Mathematics 49S, Fall 2010

The Magic of Numbers

Course materials are posted on Blackboard.

Textbook update: 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 is available as a coursepack from the Duke Textbook Store for $53.50.

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 understanding and crafting rigorous mathematical arguments, and 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.

Course syllabus