Syllabus
MATH 4810: Computational Modelling, Simulation, and Optimization
This syllabus is the authoritative reference for the course. Read it in full, and return to it whenever a question arises about requirements, deadlines, or policies.
1 Course metadata
| Field | Value |
|---|---|
| Course number | MATH 4810 |
| Course title | Computational Modelling, Simulation, and Optimization |
| Short title | Computational Modelling |
| Subject | Mathematics (MATH) |
| Discipline | Mathematical Modelling and Simulation |
| Institution | TrustOpen |
| Faculty | School of Mathematics |
| Area of study | Science |
| Academic level | Undergraduate |
| Course level | 4000 |
| Credits | 3 |
| Course type | Advanced computational mathematical modelling |
| Delivery mode | Individualized study online · asynchronous |
| Estimated duration | 18 weeks |
| Estimated student workload | 135 hours |
| Recommended weekly workload | 7–9 hours |
| Language of instruction | English |
| Challenge for credit | Not available |
| Course version | 1.0 |
| Status | Proposed |
2 Course description
MATH 4810 develops advanced methods for constructing, implementing, analyzing, and validating computational models.
Students study numerical methods for ordinary and partial differential equations, Monte Carlo simulation, stochastic state-transition models, discrete-event simulation, linear programming, duality, and sensitivity analysis. Models are implemented in spreadsheet software and, optionally, in a scientific programming environment.
Applications are drawn from the physical sciences, social sciences, finance, medicine, operations, and business. The course emphasizes reproducible model architecture, numerical stability, uncertainty analysis, verification, validation, and communication.
Each topic combines conceptual analysis with numerical simulation. Microsoft Excel is used to construct and implement models; students who wish may also use Python, a computer algebra system, discrete-event simulation software, or mathematical optimization software.
The claim the course prepares you to make
By the end of this course you will be able to state, with evidence, that a model you built is fit for a specified purpose within a stated scope — and to state honestly what it is not fit for.
3 Learning outcomes
Upon successful completion of MATH 4810, students will be able to:
Model formulation
- 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.
Numerical and simulation methods
- Analyze sources of truncation, discretization, roundoff, and sampling error.
- Apply Euler, modified Euler, and Runge–Kutta methods to ordinary differential equations.
- Use finite-difference methods for selected partial differential equations.
- Assess consistency, stability, convergence, and step-size sensitivity.
- Design Monte Carlo simulations and validate pseudorandom inputs.
- Construct and analyze Markov-chain models.
- Design elementary discrete-event simulations.
Optimization, validation, and communication
- Formulate linear programming models.
- Explain and apply the fundamental duality theorem.
- Analyze shadow prices, reduced costs, binding constraints, and sensitivity ranges.
- Verify model implementation and validate results.
- Conduct sensitivity, uncertainty, and scenario analyses.
- Compare analytical and numerical solutions.
- Create reproducible computational workflows.
- Communicate simulation assumptions, results, limitations, and recommendations clearly.
4 Prerequisites
Formal prerequisites
The following courses are required:
- MATH 265 — Calculus I
- MATH 266 — Calculus II
- MATH 270 — Linear Algebra I
- MATH 370 — Ordinary Differential Equations
- MATH 376 — Probability and Statistics
Recommended preparation
The following preparation is not required but is strongly recommended. Students who lack it may find the course more demanding.
- Single-variable calculus, including Taylor series
- Linear algebra, including matrix operations and eigenvalues
- Real analysis, including limits and continuity
- Ordinary differential equations, both analytical and numerical
- Probability, including distributions, expectation, and variance
- Spreadsheet modelling, including cell references and formulas
- Basic optimization, including linear programming concepts
Preclusions
There are no preclusions for MATH 4810. The course is not available for challenge credit.
Self-assessment
Before registering, confirm that you are comfortable with the prerequisites. If you are unsure, review a sample of the prerequisite material or contact the course tutor for guidance.
5 Delivery and workload
| Aspect | Detail |
|---|---|
| Mode | Individualized study online |
| Timing | Asynchronous; you set your own pace within the term |
| Scheduled sessions | None; the course is self-paced within the term |
| Estimated duration | 18 weeks |
| Total workload | Approximately 135 hours |
| Weekly workload | 7–9 hours per week |
| Interaction | With the course tutor, by email or LMS messaging |
What the 135 hours includes
- Reading and viewing. Approximately 40 hours across the seven modules.
- Worked examples and exercises. Approximately 30 hours of spreadsheet work and practice.
- Assignments. Approximately 30 hours across the five assignments.
- Capstone. Approximately 35 hours including proposal, report, and presentation.
Pacing advice
Students who keep to a regular weekly schedule — even a modest one — are far more likely to complete the course than students who try to work intensively at the end. The eighteen-week schedule in section 7 is a suggested pacing.
