Mathematics: Curricular Overview
| Concept | Example #1 | Example #2 | Example #3 |
|---|---|---|---|
| Geometry: power of deductive reasoning | Thales and pyramid of Giza | Eratosthenes and circumference of earth | Chinese proof of Pythagorean theorem |
| Statistics: chance | Birthday Problem | Odds of rolling a 3 versus a 7 | Simpson’s Paradox
Bayes Rule Base Rate Problem |
| Exponential Growth | The rice on the chess board | Paper folding | Inflation |
| Calculus: optimization | The optimal size of a can | The camel problem,
Dido’s problem |
The pipeline problem |
| Magic Numbers | Pi – what is so special? | The mystery of e
|
Can you visualize i? |
| Scaling | First power- lengths | Second power–areas | Third power
volumes |
| Counting | Taxes + virtues +
Income + |
Cooking ingredients | Good deeds per day; smiles; kind words |
| Calculating | Ratios: santa/Grinch
Real versus reported earnings |
Real versus nominal returns, pre tax versus after tax returns | Discounted versus non discounted cash flows or reported debt
And real debt |
| Ethics of mathematics | Is economic inequality a measure of injustice? | How to distinguish between factors behind ethnic disparities? | How to measure factors behind gender disparities?
What is a fair interest rate to charge a sibling? |
What is the biggest hole you can cut into an 8 by 11 piece of paper?
How many piano tuners in Chicago?
How does Social Security work?
How does the welfare system work? (EITC, minimum wage, TANF, Medicaid)
What is the difference between the Federal budget deficit, the Federal debt, and the real debt of the federal government?
What is the difference between real and nominal interest rates and return?
What is bracket creep? Why are benefit payments inflation-adjusted and tax brackets are not?
Which numbers are highlighted and which ignored by proponents of a flat tax?