The laws of physics work perfectly if you play time backwards, but this flies in the face of our everyday experience. Your headphones come out of your pockets tangled, but never perfectly rolled up; a drop of dye spreads in water, but never re​-​concentrates itself. In this course, we will explore why this happens, showing that it arises purely from statistics and probabilities rather than some fundamental force. Eventually, we will discover a specific quantity called "entropy", arguably the most important number in your life.

In this class, we will learn about methods of encrypting and deciphering secret messages. First, we will introduce simple methods of encryption and learn why you wouldn’t want to use these to protect your bank account information! Then, we will explore modern cryptography, discussing the motivation for developing certain methods (like public key cryptography) and the mathematics underlying them. While you will be able to break simple encryption schemes using just pencil and paper, modern cryptography often can’t be broken without extremely powerful computers or the invention of new math. We’ll see that being good at solving puzzles turns out to be extremely useful in cryptography.

The laws of physics work perfectly if you play time backwards, but this flies in the face of our everyday experience. Your headphones come out of your pockets tangled, but never perfectly rolled up; a drop of dye spreads in water, but never re​-​concentrates itself. In this course, we will explore why this happens, showing that it arises purely from statistics and probabilities rather than some fundamental force. Eventually, we will discover a specific quantity called "entropy", arguably the most important number in your life.

In this class, we will learn about methods of encrypting and deciphering secret messages. First, we will introduce simple methods of encryption and learn why you wouldn’t want to use these to protect your bank account information! Then, we will explore modern cryptography, discussing the motivation for developing certain methods (like public key cryptography) and the mathematics underlying them. While you will be able to break simple encryption schemes using just pencil and paper, modern cryptography often can’t be broken without extremely powerful computers or the invention of new math. We’ll see that being good at solving puzzles turns out to be extremely useful in cryptography.

Given a competitive scenario, how do we develop the best strategy to win? This simple question gives rise to surprisingly useful ideas and insights in the field of game theory. It turns out that many real-life situations can be modeled as “games,” giving this branch of mathematics a wide range of applicability in biology, psychology, and economics. In this class, we will directly engage with the ideas of game theory by playing a few games to get a feel for why the best strategies work. We will discuss the reasons that abstract reasoning in math turns out to be useful, as well as explore the ways that studying games can help us understand the real world.