Kenneth Cheng · Macau
I teach mathematics and explore how models help us understand the world. A notebook of questions, computations, and classroom ideas.
A little about me →Fresh from the notebook
A thermometer can be locally informative while leaving a distant heat-source explanation unresolved. A controlled heat-kernel study separates reflection symmetry, noisy classification and continuous inversion, then compares six ways of spending the same eight-reading budget.
A small forecasting model can spend extra computation fitting the trajectory in front of it. But a better fit to that context is not automatically a better forecast—or a unique identification of the underlying dynamics. Two controlled synthetic cases separate these questions.
Two positive transport networks can lose exactly the same total mass, share every eigenvalue, and still disagree about a finite-time sensor alarm. A controlled study asks what a spectrum misses, what a rigorous margin can certify, and when that margin becomes uninformative.
A few good starting points
From a modeling question to a calculation and an application.
A compact workflow for assumptions, model choice, computation, validation, limitations, and communication.
A topic guide connecting polynomial interpolation, Chebyshev nodes, and the Gibbs phenomenon.
A guide to what a synthetic reaction–diffusion experiment can—and cannot—show about climate-sensitive transmission.
Choose a direction
Questions, models, geometry and mathematical judgement.
4 articles →Numerical methods, simulation and reproducible computation.
16 articles →Learning from data while testing what can be inferred.
15 articles →Uncertainty, reliability and decisions with limits.
34 articles →Living systems, ecosystems, climate and observation.
14 articles →Transport, energy, infrastructure and engineered systems.
11 articles →Change, patterns, feedback and connected systems.
17 articles →Learning, mentoring, evidence and research design.
6 articles →From reading to doing
Interactive models, mathematics practice, and bilingual teaching resources.
