 
Summary: Chapter 1
Fundamentals
Let None But Geometers Enter Here
inscribed about the entrance to Plato's Academy.
A student who is using these lecture notes is not likely to be a geometer (person who studies geometry) but is
also unlikely to pass through the arch with the quotation on it. The original Academy was Plato's school of
philosophy. It was founded approximately 25 centuries ago, in 385 BC at Akademia, a sanctuary of Athena, the
goddess of wisdom and skill. Plato's motives for making this inscription are not recorded but he clearly felt that
an educated person needed to know mathematics.
When am I going to use this crap?
a typical exclamation from a student who is not putting in the hours needed
to pass his one required math class.
The answer to the question above may well be "never". That doesn't mean the person who asked the question
wouldn't benefit from basic mathematics. They could have benefitted from math, and its sister quantitative
reasoning, but have chosen not to. There are only a few gainful activities where math is not present. The
innumerate (this is the mathematical analog to illiterate) typically don't notice that their disability is harmful.
They do get cheated, lied to successfully, and ripped off more often than other people. They also don't get
promoted as often or paid as much. Mathematical skill also acts as a leveler between the sexes.
Although women earn significantly lower wages than men do across all levels of ed
ucation and occupational categories, the gender wage gap is not significant among
