Tom Murphy has written an open textbook called Energy and Human Ambitions on a Finite Planet.

He uses this course to teach a "gen ed" class in his physics department for non-majors.

I think that the book could be similarly used to run a "quantitative reasoning" course in most math departments. These courses often focus on skills like estimation, modeling with linear, polynomial, and exponential fucntions, and the use of logarithms. The book is about such skills in the context of asking "big questions" about our world.

Example problems from the text:

1. In one day, a typical residential solar installation might deliver about 10 kilowatt-hours of energy. Meanwhile, a gallon of gasoline contains about 37 kWh of thermal energy. But the two ought not be directly compared, as burning the gasoline inevitably loses a lot of energy as heat. Correcting the solar output to a thermal equivalent (using the 37.5% factor discussed in the text) how many gallons per day of gasoline could it displace?

2. Let’s say that the U.S. were willing to divert a one-time investment of 10 qBtu out of its 100 qBtu annual energy budget toward building a new energy infrastructure having a 10:1 EROEI and a 40 year lifetime. How many qBtu will the new resource produce in its lifetime, and how much per year? How many years before the amount of energy put in is returned by the output?

3. In the spirit of outlandish extrapolations, if we carry forward a 2.3% growth rate (10 × per century), how long would it take to go from our current 18 TW (18 × 1012W) consumption to annihilating an entire earth-mass planet every year, converting its mass into pure energy using $E = mc^2$?

Tom Murphy has written an open textbook called Energy and Human Ambitions on a Finite Planet.

He uses this course to teach a "gen ed" class in his physics department for non-majors.

I think that the book could be similarly used to run a "quantitative reasoning" course in most math departments. These courses often focus on skills like estimation, modeling with linear, polynomial, and exponential fucntions, and the use of logarithms. The book is about such skills in the context of asking "big questions" about our world.

Example problems from the text:

1. In one day, a typical residential solar installation might deliver about 10 kilowatt-hours of energy. Meanwhile, a gallon of gasoline contains about 37 kWh of thermal energy. But the two ought not be directly compared, as burning the gasoline inevitably loses a lot of energy as heat. Correcting the solar output to a thermal equivalent (using the 37.5% factor discussed in the text) how many gallons per day of gasoline could it displace?

2. Let’s say that the U.S. were willing to divert a one-time investment of 10 qBtu out of its 100 qBtu annual energy budget toward building a new energy infrastructure having a 10:1 EROEI and a 40 year lifetime. How many qBtu will the new resource produce in its lifetime, and how much per year? How many years before the amount of energy put in is returned by the output?

3. In the spirit of outlandish extrapolations, if we carry forward a 2.3% growth rate (10 × per century), how long would it take to go from our current 18 TW ($18 × 10^{12}$ W) consumption to annihilating an entire earth-mass planet every year, converting its mass into pure energy using $E = mc^2$?