Over the course of history, the number $(\sqrt{5}+1)/2\approx 1.618$, known as the Golden Ratio, has been used to provide structural elegance in architecture and other forms of art. But did you know that the Golden Ratio also appears in music? In this class, we will analyze works by Bach and Beethoven and observe how their climaxes correspond to the Golden Ratio.

You are probably familiar with the practice of dividing the octave into twelve equal parts to create the chromatic scale - but it has not always been this way. Over the centuries, musicians have experimented with different tuning systems that make some intervals particularly consonant and others particularly dissonant. In this class, we will discuss how ratios of frequencies are the mathematical basis behind tuning, and we will look at famous tuning systems such as Pythagorean, meantone, and equal. We will also discuss how the increased prevalence of chromaticism in music led to the prominence of equal temperament, and vice versa. If we have time, we will look at the theory for nonstandard scales, such as the scales of 19 or 31 notes.

You may be familiar with polyhedra such as the cube, the tetrahedron, and the octahedron. But can we generalize the concept of polyhedra to higher dimensions? What would an 8-dimensional cube look like? Is there a 4-dimensional analogue of the octahedron? How many higher-dimensional polytopes are Platonic (have rotational symmetry)? Sign up for this class if you want to answer these questions!

Do you have aspirations to write your own music? If so, you know that writing music by hand can be a slow and frustrating process. This class will teach you the basics of using Finale, a computer program that allows you to notate your own music neatly and quickly, and enables you to hear what you've written. We will cover the basics of using Finale, and then you will get a chance to play around with Finale and listen to your own music!

Did you know that the largest Mersenne Prime has over 12 million digits? Primes of the form $$2^p-1$$, known as Mersenne primes, have fascinated mathematics for centuries, and in this class, we will learn why. We will cover several important theorems about Mersenne primes, as well as the primalty test which made it possible for a 12-million-digit prime to be discovered. If we have time, we will also look at the history of Mersenne primes and the famous (often incorrect) conjectures that mathematics have made throughout the centuries.