CS382:Unit-foundation-templated

Foundations of Modelling

Overview

This unit covers all of the basic skills needed to create and vet models.

Specifically we provide the answers to three question:

1. What data do you need for a model?
2. Where do you get that data?
3. What do you do with that data?

Background Reading for Teachers and TAs

• A worked through fermi-problem
• Edward Tufte, Sparklines Theory and Practice

Reading Assignments for Students

For lecture 1

• Shiflet et al. Chapter 1 "Overview"
  • A good introduction to what models are and how to build them.
• Wikipedia on modelling

For lecture 2

• Wikipedia on scientific visualization
• Edward Tufte, Sparklines Theory and Practice

Reference Material

• a collection of fermi-problems
• Fermi's yield calculation a good example of how simple a model can be
• The Unreasonable Effectiveness of Mathematics in the Natural Sciences
• [1]
• [2]

Lecture Notes

Lecture 1

• What data do you get?
  • Modellers need to have an intuitive understanding of what is significant
    • Bring in a jar of Jelly beans. Ask students to guess how many there are. Ask for which measurements are necessary to get a good guess. Have them split into groups of 4ish to discuss what is important.
    • Ask a big question... IE what is the area of the Heart. Ask for people to state factors. (This provides a theoretical background to the measuring lab.
  • Establish a feeling for what is too detailed
    • Explain what the difference is between a back of the napkin calculation and an exhaustive one
    • Provide an example of a model and how to make it tractable.
      • Dropping a ball 10 meters (useful data: Gravity. not really useful: Drag, Gravity at our altitude, ball surface etc.)
  • Introduce the idea of orders of magnitude
    • Show powers of 10 to the class
    • Talk about fermi-problems
• Where do you get data?
  • Making all your own data is hard.
    • Unlike in high-school copying is good, just remember to cite
    • We don't want to reinvent the wheel each time we build something.
    • Ask how many piano tuners there are in Chicago
      • Work through the fermiproblem
      • discuss where assumptions were made and why they were likely good ones

Lecture 2

• • But do we trust other people's data?
    • Discuss the notion of vetting sources
    • explain scientific rigor
• What do you do with your data?
  • We need to extrapolate sometimes
    • Explain how to properly extrapolate from known data to what you need.
    • Explain how to defend your extrapolations (Show calculations, explicitly list assumptions, etc)
  • Show how to bring data together
    • Revisit the worked fermi-problem
  • Explain that data can be evaluated based on accuracy and precision. Explain the difference between them
  • Explain how to present data as information
    • In the case of monitoring springwood lake
      • take data with sensor devise and GPS
      • synchronize sensor time with GPS time, mush up those, and create table(time, data, location)
      • visualize data as you want, for instance plotting, goolge earthing, or both

Lab

Some prose describing the process, outcomes, etc.

Software

N/A

Bill of Materials

• A jar of jellybeans (to be counted by TA's) $5.00

Evaluation

CRS Questions

Which of the following represents low accuracy but high precision:

A) 5 measurements of a meter stick which measure the length as 100cm, 101cm, 99cm, 98cm, 100cm.

B) 5 measurements of a meter stick which measure the length as 80cm, 79cm, 81cm, 82cm, 78cm.

C) 5 measurements of a meter stick which measure the length as 90cm, 110cm, 109cm, 91cm, 100cm

D) 5 measurements of a meter stick which measure the length as 80cm, 95cm, 50cm, 130cm, 200cm.

Which of the following is likely to have the least impact on a model of a ball dropping:

A) Rate of acceleration due to gravity

B) Size of the ball

C) Height of the ball

D) Whether or not the ball is attached to a parachute

About how many squirrels are on Earlham's "front" campus:

A) 1 to 10

B) 10 to 100

C) 100 to 1000

D) 1000+

Quiz Questions

• A question.

<The Unit's Name> Metadata

This section contains information about the goals of the unit and the approaches taken to meet them.

Scheduling

A note about early, late or doesn't matter, dependencies.

Concepts and Techniques

This is a placeholder for a list of items from the context page.

General Education Alignment

• Analytical Reasoning Requirement
  • Abstract Reasoning - From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:
    • They focus substantially on properties of classes of abstract models and operations that apply to them.
      • Solid support
    • They provide experience in generalizing from specific instances to appropriate classes of abstract models.
      • Solid Support, we dedicate an entire lecture to this
    • They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
      • Kinda what the whole unit is about
  • Quantitative Reasoning - From the [Catalog Description] General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:
    • Using and interpreting formulas, graphs and tables.
      • The discussion of vetting materials strongly supports this objective
    • Representing mathematical ideas symbolically, graphically, numerically and verbally.
      • Tufte. Strong coverage of this
    • Using mathematical and statistical ideas to solve problems in a variety of contexts.
      • Our discussion of how to use data covers this
    • Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
      • Strong support
    • Understanding basic statistical ideas such as averages, variability and probability.
      • Strong support
    • Making estimates and checking the reasonableness of answers.
      • Vetting data covers this
    • Recognizing the limitations of mathematical and statistical methods.
      • Analysis of this unit's support or not for this item.
• Scientific Inquiry Requirement - From the [Catalog Description] Scientific inquiry:
  • Develops students' understanding of the natural world.
    • We lay the framework for understanding the world through models.
  • Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
    • One of the major take-away points of this unit is how to develop a scientific knowledge of a situation.
    • In order to test hypotheses students need to build models and apply them to the real world
    • Well established in this unit
  • Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
    • The second major point in the above lecture notes is how do we collect data
      • Collecting data is divided into first-hand experience and using other people's data (theoretical analysis)
    • Well established in this unit.

Scaffolded Learning

Some prose.

Inquiry Based Learning

Estimation of Jelly-beans and area of the heart involves students and promotes collaboration.