## Mathematics 89S, Fall 2016

### The Magic of Numbers

Office hours:

- Mondays 1:00-2:00 (though preference is given to my Math 431
students)
- Wednesdays 4:20-5:00
- Thursdays 12:30-1:30
- and by appointment.

**Course materials are 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. No technical background is
required beyond standard high school algebra and geometry; instead, we will
emphasize how to discover and analyze patterns using mathematical reasoning.

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 probability and 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.

Please note that this is a rigorous mathematics course, and you will be graded
partly on your ability to understand and craft precise mathematical
arguments. Although we won't assume familiarity with calculus or other advanced
methods, an advanced mathematical background may be helpful, not directly
for the material you may have learned in calculus, etc., but indirectly for past
exposure to mathematical lines of reasoning.

**Course syllabus**