Orientation
Before you begin
This page introduces the course and prepares you for the work ahead. Read it in full before starting Module 1.
- Orientation
- Readiness check
- Module 1
1 Welcome
Welcome to MATH 4810. This course teaches you to build, implement, test, and defend computational models of real systems. It is not a course about programming, and it is not a course about pure mathematics. It is a course about the discipline that connects the two — the discipline that turns a real-world question into a model, a model into numbers, and numbers into a decision.
By the end of the course you will have built models using ODE solvers, finite-difference PDE schemes, Monte Carlo simulation, Markov chains, discrete-event simulation, and linear programming. More importantly, you will know how to verify, validate, and communicate what you have built, and to state honestly what your model can and cannot be used to claim.
The course is designed for students who want to work at the boundary between theory and application: applied mathematicians, computing scientists, data scientists, engineers, and analysts in finance and operations research. If you are comfortable with calculus, linear algebra, and probability, and you are willing to work through problems carefully, you will do well.
The value of the course
Computational modelling is a skill that is valuable in many fields and that is genuinely difficult. The ability to build a model that someone else can trust — and to know what it says and what it does not — is rare and in demand. This course exists to help you develop it.
2 What this course is about
MATH 4810 develops advanced methods for constructing, implementing, analyzing, and validating computational models. The course sits at the intersection of numerical analysis, simulation, and optimization, and it treats the modelling process itself as a subject of study.
You will learn:
- How to formulate a model. How to choose between observational and explanatory models, deterministic and stochastic models, static and dynamic models. How to state the system boundary, the variables, the parameters, and the assumptions. How to write a claim-support statement.
- How to implement a model. The three-layer architecture that separates inputs, calculations, and outputs. The event calendar and clock-advancement mechanism of discrete-event simulation. The spreadsheet layout and solver configuration for linear programs.
- How to analyze a model. Convergence studies, error analysis, stability restrictions, sensitivity analysis, and uncertainty propagation.
- How to verify and validate a model. Analytical comparisons, limiting cases, conservation checks, held-out validation, and disconfirming evidence.
- How to communicate a model. Technical reports for the analyst and plain-language summaries for the decision-maker.
What this course is not
MATH 4810 is not a programming course. You will build models, but primarily in a spreadsheet. If you already program, you can use Python or another language to extend your work, but the course does not require it. The course is also not a survey of every numerical method; it develops a disciplined set of methods in depth.
3 How the course is organized
The course is organized into seven modules. Each module contains two units, and each unit contains three lessons. Some modules include one or two laboratories and an assignment. The final module prepares you for the integrative capstone.
| Module | Title | Units | Labs | Assignment |
|---|---|---|---|---|
| 01 | Computational Modelling Foundations | 1.1, 1.2 | 1, 2 | Assignment 1 |
| 02 | Numerical Methods for ODEs | 2.1, 2.2 | 3, 4 | Assignment 2 |
| 03 | Numerical PDE Models | 3.1, 3.2 | 5, 6 | Assignment 3 |
| 04 | Monte Carlo and Stochastic Simulation | 4.1, 4.2 | 7, 8 | Assignment 4 |
| 05 | Markov and Discrete-Event Models | 5.1, 5.2 | 9, 10 | Assignment 5 |
| 06 | Optimization, Duality, and Sensitivity | 6.1, 6.2 | 11, 12 | Assignment 5 option |
| 07 | Verification, Validation, and Decision Support | 7.1, 7.2 | 13 | Capstone preparation |
The lesson structure
Every lesson follows the same twelve-part structure so that theory, implementation, and judgement stay connected:
- Modelling context
Why this method exists and where it is used.
- Learning objectives
What you should be able to do afterwards.
- Prerequisite review
The mathematics you need before starting.
- Mathematical formulation
The model or method stated precisely.
- Worked example
A complete, runnable example.
- Verification check
How to confirm the implementation is correct.
- Interpretation
What the output means in context.
- Uncertainty and limitations
Where the result could break down.
- Common implementation errors
Mistakes to watch for.
