§ Overview

The five assignments are staged across the first six modules of the course. Each is worth 10 percent of the final grade. Together they carry 50 percent, with the remaining 50 percent allocated to the integrative capstone (45%) and its presentation (5%).

Each assignment consolidates one module's skills and prepares you for the capstone by exercising a subset of the fourteen-step modelling lifecycle. The pattern is the same in each: define the question, build the model, produce evidence, report the results. What changes is the class of model and the class of evidence.

A1 Assignment 1 · Model Architecture and Parameterization

Purpose

Assignment 1 consolidates the skills of Module 1: model classification, three-layer spreadsheet architecture, parameter estimation, and the distinction between verification, validation, and reproducibility. It also introduces the assignment format used throughout the course — a model file, a written report, and a reproducibility package — that the later assignments extend.

Task

1. Choose a small system and write a one-paragraph purpose statement. State the decision the model supports.
2. Classify the model along the three axes: observational or explanatory, deterministic or stochastic, static or dynamic. Justify each choice.
3. Write the model specification. System boundary, variables, parameters, units, assumptions, and claim-support scope.
4. Build the three-layer spreadsheet. Inputs, calculations, and outputs in clearly separated regions with a documentation sheet.
5. Estimate one parameter from data or from reasoned assumptions. Report the estimate with an uncertainty.
6. Verify the implementation using at least three tests from Unit 1.2.
7. Validate against at least one held-out observation or known behaviour. State the disconfirming evidence in advance.
8. Assemble the reproducibility package. Model file, data, readme, and documentation.

Suggested scenarios

Deliverables

A2 Assignment 2 · ODE Simulation and Error Analysis

Purpose

Assignment 2 consolidates the numerical ODE methods of Module 2. It asks you to implement a small library of one-step solvers, demonstrate their convergence orders numerically, apply them to a nonlinear model without a closed-form solution, and diagnose a stiff case.

Task

1. Implement four solvers. Euler, modified Euler, midpoint, and fourth-order Runge–Kutta, each as a reusable function of (t, y, f, h).
2. Verify against an analytical solution. Choose a problem with a known closed-form solution. Compare each method's output against the reference at a moderate step size.
3. Conduct a convergence study. Run each method at four step sizes and estimate the observed order from the ratios of successive errors. Produce a log-log plot.
4. Apply to a nonlinear model. Simulate a system with no closed-form solution — a pendulum, a predator–prey system, or an epidemic. Estimate the error by step doubling.
5. Diagnose a stiff case. Construct or choose a stiff initial-value problem. Demonstrate the stability limit of an explicit method and discuss the practical consequences.

Suggested models

Deliverables

A3 Assignment 3 · Deterministic PDE Model

Purpose

Assignment 3 consolidates the finite-difference methods of Module 3. It asks you to construct a grid, implement the FTCS scheme for the heat equation, verify against an analytical solution, demonstrate the CFL stability restriction, and report the results with full documentation.

Task

1. Choose a PDE problem. State the PDE, the domain, the initial condition, and the boundary conditions.
2. Design the grid. Choose Δx, Δt, and the diffusion number r. Compute the stability margin.
3. Implement the FTCS scheme. Three-layer spreadsheet or code. Document the boundary handling explicitly.
4. Verify against the analytical solution for a case where one exists. Compute the error at several times.
5. Conduct a convergence study. Refine the grid at three levels. Confirm the observed order matches the theory.
6. Demonstrate stability. Run at r = 0.4 and r = 0.6. Plot and interpret the difference.
7. Write the report. Include the claim-support statement and the limitations.

Suggested problems

Deliverables

A4 Assignment 4 · Stochastic Simulation Experiment

Purpose

Assignment 4 consolidates Module 4. It asks you to design and run a Monte Carlo experiment, quantify sampling error, and apply a variance-reduction technique. It is the first assignment in which the answer is a distribution rather than a single number, and it emphasises reporting uncertainty alongside the estimate.

Task

1. Choose a quantity of interest and express it as an expectation E[g(X)]. Justify the choice of g.
2. Implement the naive Monte Carlo estimator. Generate samples with a recorded seed. Report the estimate, the standard error, and a 95% confidence interval.
3. Run a convergence study. Compute the standard error at four sample sizes. Produce a log-log plot with slope near −1/2.
4. Diagnose convergence with a running-mean plot.
5. Apply one variance-reduction technique. Antithetic variates, control variates, or importance sampling. Report the variance-reduction factor.
6. Compare the estimates and discuss the tradeoff between the naive and the reduced estimator.

Suggested problems

Deliverables

A5 Assignment 5 · Markov, Discrete-Event, or Optimization Model

Purpose

Assignment 5 offers a choice between two modelling families. You may build either:

• Track A — Markov or discrete-event model (Module 5). A state-transition model or a queueing simulation, with full output analysis.
• Track B — Linear program with duality and sensitivity (Module 6). An optimization model with dual analysis and a sensitivity report.

The choice is yours. Neither track is easier or harder; they exercise different skills. Choose the track that best fits your interests and your capstone direction.

Track A — Markov or discrete-event model

Choose one of the following sub-tasks:

• Markov chain. Specify a Markov chain with 3–4 states, compute the stationary distribution, simulate the chain, and compare the empirical frequencies against the theoretical distribution.
• Discrete-event simulation. Build a discrete-event queueing simulation with an event calendar. Apply warm-up removal, run independent replications, and report performance measures with confidence intervals.

Track B — Linear program with duality and sensitivity

Formulate and solve a linear program of moderate size. Construct its dual, verify strong duality, interpret the shadow prices in decision-relevant terms, and produce a sensitivity report with ranges and at least one scenario analysis that exceeds the sensitivity range.

Deliverables

Track A

Track B

§ Common format requirements

The following requirements apply to every assignment. Failure to meet them may cost marks even when the model itself is correct.

§ Deadlines and penalties

Deadlines are confirmed in the LMS. Students should treat the suggested weeks as a planning aid and confirm the exact dates in the course schedule.

§ Integrity and AI disclosure

Every assignment is subject to the course's academic-integrity and responsible-AI-use policies. The two most important requirements for assignments are:

• The work you submit must be your own in a meaningful sense. If you cannot explain the model, reproduce the results, or justify the choices, the work is not yours.
• Any use of AI must be disclosed. Include a short appendix in every assignment stating whether an AI tool was used, which tool, and what it was used for.

The following are permitted with disclosure:

• Asking an AI tool to explain a concept or provide an example.
• Using an AI tool to check grammar or suggest rephrasing.
• Using an AI tool to help debug code you have written.

The following are not permitted:

• Submitting work produced primarily by an AI tool.
• Citing sources you have not verified.
• Submitting model files you cannot explain.
• Undisclosed use of AI.

§ Common pitfalls across all assignments