Mathematical modeling
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
Modeling process and dimensional analysis
- The modeling cycle: formulation, analysis, interpretation, validation
- Dimensional analysis and Buckingham Pi theorem
- Scaling and nondimensionalization of equations
- Sensitivity analysis and parameter estimation (introduction)
- Model comparison and goodness-of-fit measures
Deterministic models
- Growth models: exponential, logistic, and Gompertz
- Compartment models and conservation laws
- Optimization models in operations and design
- Discrete-time models: difference equations and recursion
- Equilibrium and stability analysis of models
Probabilistic and statistical models
- Elementary probability models for uncertainty
- Monte Carlo simulation (introduction)
- Markov chains for simple stochastic models
- Regression and calibration of model parameters
- Confidence intervals and prediction in applied settings
STEM / applied
Case studies across disciplines
- Population ecology and epidemiology (SIR and extensions)
- Mechanical and electrical system modeling (springs, circuits)
- Traffic flow and queueing (introductory models)
- Finance: random walk and basic option pricing models
- Climate and environmental modeling (simplified ODE/PDE models)
Computation and communication
- Simulation with MATLAB, Python, or R
- Visualization of model outputs and phase behavior
- Writing and presenting technical reports on models
- Sensitivity to assumptions and model limitations
- Peer review and reproducibility in modeling projects
Notes
Topics reflect common mathematical modeling syllabi at US colleges and universities. Courses are often project-based and draw on calculus, differential equations, and linear algebra.