Introduction to modeling

Definitions: A model is a representation of reality; a mathematical model is a model which uses mathematical objects (like functions and equations) to represent reality.

Properties of Models:

• Purpose: a model's purpose is the type of questions that the model can be used to answer.
• Resolution: a model's resolution is the level of detail that it can encompass.
• Accuracy: a model's accuracy is how well it represents reality (within its Purpose and Resolution).
• Flexibility: a model's flexibility is the range of realities that it can accurately represent.

• Identification: form initial question, identify possible features
• Simplification: identify signicant features and relationships (make ASSUMPTIONS)
• Evaluation: express relationships mathematically and solve them analytically, qualitatively, numerically or however.
• Interpretation: express solution in terms of reality, answer the original question
• Verification: test the results of the model against reality, test the assumptions

• Over-simplification: removing critical or significant features, making the model inaccurate or inflexible
• Kitchen-Sinkification: keeping every possible feature, making the model impossible to solve (related to Immeasurability)
• Over-extension: using a model for a reality beyond its range, or using a model beyond its purpose (related to Over-simplification)
• Living in Math World: never testing the results of the model to see if they make sense
• Immeasurability: including quantities that are impossible to measure, or impossible to measure to the accuracy needed