## Mathematics 89S, Fall 2013

### The Magic of Numbers

**Course materials will posted on Sakai.
**

**Textbook:** We will be using *The Magic of Numbers* by
Benedict
Gross and Joe Harris as the text for this course. The book is out of print
(one can find used copies online)
but will be available as a coursepack from the Duke Textbook Store.

Course synopsis:

This course will explore some of the intriguing and beautiful mathematics
that underlies the arts, technology, and everyday life. If you are
interested in learning about how to discover and analyze patterns using
mathematics, but don't necessarily have a strong technical background in
math, this may be the seminar for you.

We will explore a selection of elegant and accessible subjects that will
expose us to a broad variety of mathematical disciplines, from
combinatorics (the mathematics of counting) to geometry (the mathematics
of shapes) to number theory (the mathematics of whole numbers). We'll see
how the golden ratio and a number sequence called the Fibonacci numbers
appear throughout nature, music, and other "non-mathematical" areas; how
games of chance can be understood through some simple counting arguments;
how the ancient Greeks found order and symmetry in three-dimensional
shapes; and how factoring whole numbers leads to "unbreakable" codes like
the ones that underlie internet security. Emphasis will be placed on
appreciating ways in which mathematical
patterns can be applied to society and the natural world. The seminar will
be interactive and will feature hands-on demonstrations and multimedia
where appropriate.

**Please note this is a rigorous mathematics course, and you will be
graded
partly on your ability to understand and craft precise mathematical
arguments.**

**Course syllabus** (tentative)