Class Schedule for Spring 2021

Reading a book like “Harry Potter and the Sorcerer’s Stone” is fairly straightforward: each sentence conveys a direct idea on what a char- acter did, said, or thought, and these ideas fit together easily to make a simple story. Reading a play by Shakespeare is quite different: sentences can convey multiple ideas at once, characters can say one thing and mean another, and the stories have layers upon layers of meaning. Reading Shakespeare takes training and practice.

Reading mathematics, and learning mathematics, is a lot like reading Shakespeare. One doesn’t just sit down and read each sentence, and have the ideas fit together easily. One has to find the deeper meaning in the sentences, and carefully put together the story that they are trying to tell. This is difficult, and sometimes frustrating, but learning to do it opens up a wonderful and exciting world.

In this course we will read some mathematics together. We will talk about ways to make sense of what you read, and we will do a lot of exploring. Some of the skills we will focus on are: trying examples, looking for patterns, making conjectures, testing conjectures, and modifying conjectures. These might sound easy, but when you are reading mathematics you need to be constantly doing all five of these things! It takes practice.

Probability is all around us in the modern world. It originated in attempts to mathematically analyze games of chance (like dice games or card games), but it has exploded and now has applications in physics, chemistry, genetics, speech recogni- tion, music—almost any field you can imagine. In this course we will learn some basic probability theory, as the backdrop for learning how to read and think about mathematics.