6 Course structure
The course is organized into seven modules. Each module contains two units of three lessons each, together with laboratories and an assignment. The final module prepares students for the capstone.
| Module | Title | Units | Labs | Assessment |
|---|---|---|---|---|
| 01 | Computational Modelling Foundations | 1.1, 1.2 | 1, 2 | Assignment 1 |
| 02 | Numerical Methods for Ordinary Differential Equations | 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 |
7 modules
Thematically organized around the modelling cycle.
14 units
Two per module, each pairing concept and implementation.
42 lessons
Three per unit, following a consistent anatomy.
13 laboratories
Hands-on spreadsheet and code modelling.
7 Study schedule
The following eighteen-week schedule is a suggested pacing. The deadlines for each assignment and for the capstone are listed in the LMS. Adjust the pace to your own circumstances, but keep the deadlines.
| Week | Focus | Deliverable |
|---|---|---|
| 1 | Orientation; Module 1, Unit 1.1 | Readiness checklist |
| 2 | Module 1, Unit 1.2; Module 1 capstone | Assignment 1 |
| 3 | Module 2, Unit 2.1 | — |
| 4 | Module 2, Unit 2.2; Module 2 capstone | Assignment 2 |
| 5 | Module 3, Unit 3.1 | — |
| 6 | Module 3, Unit 3.2; Module 3 capstone | Assignment 3 |
| 7 | Consolidation; review of Modules 1–3 | — |
| 8 | Module 4, Unit 4.1 | — |
| 9 | Module 4, Unit 4.2; Module 4 capstone | Assignment 4 |
| 10 | Module 5, Unit 5.1 | — |
| 11 | Module 5, Unit 5.2; Module 5 capstone | Assignment 5 |
| 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 |
| 15 | Capstone: formulation and implementation | — |
| 16 | Capstone: verification and validation | — |
| 17 | Capstone: analysis, results, draft review | Draft to tutor |
| 18 | Capstone: revisions and submission | Capstone report and presentation |
8 Assessment scheme
The course uses five applied assignments and an integrative simulation capstone. Both the assignment component and the capstone component must each be passed (≥ 50%) for the course to be passed.
Five applied assignments
10 percent each. One per module across Modules 1–5 (with Module 6 as an option).
Simulation capstone
Integrative project assessed against the capstone rubric.
Capstone presentation
An accessible presentation of the model to a mixed audience.
| Assessment | Weight | Covers |
|---|---|---|
| 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, Discrete-Event, or Optimization Model | 10% | Module 5 or 6 |
| Simulation Capstone | 45% | All modules |
| Capstone Presentation | 5% | Communication |
| Total | 100% |
Credit requirements
To pass the course, students 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.
- Meet academic-integrity requirements.
Grading scale
| Grade | Percentage | Description |
|---|---|---|
| A+ | 90–100% | Exceptional |
| A | 85–89% | Excellent |
| A− | 80–84% | Very good |
| B+ | 77–79% | Good |
| B | 73–76% | Satisfactory |
| B− | 70–72% | Satisfactory |
| C+ | 67–69% | Acceptable |
| C | 63–66% | Acceptable |
| C− | 60–62% | Acceptable |
| D | 50–59% | Minimal pass |
| F | 0–49% | Fail |
9 Assignment descriptions
- Assignment 1 Computational model design and audit Full brief →
- Assignment 2 ODE simulation and error analysis Full brief →
- Assignment 3 Deterministic PDE model Full brief →
- Assignment 4 Stochastic simulation experiment Full brief →
- Assignment 5 State-transition, queueing, or optimization model Full brief →
Format
-
Each assignment is submitted as a single ZIP archive named
MATH4810-aN-studentID.zip. - Each archive contains the model file, any data used, the written report, and the documentation required by the brief.
- Reports are typically 4–8 pages unless the brief specifies otherwise.
Deadlines and penalties
- Deadlines are listed in the LMS course schedule.
- Late submissions are subject to a 5 percent penalty per day, to a maximum of 25 percent.
- Extensions must be requested from the course tutor before the deadline.
10 Capstone requirement
The capstone is the largest single component of the course, carrying 45 percent of the grade for the report and 5 percent for the presentation. It is an integrative project in which the student constructs, verifies, validates, analyzes, and communicates a substantial computational model.
The capstone is described in detail on the capstone page. The following is a summary of the requirements.
| Aspect | Requirement |
|---|---|
| Format | Individual project |
| Topic | Student's choice, subject to tutor approval |
| Timeline | Proposal in week 14; draft in week 17; final submission in week 18 |
| Report length | Typically 20–30 pages including figures and appendices |
| Presentation | 10–15 minutes, plus 5 minutes for questions |
| Minimum to pass | 50 percent on the capstone |
Capstone rubric
The full rubric is on the capstone page. Ten criteria with weights summing to 100 percent.
