Introduction to modeling
A Collection of Lists
From Charles Collins:
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.
Modeling Cycle:
- Identication: 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
- Verication: test the results of the model against reality, test the
assumptions
Common Modeling Mistakes:
- Oversimplification: remove significant features, making the model
inaccurate or inflexible
- Kitchen-Sinkification: keep every possible feature, making the
model impossible to solve (related to Immeasurability)
- Overextension: using a model for a reality beyond its flexibility,
or using a model beyond its purpose (related to Oversimplification)
- Living in Math World: never testing the results of the model to see
if they make sense
- Immeasurability: include quantities that are impossible to measure
to the accuracy needed
Website maintained by Andy Long.
Comments appreciated.