MATH 4810 Computational Modelling

Module 01 · Foundations

Computational Modelling Foundations

Before any numerical method, you need a defensible model. This module establishes the vocabulary of modelling, the computational modelling lifecycle, and the spreadsheet architecture that the rest of the course builds on.

2 units · 6 lessons 2 laboratories Assignment 1 · 10% ≈ 18 hours

Module 01

Computational Modelling Foundations

Establish the modelling vocabulary, the lifecycle, and the transparent spreadsheet architecture used throughout MATH 4810.

§ Overview

This module separates modelling from computation. You will learn to classify models, translate a real-world system into a specification, and build a spreadsheet architecture that makes every input, calculation, and output visible. Parameter estimation, calibration, verification, validation, and reproducibility round out the foundation.

Unit 1.1

Model types and computational workflows.

Unit 1.2

Model architecture and parameterization.

Laboratories 1–2

Spreadsheet architecture and parameter estimation.

Assignment 1

Computational model design and audit.

§ Learning outcomes

By the end of Module 1 you will be able to

  • Distinguish observational, explanatory, deterministic, stochastic, static, and dynamic models.
  • Translate a real-world system into a computational model specification.
  • Design transparent spreadsheet or code-based model architectures.
  • Estimate and document model parameters, including their uncertainty.
  • Explain the difference between verification, validation, and reproducibility.

1.1 Model Types and Computational Workflows

What kind of model are you building, and what can it legitimately be used to claim? This unit sets the classification scheme that every later module depends on.

Lesson 1

Observational and explanatory models

Describe versus explain: what each model type can and cannot support.

 Lesson 2

Deterministic and stochastic models

When randomness is structural, when it is nuisance, and how that choice propagates.

 Lesson 3

The computational modelling lifecycle

From purpose and boundary to archived, reproducible model files.

1.2 Model Architecture and Parameterization

A model that cannot be inspected cannot be trusted. This unit covers the layout conventions that keep spreadsheet models auditable, and the discipline of estimating parameters without overfitting.

Lesson 1

Inputs, calculations, outputs, and documentation

Lay out a model so its logic is visible, testable, and safe to modify.

 Lesson 2

Parameter estimation and calibration

Fit parameters to data, record uncertainty, and avoid overfitting.

 Lesson 3

Verification, validation, and reproducibility

Separate the two activities and leave a trail another analyst could rerun.

§ Laboratories

Lab 1

Spreadsheet model architecture

Build a documented, three-layer spreadsheet model with separated inputs, calculations, and outputs.

Lab 2

Parameter estimation

Estimate parameters from data, report uncertainty, and check sensitivity to the estimate.

§ Assignment 1

Computational model design and audit · 10%

Specify a model for a system of your choice, document its purpose, boundary, variables, parameters, and assumptions, and audit an existing spreadsheet model for transparency and correctness.

Full assignment brief →

§ Common pitfalls

Watch for these

  • Verification and validation are different activities. Verification asks whether the implementation matches the specification; validation asks whether the model represents the real system well enough for its purpose.
  • Spreadsheet transparency does not guarantee formula correctness. A visible formula can still reference the wrong cell, use the wrong units, or copy incorrectly down a column.
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