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Revision as of 14:50, 6 March 2009
Contents
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:
- What data do you need for a model?
- Where do you get that data?
- What do you do with that data?
Background Reading for Teachers and TAs
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
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
- Modellers need to have an intuitive understanding of what is significant
- 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
- Making all your own data is hard.
Lecture 2
- But do we trust other people's data?
- Discuss the notion of vetting sources
- explain scientific rigor
- But do we trust other people's data?
- 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
- In the case of monitoring springwood lake
- We need to extrapolate sometimes
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
- They focus substantially on properties of classes of abstract models and operations that apply to them.
- 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.
- Using and interpreting formulas, graphs and tables.
- Abstract Reasoning - From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:
- 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.
- The second major point in the above lecture notes is how do we collect data
- Develops students' understanding of the natural world.
Scaffolded Learning
Some prose.
Inquiry Based Learning
Estimation of Jelly-beans and area of the heart involves students and promotes collaboration.