Math and Sustainablity Syllabus
Intro: Use quantitative methods to decide what is an effective action/strategy.
Assignment: Find article talking about new alternative energy and how many
houses/people it can serve (dissonance – this will be shown to be misleading).
1.
Pre assignment:
a. Map home,
b. Energy bills
c. List of energy appliances at home
List energy appliances in dorm
a. How much energy do they use? Cost, CO2.
b. Are there more efficient models available?
c. How much savings would there be to buy the newest model?
d. What is payback time?
Each student (or team of 2) becomes expert on one (or two) appliance(s).
2.
Story: determine if and when you should buy the new appliance. Provide mathematical
justification. (Consider carbon footprint).
3.
Social Network Analysis
a. Map the network of connections in the class (pre/post).
b. Discuss importance of social networks to bring about change.
c. Karen Stephenson’s work: different types of connectors.
d. Malcolm Gladwell: The Tipping Point with a focus on connectors.
e. Math of SNA: different ways to measure key connectors
f. (Enrichment: some way for math students to do more here).
4.
Energy: (general)
a. Energy units
i. Units (watt, kwh, joules, but)
ii. Cost $ and carbon
b. Buildings
c. Transportation; Cars, Planes, Buses, Trains, Bikes
d. Solar
e. Wind
f. Ocean
(which of these topics do we do in more detail at a more advanced level?)
Energy production per person.
5.
Energy associated with Buildings (detailed).
Story: Homeowner has a high energy bill. Would like to save money. Receives in
the mail a flier from the window company telling about the great, energy efficient
windows. Or put solar panels on the roof. Also gets flier from contractor about
insulation. She has $20,000 to spend. How should she use her money?
Heating a building
Energy efficiency of heaters/coolers.
Heat pump/geothermal systems. (Swimming pool, Rec Center
geothermal).
iv. Leakiness of building. U value, R value
1. Do range of examples from simple to more complicated.
Teach the modeling process. Both in developing the
equations and then in applying it to more and more
complicated situations.
v. Apply model to college building(s)
i.
ii.
iii.
6.
Water:
1. calculate water run off from parking lot, from building
2. learn about underground basins.
3. Calculate something about this using true data; type of soil, filtration rates.
4. Learn about water absorption of various green features. (Ex. parking lot
swale; green roofs; trees; permeable pavement). Link with Philadelphia
Green City, Clean Waters plan.
5. http://www.phillywatersheds.org/what_were_doing/documents_and_data/cso_
long_term_control_plan
7.
Dynamical Systems and Iteration:
a. Population growth with linear models
b. Logistic growth and carrying capacity. Non-linear map. Bifurcations.
c. Harvesting. Bifurcation and tipping points.
Fish Simulation game
Readings from Collapse
Tipping Points – link of math with society
Water, Trees, soil,
d. Climate change issue; bifurcation. Non-linear feedbacks. Ex. melting ice,
frozen methane.
Questions:
Will students, in addition to their large, interdisciplinary group Praxis project, do
smaller math focused projects?
2. Can we structure the course so each “unit” culminates in some type of
product/paper/presentation – but on a small scale? Range of options. Maybe
students choose out of the total of X, they must do Y mini-projects?
3. How to keep the “math project” focus for all students while also having the larger
interdisciplinary focus? Or is this not necessary. In the real world, a team does a
project and different people bring different skills.
1.
Heating Efficiency Calculations;
●
●
●
how much energy to heat a room to a certain temp.
efficiency of boiler. AC unit.
compare with Geothermal, heat pump unit.
Then do calculations taking leakiness into account.
Project:
a. Develop a display for the lobby of the gym that describe the energy conservation
features including the heat pump feature of the swimming pool.
b. Develop display(s) for the Recreation Center that describe the energy efficiencies
of that LEED building: ex. Geothermal, passive solar heat gain, light, etc.
c.
Building Energy Calculations
Potential Buildings
Meeting buildings:
Cambrian Row – newly renovated, energy efficient. Multi-Cultural Center.
Gateway Building – new construction
Classroom/Offices
Dalton - ? possible closing
Taylor – old, not renovated? But recently fixed up. How?
Betsy –Y-Coed- 1914/renovated 2004. Gas but not electric? ?
School of Social Work
Goodhart
Chemistry vs Science Complex.
Dorms:
Brecon – very old, not renovated recently.
Merion – oldest dorm, not renovated recently.
Are these buildings one for which we can get reasonable estimates for insulation,
etc.
a.
b.
c.
Have whole class do calculations for one building:
Having done energy estimates for houses (u values and k values), make a
prediction for one of the college buildings.
Look at actual data for that building and compare. Get the data by % of GSF of
college total.
Look at more detailed data from break and calculate refined estimate.
Project: Do this on more buildings. Then develop a document and give presentation .
Consider the function and the number of people using it and location.
Jim – is it ok if students come to you for all this more detailed data? (Rather than teacher
gives it to them directly).
Water Calculations:
●
●
●
●
calculate water run off from parking lot, from building
learn about underground basins.
Calculate something about this using true data; type of soil, filtration rates.
Learn about water absorption of various green features. (Ex. parking lot swale;
green roofs; trees; permeable pavement). Link with Philadelphia Green City,
Clean Waters plan.
● http://www.phillywatersheds.org/what_were_doing/documents_and_data/cso_lon
g_term_control_plan
Project:
a. some type of exhibit/web description of how the water run-off system works at
the college with a math component.
b. Develop more advanced materials for the Waterworks site.
c.
Possible 360 Projects:
1.
(BMC) Develop a display for the lobby of the gym that describe the energy
conservation features in the building including the heat pump feature of the
swimming pool.
2.
(Hav Reserve) Develop display(s) for the Recreation Center that describe the
energy efficiencies of that LEED building: ex. Geothermal, passive solar heat
gain, light, etc.
3.
(BMC) Calculate energy usage in variety of buildings around campus. Link this
with usage levels of buildings. Determine potential savings (CO2, $) if heat is
turned down over night or base temperatures is lowered. Develop a document and
give presentations to “inhabitants” of various buildings on campus wtih a goal of
achieving immediate change in behaviour.
4.
(BMC) Develop exhibit/web description of how the water run-off system works
at the college with a math component.
5.
(Waterworks) Develop more advanced materials for the Waterworks site on water
issues.
6.
(BMC) Analyze LED lighting conversion on campus and develop educational
information about CO2 and $ savings.
7.
(BMC) Develop a plan for bike use, storage on campus. Ex. More bike rackes.
Where? Design issues.
Link with Carola:
- house in larger context. Transport costs, analysis. Ships vs trucking. Where do
goods come from?
College energy/carbon footprint.
Look at the numbers. Find data.
Sustainability of a city. How do we measure this? Ex. Paris self sufficient (but not
counting the airport).
How much energy would we save without blue bus - all students get a bike from
college? Mini Analysis.
5 math problems; you do two of them.