We will go through the basics of music theory, such as notes on a staff, dynamic markings, rhythms, and chord construction. Absolutely no experience necessary!

This is a competition of sorts. I give you general steps to game design and form teams based on who attends.
Then, I give you a problem to solve and the audience for whom you are designing the game.
Your team designs the game (Section 1)

Your team presents the results (Section 2)


Prerequisites
You can think on your feet and work well in a group. There is no time to lose in unnecessary bickering.

Everybody knows about the wonders of the Renaissance in Italy, the Impressionists in 19th-century France, Picasso, the Dadaists, blah blah blah. But there's a whole other half of European painting that is never given its due: the art of Germany and the Netherlands. In this class, we will explore the greatest painters of all time, from the inventor of oil painting to the most famous painter of them all, Van Gogh, and everyone in between. Bosch, Bruegel, Van der Weyden, Memling, Rembrandt, Vermeer, and many, many more will be explored in depth, charting a trajectory of all the best painters you don't know.


Prerequisites
None.

A quick fun overview of Greek pottery - how it was made, why it was made, and what it represents.

We will do some fun origami projects and some crocheting. Sewing and stuffed animal making.

Do you ever hear about climate change in the news and feel scared and hopeless? It turns out there is plenty of hope and optimism to be found in a number of solutions to climate change!

In this class, we will talk about proposed solutions such as carbon capture and storage, renewable energy, emissions reductions, geoengineering, sustainable development, and hydrogen fuel cells! (note: this list of solutions is subject to change before the actual class) We will discuss the pros and cons of these solutions and obstructions in implementing them.

This class will be part lecture and part discussion. You are invited but definitely not required to participate.


Prerequisites
You will get more out of this class if you have a little background in chemistry and physics (i.e. you have taken 1 year of chemistry and physics), but they are not necessary.

An interdisciplinary overview of aerospace, with particular focus in astronautical engineering. Co-taught by members of Columbia Space Initiative. No prerequisites.

Where will AI take us?
Will humanity survive?


Prerequisites
Would be good to know what a computer is

Students will be introduced to the basics of Chinese pronunciation including tones and pinyin. The students will also learn commonly used phrases and basic grammar structure. We will use calligraphy as an aid to introduce character writing.

What makes a good argument? How can we tell when someone makes a bad argument? Logic plays a role in our daily lives, and we need to use it correctly when listening to the news, talking with friends, and forming our own opinions. It's a great tool when dealing with topics not everyone agrees with, and is an important building block for critical thinking. In this class, we will go over logical fallacies, also known as common mistakes people make when constructing an argument, and how to properly debate ideas. We will also cover basic logic skills, which can be applied to a range a things, from computer science to the law.

We will be critically analyzing and discussing different artworks from different periods and of different media including paintings, photographs, sculptures, etc. This is an interesting opportunity for students to learn how to look at and talk about art. Students are more than welcome to propose artwork for class discussion.


Prerequisites
None

Why are football players kneeling during the national anthem, and why is our president so upset about it?

It all comes down to *property* -- the world's most contentious subject, according to the famous William Blackstone.

*What is property?* Has there *ever* been a universally agreed-upon definition?

From plagiarism to city planning, cultural appropriation to music "sampling" (https://www.youtube.com/watch?v=P2buaOnQ6dc), health insurance to environmental regulation policy, just about every topic involves the concept of property -- the issue is that we do not always agree on what our rights are (or ought to be).

We will examine various examples of property claims and noted philosophers in different contexts, but I encourage you to bring up an issue that you find especially intriguing/complex. Examples: Have you been a victim of plagiarism? Do you firmly believe that your favorite song has every right to sample from an old song without paying the writer?


Prerequisites
This is a discussion-heavy course. The concept of property is contentious and evolving, so I will not be straight-up lecturing you for 2 hours, but there will be a balance.

The self portrait is one of the most remarkable traditions in painting. This course is an overview over the history of that tradition from the Renaissance to the 21st century.

This class is very interactive.
No prior knowledge of art history necessary.


Prerequisites
none

This course is going to be a college workshop designed to make the application process enjoyable! Learn how to make college applications an opportunity to learn about yourself and to set yourself up for a successful future.
Topics of the workshop will include:
Coming up with a college list
Drafting a personal statement
How to write focused supplements
Extra-curriculars

"The sleep of reason produces monsters"
Demons, battles, gore, and giants: enter the world of Goya's mind, imprinted with the horror of Napoleon's invasion of Spain during the Peninsular War.

