College-level mathematics can broadly be divided into three categories: analysis, algebra (not like high school algebra), and geometry (not like high school geometry). In this class I hope to give you a taste of abstract algebra, a preview of what you might expect in a first college algebra course (sets, rings, fields, groups, categories). Due to time constraints I'll aim to give the shallowest possible treatment while still conveying the flavor of and my appreciation for each topic. That being said, I'll also be providing lots of (optional) problems and resources for you to explore at your leisure. Each class will be 90 minutes long, split into three 30-minute "modules". The third of these will either be an extension module, or "unstructured time" where I'll take any questions or e.g. provide some fun problems to think about. In either case, this is completely optional, but it will probably be a little less difficult and also more relaxed and fun! Unfortunately, due to the structure of the class, it will be quite difficult to keep up if you miss a day, but I'll still try my best to keep the classes independent of each other. I will also make available the notes for each week of class which you can reference just in case. Please email me if you have any questions about the course!

Does human behavior sometimes confuse you? How do people think about thinking, and how can we get better at it? We’ll start this class by learning clearer, more precise vocabulary to describe our world and our perceptions of it. But we’ll also see that our brains themselves are imperfect instruments, so we’ll develop strategies to correct for it. Finally, equipped with a better understanding of how our brains can work for (or against) us, we’ll discuss how to become better calibrated in decision-making and navigating the world.

Abstract algebra is one of the first "advanced" courses that pure math majors are required to take. It's a huge subject with many beautiful facets, so the goal of this class is merely to give you as many glimpses as I can of the prettiest things I know of. It will be quite hard (see prerequisites), but I hope that I can convince you to continue studying math in your future. [schedule/class structure forthcoming] Pure math ("college math") is very different from high school math, and even competition math (if you're familiar with this), in a number of ways. The main thing I want to convey is that math is not very different from hard sciences, in that you're building up mental models of how things "should" behave, and then checking if that matches up with reality. (Unfortunately, this is the sort of thing that you can only really understand after having taken a few courses... I hope this counts as one of them.) Think of math as a huge [civilization, computer, dragon, any fascinating object of your choice], and your study of math as just understanding "how this thing works". A few notes: 1. The exact nature of "how this thing works" is very personal -- though we have a common language for describing common parts, everyone has very different pictures in their own head (this is partly why I love math so much!) 2. The kind of thinking in high school math (calculations, solving problems) can be helpful, but ultimately they're just a tool to help you understand how this thing works.

You may have heard of topology as the branch of math where "a donut is the same as a coffee cup" -- we'll be learning precisely what this means, and more. One of the biggest hurdles will be understanding exactly what we mean by "same". Grappling with this question will lead us to explore the idea of an "invariant", one of the main themes of topology. There will be lots of pictures.

How do scientists analyze language? How do babies learn languages? Do you want to become more aware of your tongue? Come learn about all the things about language you already technically know but don't even know you know!

Come solve puzzles with us! These aren't jigsaw puzzles though - think secret messages in the style of The DaVinci Code, National Treasure, or 39 Clues. If you like finding patterns, decoding ciphers, logic puzzles, or leaps of intuition, there's probably a puzzle for you!

How do we think about our own thoughts, and how confident should we be in our beliefs? We'll see how our brains are imperfect instruments and how we can improve our self-calibration.

You've probably heard that topology is the branch of math where "you can't tell a coffee cup and donut apart". We'll start with a short discussion of different infinities, define homeomorphism (a tool for "telling things apart") and define homotopy equivalence (a more complicated tool for "telling things apart"). We'll be using quite a few symbols, but I'll define them as we go and you won't need to understand them to understand the geometric idea.

How much of organic chemistry do you think can be covered in 2 hours? How about all of it..? - at least that's what we'll try! From the basics of classes of compounds and simple reactivity to total synthesis, all will be covered in this Clais(s)-en condensed form.

Learn how to use logical reasoning to decipher the words and properties of different languages! First we'll go over the general process of solving a NACLO puzzle and how to organize your thoughts while doing so. Then you'll have the opportunity to solve different puzzles of your choice! No prior linguistics knowledge is required!

Does human behavior sometimes confuse you? How do people think about thinking, and how can we get better at it? We’ll start this class by learning clearer, more precise vocabulary to describe our world and our perceptions of it. But we’ll also see that our brains themselves are imperfect instruments, so we’ll develop strategies to correct for it. Finally, equipped with a better understanding of how our brains can work for (or against) us, we’ll discuss how to become better calibrated in decision-making and navigating the world.

Come solve puzzles with us! These aren't jigsaw puzzles though - think secret messages in the style of The DaVinci Code, National Treasure, or 39 Clues. If you like finding patterns, decoding ciphers, logic puzzles, or leaps of intuition, there's probably a puzzle for you!

How do scientists analyze language? How do babies learn languages? Do you want to become more aware of your tongue? Come learn about all the things about language you already technically know but don't even know you know!

Want to think about problems that seem impossible? In this class, we'll examine some famous paradoxes that stumped history's greatest scientists, and try to understand them ourselves. A healthy interest in learning physics required - but you don't need to know anything yet!