- Independent modelling task
Your turn to build and test.
- Reflection prompt
Consolidate what changed in your thinking.
- Lesson summary
The key takeaways in brief.
Every lesson is followed by an assessment block: a five-question self-quiz with revealed answers, four practice exercises, three homework problems, and one mini project. Complete these in order. The self-quiz tells you whether you have understood the lesson; the practice exercises consolidate the skills; the homework problems and mini project are the basis of the module assignment.
The module capstones
Each module ends with a small capstone project that consolidates that module's skills. The module capstones prepare you for the course's final integrative capstone, which draws on all seven modules and carries the largest single weight in the course.
4 The modelling cycle
The course is organized around a single recurring process: the fourteen-step computational modelling lifecycle. It appears in every module, and it is the structure you are expected to follow in every assignment and in the capstone.
- Define the question and model purpose What decision or understanding must the model support?
- Establish the system boundary What is inside the model, and what is treated as external?
- Define variables, parameters, units, and assumptions Make every quantity explicit and dimensionally consistent.
- Select the modelling approach Deterministic or stochastic, static or dynamic, analytical or numerical.
- Choose a numerical or simulation method Match the method to the problem's structure and the required accuracy.
- Implement the model Follow the three-layer architecture.
- Verify formulas, code, and model logic Confirm the implementation matches the specification.
- Test numerical stability and convergence Vary step size, grid, and replication count deliberately.
- Validate the model against evidence Compare with data, analytical solutions, and limiting cases.
- Conduct uncertainty and sensitivity analysis Identify which inputs drive the outputs.
- Compare scenarios Run designed experiments rather than one-off trials.
- Interpret limitations State what the model cannot tell you.
- Communicate findings Write for both technical and non-technical readers.
- Archive reproducible model files Leave a trail another analyst could rerun.
5 How to study
The course is designed for individualized, asynchronous study. There are no scheduled lectures or tutorials. You set your own pace within the term, and you work through the material on your own, with support from the course tutor and the learner support services.
Based on what works for students in this course, the following practices are recommended:
Read the lesson first
Read the entire lesson before attempting the exercises. The exercises assume you have read the worked example and the interpretation section.
Build the model yourself
When a lesson includes a worked example, rebuild it in your own spreadsheet. Reading someone else's spreadsheet is not the same as building one.
Take the self-quiz before the practice
The self-quiz tells you whether you understood the lesson. If you miss more than one question, re-read the relevant section before proceeding.
Do the homework problems
The homework problems are not optional. They are the basis of the module assignment. Attempt each before comparing against any solution.
Keep a modelling journal
Record your decisions, the alternatives you considered, and why you chose as you did. The journal will help you write the capstone.
Review before each assignment
Before starting an assignment, re-read the module's learning outcomes and the relevant lifecycle steps.
A note on struggle
Modelling is genuinely difficult. If you find yourself stuck, that is normal, and it is not a sign that you are in the wrong course. Take a break, re-read the relevant section, and try again. If you remain stuck, contact the course tutor. Do not spend more than an hour on a single problem without asking for help.
6 Workload and pacing
MATH 4810 is a three-credit course. The total expected workload is approximately 135 hours over 18 weeks, which works out to about 7 to 9 hours per week. The table below shows a suggested pacing.
| Weeks | Focus | Milestone |
|---|---|---|
| 1 | Orientation; Module 1, Unit 1.1 | Readiness checklist submitted |
| 2 | Module 1, Unit 1.2; Module 1 capstone | Assignment 1 drafted |
| 3 | Module 2, Unit 2.1 | — |
| 4 | Module 2, Unit 2.2; Module 2 capstone | Assignment 2 drafted |
| 5 | Module 3, Unit 3.1 | — |
| 6 | Module 3, Unit 3.2; Module 3 capstone | Assignment 3 drafted |
| 7 | Consolidation week; review Modules 1–3 | — |
| 8 | Module 4, Unit 4.1 | — |
| 9 | Module 4, Unit 4.2; Module 4 capstone | Assignment 4 drafted |
| 10 | Module 5, Unit 5.1 | — |
| 11 | Module 5, Unit 5.2; Module 5 capstone | Assignment 5 drafted |
| 12 | Module 6, Unit 6.1 | — |
| 13 | Module 6, Unit 6.2; Module 6 capstone | — |
| 14 | Module 7, Units 7.1 and 7.2; Module 7 capstone | Capstone proposal submitted |
| 15–17 | Capstone work | Draft reviewed by tutor |
| 18 | Final revisions; submission | Capstone submitted |
The pace is a guide
The schedule above is a suggestion. You may work faster or slower, as long as you complete the required assessments by their deadlines. The important thing is to keep moving and to avoid leaving large gaps.
7 Technology setup
You will need a small set of tools to complete the course. Set them up before you begin Module 1.
| Tool | Status | Purpose |
|---|---|---|
| Modern web browser | Required | Access the course content and the LMS |
| Microsoft Excel 2010 or later (or an approved equivalent) | Required | Spreadsheet modelling, numerical methods, LP solver |
| Solver add-in (Excel) or equivalent | Required for Module 6 | Solve linear programs |
| Scientific calculator | Required | Quick numerical checks |
| Accessible equation rendering | Required | Read the mathematical notation in the course |
| Python notebook environment | Optional | Extend modelling work; not required |
| Computer algebra system | Optional | Symbolic verification; not required |
| Discrete-event simulation software | Optional | Extend Module 5 work; not required |
| Mathematical optimization software | Optional | Extend Module 6 work; not required |
Setting up the Excel solver
If you use Excel, you will need the Solver add-in for Module 6. Enable it via File → Options → Add-ins, then select Solver Add-in from the list and click Go…. If your environment does not include the Solver, contact the course tutor for an approved alternative.
Optional: Python environment
You may extend your modelling work with Python. The course does
not require it, and no assessment depends on it, but students who
already program sometimes find it helpful for the numerical
methods and simulation modules. A minimal setup uses Python 3.10+
with numpy, scipy, and
matplotlib.
Test your setup before Module 1
Open a blank spreadsheet, enter a formula, and confirm it evaluates. Open the solver and confirm it launches. If either step fails, resolve the issue before beginning the course.
8 Assessment at a glance
The course uses five applied assignments and an integrative simulation capstone. The table below summarises the weights.
| Component | Weight | What it assesses |
|---|---|---|
| Assignment 1: Model architecture and parameterization | 10% | Module 1 |
| Assignment 2: ODE numerical simulation | 10% | Module 2 |
| Assignment 3: PDE finite-difference model | 10% | Module 3 |
| Assignment 4: Monte Carlo simulation | 10% | Module 4 |
| Assignment 5: Markov, DES, or optimization | 10% | Module 5 or 6 |
| Simulation capstone | 45% | All modules |
| Capstone presentation | 5% | Communication |
| Total | 100% |
Credit requirements
You must achieve at least 50 percent overall, submit all five assignments, achieve at least 50 percent on the simulation capstone, submit functioning model files, submit the capstone presentation, and meet academic-integrity requirements.
Full details of each assignment are available on the course assignments page. The capstone has its own page with the full brief and rubric.
9 Academic integrity
Academic integrity is a condition of every assessment in this course. You are expected to submit work that is your own, to cite sources properly, and to be honest about what you have and have not done.
What is expected
- Your own work. Unless an assessment explicitly invites collaboration, submit work that you have produced yourself.
- Proper citation. Any external source — a textbook, a paper, a website, a piece of code — must be cited.
- Honest reporting. Report the results you actually obtained. Do not fabricate data, cherry-pick results, or adjust parameters until a desired answer emerges.
- Model files that work. When an assignment requires a functioning model file, submit one that actually runs.
What is not permitted
- Copying work from another student.
- Submitting work obtained from a commercial service.
- Presenting another person's model as your own.
- Falsifying results or misrepresenting what you did.
Consequences
Violations of academic integrity are taken seriously and are addressed under the university's academic misconduct policy. Penalties range from a failing grade on the assessment to a failing grade in the course, depending on the severity and the circumstances.