11 Technology requirements
| Tool | Status | Purpose |
|---|---|---|
| Learning management system (LMS) | Required | Access course materials; submit assignments |
| 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 mathematical notation |
| Python notebook environment | Optional | Extend modelling work |
| Computer algebra system | Optional | Symbolic verification |
| Discrete-event simulation software | Optional | Extend Module 5 work |
| Mathematical optimization software | Optional | Extend Module 6 work |
12 Course materials
The course materials are provided online. There is no required textbook. The following are recommended references for students who wish to consult additional sources.
- Numerical methods
- Any standard numerical analysis textbook will cover the material in Modules 2 and 3. Common choices include Burden and Faires, Numerical Analysis, and Heath, Scientific Computing.
- Simulation
- For Module 5, Law, Simulation Modeling and Analysis, is a standard reference. For Monte Carlo, any introductory probability and simulation text will cover the material in Module 4.
- Optimization
- For Module 6, any standard operations research or linear programming textbook will cover the material. Vanderbei, Linear Programming: Foundations and Extensions, is a thorough treatment.
- Modelling and validation
- For Modules 1 and 7, most introductory modelling textbooks cover the lifecycle and verification/validation concepts.
All references cited in the course materials are listed in the course FAQ.
13 Course policies
Attendance and participation
There are no scheduled sessions. Participation is demonstrated through the timely submission of assignments and the capstone. Students are expected to check the LMS regularly for announcements.
Communication
Communication with the course tutor takes place by email or by LMS messaging. Replies usually arrive within two business days. Students should include the course number, their student ID, and a clear subject line in all messages.
Deadlines
Deadlines for each assignment and for the capstone are listed in the LMS. Extensions must be requested from the course tutor in advance. Late submissions are subject to the penalty described in section 9.
Grade appeals
Students who wish to appeal a grade should follow the university's grade-appeal procedure. The course tutor is the first point of contact for informal discussion.
Withdrawal
Students who wish to withdraw from the course must do so through the university's registration system by the withdrawal deadline. Withdrawals are not processed through the course tutor.
Accommodation
Students requiring accommodation for a disability should contact the university's accessibility services. Accommodation requests are confidential and are handled outside the course.
14 Academic integrity
Academic integrity is a condition of every assessment in this course. Students are expected to submit work that is their own, to cite sources properly, and to be honest about what they have and have not done.
Expectations
- Submit your own work unless an assessment explicitly invites collaboration.
- Cite every external source — textbook, paper, website, or code — that informs your work.
- Report the results you actually obtained. Do not fabricate data, cherry-pick results, or adjust parameters until a desired answer emerges.
- Submit model files that actually run.
Prohibited conduct
- 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 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.
15 Responsible use of AI
Generative AI tools are widely available and are not prohibited in this course. However, the course requires that any use is disclosed and that the resulting work is yours in a meaningful sense.
Permitted
- 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, with disclosure.
Not permitted
- Submitting work produced primarily by an AI tool with little or no contribution from you.
- Undisclosed use. All use of AI must be disclosed in the submission.
- Citing sources you have not verified. AI tools sometimes generate plausible but nonexistent references.
- Submitting model files that you cannot explain.
An honest-use test
Before submitting any work, ask: 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.
16 Accessibility
The course is designed to be accessible. The following commitments have been made:
- Semantic HTML and keyboard-accessible navigation.
- Accessible equation notation.
- Accessible spreadsheet templates.
- Text descriptions of all charts and figures.
- Captions and transcripts where audio or video is used.
- High colour contrast; 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, please contact the course tutor or the university's accessibility services. You are entitled to reasonable accommodation, and you should not hesitate to ask.
17 Learner support
Course content
Questions about concepts, methods, or exercises go to the course tutor through the LMS.
Technical support
LMS, spreadsheet, and other technology problems go to the university's IT support services.
Academic skills
Study skills, writing, time management, and exam preparation go to the academic support services.
Accessibility
Accommodation requests go to accessibility services. Confidential.
Personal or financial
Personal, financial, and family concerns go to student services. Support is confidential.
Extensions
Extension requests go to the course tutor before the deadline.
18 Contact information
| Need | Contact |
|---|---|
| Course content questions | Course tutor (via LMS messaging) |
| Assignment and capstone questions | Course tutor (via LMS messaging) |
| Extension requests | Course tutor (before the deadline) |
| Technical support | University IT support services |
| Academic skills support | University academic support services |
| Accessibility accommodation | University accessibility services |
| Withdrawal and registration | University registration services |
| Grade appeals | University appeals office |
Before you begin
Read the orientation and complete the readiness checklist before starting Module 1. If you have questions about the syllabus, contact the course tutor.