Mathematical modeling library
From a first assumption to a defensible model.
Twenty-seven teaching units connect mathematical foundations, model construction, computational experiments, decision-making, and technical writing. Every unit includes Traditional Chinese Notes, English Notes, and English slides.
01
Main lectures
Twelve core units from formulation to dynamics and decisions
- 01120 minOpen unit
Modeling Change
Purposeful simplification, difference equations, equilibria, and constrained growth.
- 02120 minOpen unit
The Modeling Process and Scaling
Problem formulation, decomposition, units, and geometric scaling.
- 03120 minOpen unit
Model Fitting and Residual Analysis
Least squares, residuals, validation splits, and error metrics.
- 04120 minOpen unit
Empirical Models, Interpolation, and Splines
Interpolation, extrapolation, polynomial behavior, and splines.
- 05120 minOpen unit
Monte Carlo and Discrete-Event Simulation
Random sampling, event simulation, replication, warm-up, and confidence intervals.
- 06120 minOpen unit
Linear Programming and Decision Optimization
Decision variables, constraints, feasible regions, integer decisions, and sensitivity.
- 07120 minOpen unit
Decision Theory and Risk
Expected value, decision trees, Bayes updating, information value, and tail risk.
- 08120 minOpen unit
Game Theory and Strategic Modeling
Zero-sum games, mixed strategies, Nash equilibrium, and repeated interaction.
- 09120 minOpen unit
Differential Equations and Dynamic Models
Continuous change, phase lines, numerical integration, and interacting populations.
- 10120 minOpen unit
Continuous Optimization and Model Design
Single- and multivariable optimization, constraints, solver error, and shadow prices.
- 11120 minOpen unit
Dimensional Analysis and Similitude
Dimensional compatibility, Buckingham Pi, and experimental similitude.
- 12120 minOpen unit
Graphical and Qualitative Modeling
Response curves, qualitative dynamics, comparative statics, and modern modeling bridges.
02
Foundation supplements
Ten on-demand mathematical bridges for modeling
- 01120 minOpen unit
Sets, Functions, and Mathematical Language
Notation, logic, sets, functions, and clear quantitative statements.
- 02120 minOpen unit
Numbers, Coordinates, and Geometric Models
Number systems, coordinates, distance, and geometric representation.
- 03120 minOpen unit
Graphs, Transformations, and Periodic Models
Function transformations, logarithmic scales, trigonometric patterns, and periodicity.
- 04120 minOpen unit
Limits, Continuity, and Asymptotic Thinking
Limits, continuity, asymptotic comparison, and model boundaries.
- 05120 minOpen unit
Derivatives, Rates, and Local Linear Models
Derivative meaning, rules, local approximation, and elasticity.
- 06120 minOpen unit
Applications of Derivatives and Optimization
Monotonicity, curvature, extrema, and one-variable optimization.
- 07120 minOpen unit
Definite Integrals, Accumulation, and Numerical Integration
Accumulation, areas, integral models, and numerical quadrature.
- 08120 minOpen unit
Probability Essentials for Modeling and Simulation
Probability rules, random variables, distributions, expectation, and sampling.
- 09120 minOpen unit
Linear Algebra Essentials for Modeling
Vectors, matrices, linear systems, transformations, and eigenvalue intuition.
- 10120 minOpen unit
Multivariable Calculus and Lagrange Multipliers
Partial derivatives, gradients, Hessians, and equality-constrained optimization.
03
Competition and technical writing
Five units for turning results into a traceable argument
- 01120 minOpen unit
Paper Architecture and Judge Navigation
Design a modeling report whose reasoning and evidence are easy to audit.
- 02120 minOpen unit
The Summary — Claim, Evidence, and Decision
Write a decision-ready summary with calibrated findings and uncertainty.
- 03120 minOpen unit
Building Trust — Assumptions, Validation, and Sensitivity
Make assumptions, verification, validation, uncertainty, and sensitivity auditable.
- 04120 minOpen unit
Academic Prose — Precision, Flow, and Evidence
Turn quantitative evidence into precise English analytical prose.
- 05120 minOpen unit
Visual Evidence, LaTeX, and Submission Engineering
Design equations, tables, figures, captions, and a reproducible submission workflow.
Complete collections
Choose the format that fits the lesson.
Use the collected editions for offline reading, or choose an individual unit for classroom sharing.
Student dataset pack
Start a trustworthy model with data provenance.
Eight teaching datasets with sources or explicit synthetic labels, data dictionaries, and units.
Materials are released under CC BY-NC-SA 4.0; third-party material retains its own credit and licence terms.