Many questions which seem impossible to answer are actually not so hard if you are willing to make a few good estimates and combine them in the right way. These are known as "Fermi problems," named after a physicist who was famously good at coming up with approximate solutions to hard problems. In this class, we'll cover the basic techniques for solving Fermi problems, and practice some together. Possible questions include: - How many pennies would you have to melt down to build a copy of the Statue of Liberty? - How many laptops would it take to store a photo of everyone in the world? - If you could fold a piece of paper in half 30 times, how tall would it be? - How long would it take all the bees in the world to fill a swimming pool with honey?

What counts as a "computer," and what are the limits of computation? Alan Turing answered these questions by describing an imaginary device, now called a Turing machine, which could perform any possible calculation. It turns out that many systems, including Minecraft, are "Turing-complete," meaning they are equally powerful as Turing machines. For example, it is possible to build a fully functioning computer inside Minecraft. In this class, we will define Turing machines and see how they work. We'll also discuss examples of Turing-complete systems.

Quantum mechanics was developed about 100 years ago, and predicts strange or even "spooky" effects in physics. Later, it was discovered that quantum mechanics can be used, at least in theory, to build more powerful computers. In this course, we will answer the following questions: - What is quantum mechanics? - What are superposition and entanglement? - How could a quantum computer solve problems? - What do real quantum computing experiments look like?

Bitcoin is an electronic currency based on math. We will give a brief overview of its history and purpose, then discuss how the technology works. For example, we'll discuss: - the philosophy of money - hashing - digital signatures - Bitcoin mining

People have always asked seemingly impossible questions, like: How big is the earth? How much does it weigh? Do atoms exist? Do electrons exist? In this course, we'll discuss the brilliant and surprisingly simple ways in which these questions were answered.

There are some problems in mathematics that sound simple, but have never been solved by anyone. In this elective, we'll explore what some of these problems are. (Maybe you can solve one!)

Mathematical induction is a method of proving patterns. For example, you can use it to show that adding up the first $$n$$ odd numbers always equals $$n^2.$$ (Try it! The first five odd numbers are 1, 3, 5, 7, and 9. If you add them, you get 25, which is five squared. This pattern continues forever.) While it cannot be applied to every problem, it does have various applications throughout math. In this one-hour session, I'll explain what induction is and how it works. The rest of the time will be spent on a brief tour of examples, touching on algebra, geometry, and puzzles. If time permits, I'll introduce structural induction and context-free grammars.