proximal and splitting algorithms, and risk-aware models through proofs and a real CUMCM crop-planning case.

Construct Pareto frontiers, expose stakeholder trade-offs, and derive decisions that remain feasible under uncertain inputs.

Understand GA, differential evolution, PSO, and simulated annealing through representation, constraints, convergence evidence, and a real CUMCM case.

Solve and diagnose an original synthetic pose-graph estimation case.

Build differential-equation models from changing states, derive their governing laws, and test them against physical and population examples.

Model interacting populations and compartments, analyze equilibria and stability, and connect coupled dynamics to real competition decisions.

Work with boundary conditions, distributed systems, stiffness, and sensitivity.

Build complete original cases from a physical mechanism to tested decisions.

Audit the time index, isolate patterns, and forecast without information leakage.

Compare smoothing, ARIMA, volatility, and multivariate models over honest rolling origins.