Mathematics 89S, Fall 2018

The Magic of Numbers

Office hours: TBA.

Course materials will be 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 (tentative)