01
Formulate before calculating
A useful model begins with a focused question, a system boundary, quantities, and units.
Teaching mathematical modeling
Make every modelling decision visible.
I teach mathematics as a way to frame uncertain questions, build defensible models, test computational evidence, and communicate conclusions with honest limits.
New bilingual teaching library
Twenty-seven units, three ways to learn.
Read Traditional Chinese Notes, English Notes, and English slides unit by unit—or download the complete collections and student datasets.
Teaching principles
Rigour that students can inspect.
Open-ended work becomes teachable when the invisible choices are turned into artefacts that can be discussed, checked, and improved.
02
Build a baseline first
Simple reference models make later complexity explainable and give every improvement something to beat.
03
Treat validation as mathematics
Limiting cases, sensitivity, alternative baselines, and numerical checks belong inside the solution.
04
Write claims from evidence
Students separate numerical output, interpretation, limitations, and the next evidence a decision would require.
Curriculum in use
A complete modeling sequence, not a collection of isolated activities.
The lecture archive connects mathematical foundations, empirical models, simulation, optimization, decisions under uncertainty, differential equations, dimensional analysis, and technical writing.
- 12
- main lectures
- 10
- foundation supplements
- 5
- writing classes
- 189
- worked examples
- 82
- exercise sets
- 8
- teaching datasets
Curriculum architecture
From first model to independent research.
The sequence increases mathematical and computational independence while keeping question quality, validation, and communication visible at every level.
- 01
Instructor
Mathematical Modeling Lecture Library
A bilingual 27-unit library connecting mathematical foundations, model construction, computation, decision-making, validation, and technical writing.
- 02
Advanced
Python Laboratories for Modelers
Reproducible laboratories for simulation, numerical methods, optimization, and figure generation.
- 03
Competition
Competition Modeling Studio
Structured practice in problem framing, team workflow, rapid computation, validation, and report design.
- 04
Competition
Macau School Mathematics Competition Archive, 2019–2026
A source-verified archive of 214 Junior and Senior competition solutions, with strategy notes, knowledge maps, diagrams, and three expandable examples.
- 05
Advanced
Student Research Studio
A supervised pathway from reproducing one result to formulating, testing, and communicating an independent mathematical-modeling question.
Evidence in practice
Cases built for mathematical judgement.
Public articles and approved figures become teaching cases only after the learning question, expected artefacts, and claim boundaries are made explicit.
Competition mathematics
Macau competition solution archive
Work through 214 source-verified Junior and Senior solutions from 2019 to 2025/2026, with official-paper links and expandable examples.
Topology and observation
Melt-pond topology observation lab
Test whether blur, pixel size, segmentation-boundary displacement, or digital connectivity can create a false spanning threshold in a fixed synthetic pond field.
Quantum networks
Quantum repeater scheduling lab
Balance probabilistic link generation, swap failures, memory decay, fidelity, and tail latency in a five-node repeater chain.
Research design
Research inquiry studio
Investigate identifiability, causal spillovers, and robust decisions with assumptions, claim limits, articles, and academic references.
Interactive examples
Interactive model laboratory
Find twelve experiments by research question, from foundation dynamics to inferential and decision models.
Research-facing models
Frontier model studio
Explore tipping points, equation discovery, active matter, higher-order contagion, operator learning, and persistent homology.
Foundations
A model-building workflow
Question framing, assumptions, baselines, validation, and reproducibility.
Numerical methods
Interpolation and numerical judgement
Node choice, error, oscillation, and why a smooth curve is not automatically a reliable one.
Environmental modeling
Reading a spatial dengue model
Boundary conditions, synthetic evidence, verification, and claim limits.
Worked case
Ventilation under a wrong timetable
Mass balance, predictive control, shared constraints, and conflicting evaluation metrics.
Learning evidence
Students produce an argument, not only an answer.
Each pathway is organised around artefacts that expose how the result was obtained and how confidently it should be used.
- Model briefdecision, question, system boundary, and stakeholders
- Assumption registerunits, provenance, justification, and likely effect
- Reproducible experimentconfiguration, code or notebook, saved result, and numerical check
- Validation memobaseline, sensitivity, failure case, and unresolved uncertainty
- Technical explanationclaim-evidence map, figure captions, limitations, and next evidence
Teaching resources
Pathways, cases, and instructor tools.
Resources are written as complete teaching designs rather than as a list of files. Each page identifies its audience, sequence, artefacts, and assessment emphasis.
Beginner · Course pathway
Foundations of Mathematical Modeling
A beginner pathway from a real question to variables, assumptions, a baseline model, and a defensible conclusion.
Competition · Course pathway
Competition Modeling Studio
Structured practice in problem framing, team workflow, rapid computation, validation, and report design.
Competition · Competition archive
Macau School Mathematics Competition Archive, 2019–2026
A source-verified archive of 214 Junior and Senior competition solutions, with strategy notes, knowledge maps, diagrams, and three expandable examples.
Advanced · Worked example
Case Clinic: Ventilation Under a Wrong Timetable
A worked teaching case for mass balance, predictive control, competing metrics, and the difference between a study target and a health claim.
Advanced · Python lab
Python Laboratories for Modelers
Reproducible laboratories for simulation, numerical methods, optimization, and figure generation.
Advanced · Student research
Student Research Studio
A supervised pathway from reproducing one result to formulating, testing, and communicating an independent mathematical-modeling question.
Instructor · Instructor resource
Instructor Resources and Assessment
Planning notes for case selection, formative critique, assessment rubrics, and reproducibility review.
Instructor · Course pathway
Mathematical Modeling Lecture Library
A bilingual 27-unit library connecting mathematical foundations, model construction, computation, decision-making, validation, and technical writing.
Teaching and mentoring
Mathematics, computation, and research habits in one learning sequence.
For discussion of curriculum design, mathematical-modeling instruction, or student research mentoring, contact me directly.
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