Math and Culture Course outline
(skeletal outline, expanded as course
progresses)
For the first
part of the course we will be mainly in the Hersh book and we will also
supplement that with readings from the web and other sources. We want to take an almost historical,
cultural overview of some of the highlights of what occurred in “mathematics”
with some tangential explorations along the way. After this survey, we will discuss again,
what is mathematics.
Next, we move
on to exploring the particular mathematical problem that was birthed soon after
the French Revolution and is unsolved (and worth a whole lot of money) still
today. We examine some of the
mathematics behind this problem in an attempt to understand the significance of
the problem. As we are doing this we
will also participate in more tangential explorations of mathematical topics
that are either related by content or by chronology. In this portion of the course we will be
using the Derbyshire book as well as supplemental readings.
0. Introduction- Mathematics and culture, what
are they?
Week 1 readings and discussion (see assignments page)
Phil’s research found the following
sites:
Did the
Chinese invent the first numeral system??
More on the Chinese
Rod numeral system
Alex looked up some stuff on the abacus
Ashley found the most current way of
writing Chinese numerals
that had a cool converter
David found more on Mayan
numerals
·
Our
current number system and our view of “number”
·
Square
roots and other such things
·
The
concept of the unknown
·
Cartesian
coordinate system
·
Modern
comfort (yes- comfort) with algorithms
iii. Game theory
Some set theory and the axiom of
choice.
V. What are complex numbers anyway….
Functions and some mathematical animals
A potpourri of mathematics