Lecture 1

I want to provide motivational basis for this course.

Why do people go to college?

What do universities think they provide to students? What is the value of their product (their degree)?

http://www.stonybrook.edu/commcms/cas/liberalartseducation.html

Liberal arts schools' value proposition is that students learn critical thinking skills. How do they know this (critical thinking question)? They need to measure that these skills are increased to justify this statement (voltmeter → critical thinking meter). This meter, like a voltmeter, must be reliable (same measurement when repeated) and valid (actually measures what is says it measures).

What would someone at a Liberal Arts school say about Mines? “They just train you to use Newton's laws (plug and chug). You don't learn when the formulas are not valid. You don’t look at the assumptions of the model (R and C are constant). You don’t learn critical thinking.”

For example, you have some formula to test if a model fits the data. You plug and chug but don’t really understand what the limits of those formulas are and therefore when they breakdown.

In this class I want you to focus on data and its error to determine if the data supports a model within error.

I want to focus on the critical thinking aspect since that’s a common theme for value propositions in most universities. What is critical thinking? First how do we think?

https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow

These people won the nobel prize in economics but are psychologists

Use this link to talk about heuristics or models we make of the world.

What is an example of system 1 thinking? -heart beat. Musician plays without thinking. Athlete performs without thinking. What’s the difference between these? Training vs. innate ability.

What is an example of system 2 thinking? “Slow, effortful, infrequent, logical, calculating, conscious” OR critical thinking.

What’s common with these two ways of thinking? -models or heuristics are use to generate behavior. However, in system 2 you critically check model assumptions, see if data support the model.

You can learn to make some skill system 1 thinking. Examples are playing an instrument, athletic performance, playing chess, etc. This requires lots of experience and you become an expert. However, the models/heuristics you use are not always valid. Experts need to know what are the limits of their models.

For both experts and novices system 2 or critical thinking skills are needed.

We are by nature creatures who look for models or create models about how the world works. Humanity has sacrificed people based on the model that such a sacrifice will improve the weather. We will wear a rabbit's foot based on the model that it will improve our future. Look at what a professional athlete wears or ritual he or she performs before a competition.

This creation of models or heuristics helps us survive. We have the model that the gazelles go to the watering in the evening and that helps us get meat to survive.

RC circuit example: -System 1 thinking: go on autopilot and start plugging components in the circuit board. This works only for an expert who has the training. Drawing a schematic and troubleshoot the schematic requires system 2 thinking. How about the RC model? Where did exponential decay come from? Derive from Kirchhoff's law. Sketch log of the data indicating that the model doesn’t work. Why not? This is an example of system 2 or critical thinking.

In all lab expts I expect you to formulate a model and see if the data supports that model.

Propagation of errors for a thin lens. Need to determine errors in variables to see how that affects error in the model. Given data for s0 and si determine f. Is it constant within error? Data visualization: how would you present this data? Graph f vs s0 and si and see if it forms a flat plane within error. Note that the errors are not constant since the derivatives are evaluated at different values of s0 and si.

Use e/m example of a working equation.