10 Responsible use of AI
Generative AI tools are widely available, and this course does not prohibit their use. However, the course does require that any use of AI is disclosed and that the resulting work is your own in a meaningful sense. The purpose of the course is for you to learn to build models, and AI tools can help or hinder that learning, depending on how they are used.
Permitted use
- Learning support. Asking an AI tool to explain a concept, provide an example, or suggest a study strategy is permitted.
- Editing. Using an AI tool to check grammar, suggest rephrasing, or improve the clarity of your writing is permitted, provided the content remains yours.
- Code assistance. If you extend your work with Python or another language, using an AI tool to help debug or suggest implementations is permitted.
Not permitted
- Generating entire submissions. Submitting work that was produced primarily by an AI tool, with little or no contribution from you, is not permitted.
- Undisclosed use. Any use of AI must be disclosed in the submission. An appendix or a short note stating what tool was used and how is sufficient.
- AI-generated citations. Do not cite sources that you have not verified. AI tools sometimes generate plausible but nonexistent references.
- AI-generated model files that you do not understand. If a model file is submitted, you must be able to explain every part of it. A model you cannot explain is not your model.
An honest-use test
Before submitting any work, ask yourself: could I reproduce this work without the AI tool, and could I explain it to a classmate? If the answer to either question is no, the work is not yours in the sense the course requires.
11 Accessibility
The course is designed to be accessible and is committed to removing barriers to your learning. The following design commitments have been made:
- Semantic HTML and keyboard-accessible navigation.
- Accessible equation notation throughout the course pages.
- Accessible spreadsheet templates.
- Text descriptions of all simulation charts and figures.
- Captions and transcripts where audio or video is used.
- High colour contrast and no reliance on colour alone.
- Static alternatives to interactive dashboards.
- Screen-reader-compatible assessments.
- Downloadable model files.
- Plain-language descriptions of algorithms.
- Explicit input and output labels on every model.
- Reproducible software instructions.
- Mobile-responsive content pages.
If you encounter a barrier to your learning — an inaccessible document, a technical problem, a formatting issue — please contact the course tutor or the university's accessibility services. You are entitled to reasonable accommodation, and you should not hesitate to ask.
12 Where to get help
Support is available at several levels. Use the source that fits your question.
Course content
If you have a question about a concept, a method, or a specific exercise, contact the course tutor through the LMS. The tutor can also review drafts of your assignments and capstone work.
Technical support
For problems with the LMS, the spreadsheet software, or other technology, contact the university's IT support services.
Academic skills
For help with study skills, writing, time management, or exam preparation, contact the university's academic support services.
Accessibility
For accommodation requests or accessibility concerns, contact the university's accessibility services. Requests are confidential.
Personal or financial concerns
If personal, financial, or family circumstances are affecting your studies, contact student services. Support is available and confidential.
Assignment extensions
If you need an extension, contact the course tutor before the deadline. Extensions are considered on a case-by-case basis and are usually granted when requested in advance.
Do not wait
If something is not working, or if you are stuck, contact the appropriate source early. The longer you wait, the harder it is to resolve.
13 Readiness checklist
Before you begin Module 1, confirm that you have completed the following steps. If any step is not complete, complete it before proceeding.
Readiness checklist
- I have read the course overview and understand what the course covers.
- I have read the syllabus and understand the assessment scheme.
- I have read this orientation in full.
- I have confirmed that I have access to the required technology: a web browser, Microsoft Excel (or an equivalent), and the Solver add-in for Module 6.
- I have tested my spreadsheet and confirmed that formulas evaluate and the solver launches.
- I have located the course tutor's contact information in the LMS.
- I have read and understood the academic-integrity and responsible-AI-use sections of this orientation.
- I have reviewed the eighteen-week pacing suggestion and confirmed that I can commit the required time.
- I know where to go for help if I need it.
When all nine steps are complete, you are ready to begin Module 1.
Ready to start?
Begin with Module 1: Computational Modelling Foundations.