Magic of Numbers
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. However, this is a rigorous mathematics course, and students are graded partly on their ability to understand and craft precise mathematical arguments. 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.
Links to some prior courses: