ISP 120 Mathematical

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ISP 120 Mathematical Technological Literacy I

• Benjamin Graham, MS, LCPC

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Agenda for Today

• Introductions
• Overview of course
• Syllabus

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Mathematical Modeling

• Mathematical Modelan equation, graph, or
  algorithm that fits some real data reasonably
  well and that can be used to make predictions.
• There are two kinds of predictions
• Interpolationspredictions made in between
  existing data points
• Extrapolationspredictions outside the range of
  existing data (usually the point of modeling)

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Allow me to extrapolate

• Extrapolationwhere mathematical models get
  EXCITING!
• The further we go from our actual data, the less
  confident one becomes about ones predictions
• A prediction very far from our actual data may
  end up being correct, but even so we have to hold
  out on our confidence b/c we cant say for sure
  if the model will hold.

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Applied Modeling Hurricane Paths

• Where will a hurricane go in its next 500 yards?
  
• Where will it go in its next 500 miles?

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Steps to Developing a Mathematical Model

• Step 1 Gather your data
• Step 2 Create your graph
• Step 3 Fit mathematical models to your existing
  data
• Step 4 Use the model to make predictions
• Step 5 Judge the amount of confidence you have
  in your predictions.

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Step 1 Gather your data

• Where do we get our data?

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Step 2 Create your graph
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Step 3 Fit mathematical models to your existing
data
y mx b
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Step 4 Use the model to make predictions

• If Joe weighs 167 pounds, what is his predicted
  height?
• If Christina is 53, what is her predicted
  weight?

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Step 5 Judge the amount of confidence you have
in your predictions.

• Assess how confident are we in our predictions of
  weight and height.
• Would it be different if we were comparing age
  and height for children age 0-13?