Building your mathematical toolbelt

In this class, we use math not just to carry out calculations but to help us understand and model the physical world and how it behaves. This is a bit of a tricky business and most math classes, while they introduce you to mathematical structures, manipulations, and calculation, do little to help you build the  tools we need. To help you make the transition from math-in-math to math-in-science, we have identified a set of general procedures and methods that you can use to help you. We call learning to use these tools "building your toolbelt". 

Note that we are calling these tools — general purpose devices to be brought to bear whenever you understand the situation and see that it might call for them. So you have to learn when it's appropriate to use a screwdriver and when it's appropriate to use a hammer. Learning this will take some time and seeing how to use them in specific examples.

In your introductory science classes you might have focused on learning facts and procedures. These are important, but not the whole story. To make sense of science, we have to also understand the mechanism of what's happening and we have to put it all together in a coherent whole -- synthesize. And in many sciences (physics especially), equations can play a pivotal role in pulling this all together. If you're not used to this, don't worry. We'll learn it a bit at a time, as we need it. 

Here are the tools we'll be developing throughout the year to use math to make meaning in the physical world:

The dimensional analysis tool
The scaling tool
The special case tool
Toy models
Reading the physics in a graph (EX)
Anchor equations -- Reading the physics in an equation
The repackaging tool: Changing physics equations to math (and back)
Telling the story
Building equations from the physics (EX)
The diagram tool
The estimation tool
Putting your tools together

Joe Redish 7/3/17