Question first
State the objective, units and assumptions before choosing an algorithm.
MATHEMATICAL MODELING WORKSHOP / UNIVERSITY & RESEARCH
From a question
to reproducible research.
Every equation makes assumptions. Every computation needs evidence. Build six models and learn to explain when they deserve your trust.
PhenomenonAssumptionsModelPythonEvidenceRevision
01 — 06Solve it.
Then question it.Your question connects every step.
Build evidence
Write Python in your browser; compare exact solutions, baselines and failures.
Take your work with you
Save locally and export notebooks, data, figures and your research record.
THE CORE PATH
Six questions. Six ways to model.
A tank, a boundary, a balance
How do flow, volume and reaction change concentration?
Build a mass balance, uncover its dimensionless structure, and verify your first numerical solver.
Start modelingA good fit, an uncertain future
Can early observations identify a long-run carrying capacity?
Fit competing models, withhold future data and inspect the shape of parameter uncertainty.
Start modelingMechanisms become trajectories
How do contact assumptions and intervention timing reshape a curve?
Derive compartment flows and compare Euler, RK4 and an adaptive reference.
Start modelingLocal choices, collective patterns
Can changing the update schedule change an emergent pattern?
Build an original Schelling-type experiment and compare paired stochastic replications.
Start modelingThe assumptions behind an optimum
How should limited labor and material be allocated?
Formulate a linear program, verify it geometrically and challenge its decision assumptions.
Start modelingWhen a smooth picture lies
How do spatial resolution and boundary conditions change diffusion?
Derive a diffusion equation and test explicit and implicit schemes against an exact mode.
Start modelingA QUICK READINESS CHECK
Refresh what you need. Start when you want.
Mark the skills you want to refresh to find the matching Notes. This is a reading guide; it never locks a lesson.
BEYOND THE CORE
Carry the methods into your own question.
These branches offer reading and research roadmaps; complete interactive workshops are not yet available.
Biology & nonlinear dynamics
When does a reduced enzyme model preserve transient behavior?
Prerequisites: Units 1–3; phase planes and linear algebra
Segel ch. 8 → Mickens ch. 7 → Gumel (nonstandard finite differences) → Childress & Percus ch. 3
Engineering & continuum models
Which transport scale makes a well-mixed approximation fail?
Prerequisites: Units 1 and 6; multivariable calculus
Chidambaram ch. 2–3 → Rice & Do (ODE/PDE methods) → Temam & Miranville (energy and continuum balances)
Social systems & networks
Does an update-rule effect survive changing network structure?
Prerequisites: Unit 4; probability and game theory
Smaldino ch. 3 → ch. 8 → ch. 9–10
Financial models
Do two discretizations agree on a known option-pricing benchmark?
Prerequisites: Units 5–6; probability, calculus and numerical methods
Ruttiens (probabilistic environment) → Wilmott, Dewynne & Howison ch. 3–4, 16–19
Data-driven & learned models
When does a learned surrogate fail outside its training regime?
Prerequisites: Units 2 and 5; gradients and matrix algebra
Spiliopoulos et al. (regression → networks → generalization); Sahni et al. (application critiques)
27 Notes units, one companion library.
Twelve core lectures, ten mathematical refreshers and five writing units are mapped to the workshops. Books supply chapter references; teaching text, examples and code are original.
Progress stays in this browser. Clearing site data removes it; export JSON regularly. The first Python startup needs a network connection to load the scientific runtime.