1. Modeling with Mathematics
Definition

2. What do we mean by mathematical modeling?
Is this mathematical modeling?
An engineer may make a mechanical
“model,” with weights and springs, of an
electrical circuit with capacitances and
resistances.
One real-world object is represented by another.

3. What do we mean by mathematical modeling?
Is this mathematical modeling?
A switching circuit may be a “model” for a
Boolean function.
A mathematical object is represented by a real-world object

4. What do we mean by mathematical modeling?
Is this mathematical modeling?
A real number may be a “model” for a point
on a line, and vice versa.
A mathematical object by a different mathematical object

5. What do we mean by mathematical modeling?
Is this mathematical modeling?
A logistic function may be a “model” for the
growth of a bacterial population.
Represents a real-world situation by a mathematical one.

6. What do we mean by mathematical modeling?
The first three all represent meanings of a model in a scientific or mathematical setting. However, we are concerned with the forth and last meaning, a mathematical model, which represents a real-world situation by a mathematical one.

7. Our Definition
“Mathematical modeling is the link between mathematics and the rest of the world.” (Meerschaert, M., Mathematical Modeling, Elsevier Science, 2010)
 The process of beginning with a situation and gaining understanding about that situation is generally referred to as “modeling”. If the understanding comes about through the use of mathematics, the process is known and mathematical modeling.

8. What is the process? What in the reading stood out for you?
Let’s read Mathematical Modeling.
What in the reading stood out for you?
What was interesting?
What are the implications for the classroom?

9. Modeling Meteorology
In this lesson, students will model temperature data. They will use “known temperature stations” in order to estimate temperatures at any given point accurately. Websites that give the temperature at a specific place typically do not give the actual values; they give an estimate based on meteorological data.
This is a two day lesson.