This course focuses on the works of Spanish painter Francisco Goya. It is very interactive, no prior knowledge of art history is necessary.


Prerequisites
none

The significance of the Hellenistic literary and philosophical tradition and its influence on modern literary movements.

Close analysis of a modernist poem emblematic of the era and a survey of broader modernist themes.

As the danger of xenophobia and isolationism is looming large, we will use this class as an opportunity to examine the evolution of nationalism in a global context. The main theories we will study are Samuel Huntington's Clash of Civilizations and Edward Said's Orientalism. Using those texts as a springboard for discussion, we will investigate the development of the Other in a nationalistic point of view, and how this concept has become more and more threatening as civilizations come into contact with one another in today's world.

Plato, Aristotle, Kant, Sartre: these are familiar household names. But did you ever wonder about who the first philosopher was? Did you know that there was a man whose philosophy centered around acting like a dog? Learn about Thales, Diogenes, Bentham, Nietzsche, and others in this class about the philosophers who had genius and personality.


Prerequisites
None.

Ever wanted to say something other than "babushka" and "vodka" in Putin's mother tongue? If you said "da," then this course is for you!

In this course, you'll learn the Cyrillic alphabet and basic Russian expressions ! Course will include fun cultural facts and short movie clips!
Мы говорим по-русский!


Prerequisites
Some familiarity with the Greek alphabet is recommended, but not required.

Was your favorite movie growing up Hercules? Do you find yourself eagerly awaiting the next Rick Riordan novel? Then you will certainly enjoy this class on all things Greek and mythological!

Graph theory is a relatively young area of mathematics, focused on studying structures that show the relationships among people, places, or objects. We'll talk about two of the first key questions in graph theory, the Königsberg bridge problem and the Four Color Theorem. We'll also explore some applications of graph theory, such as modeling social networks or the spread of information or disease.

Math modeling is how we use mathematics to study open-ended questions about real-world phenomena. What's the best location for a food truck? How does an invasive species affect an ecosystem? How do we clean up space debris? These are all questions that we can start to answer with math modeling. The goal of this class is to introduce you to the modeling process. By the end, you'll have developed models to answer questions about a couple of different scenarios, and you'll know about some of the tools you can use to tackle more significant modeling problems.


Prerequisites
Comfort with basic algebra and a willingness to tackle very open-ended problems.

In order to know how to build secure websites and programs, you need to know the common vulnerabilities and vectors of attack. Time permitting, we'll cover overviews of SQL injection, path traversal attacks/Inclusion Vulnerabilities, Cross-site Scripting (XSS), and buffer overflow attacks.


Prerequisites
Interest in cybersecurity. Some prior experience with computer science ideas (ie. boolean logic etc.) will be helpful, but is not required.

An introduction to the theory underlying the numbers we use in everyday life. Ever wonder why addition works the way it does, or why certain things, like the symmetries of a triangle almost work like addition or multiplication? Come learn group theory then!


Prerequisites
Ability to do addition and multiplication

Finance class

Come learn how to make some mathematical art with pipe cleaners! We'll make models of the hyperbolic plane using a Borromean linkage technique and discuss some of the math behind these things.


Prerequisites
We'll be talking about non-standard math. No technical experience necessary --- only curiosity, a willingness to work with your hands, and enjoy art.

A quick overview of advanced mathematics techniques that are useful in solving advanced physical problems. This course will cover techniques to simplify classes of problems.We will look at change of coordinates and symmetry, Gaussian integrals/ Normal distributions, and if time allows a bit of complex integration techniques


Prerequisites
Some familiarity with Calculus, and complex numbers.

A complex number is called algebraic if it is the solution so some polynomial with rational coefficients. The question remains, are all complex numbers algebraic? The answer, given by Cantor, is a resounding NO. Almost all complex numbers (in a technical sense) are not algebraic, rather, they are transcendental because they "transcend" algebraic definition. However, Cantor's proof does not construct an explicit example. In this class we will undertake the task of constructing explicitly a family of transcendental numbers. On the way, we will prove Cantor's theorem and define a measure of how irrational a number is.


Prerequisites
Some knowledge of differential calculus including the mean value theorem.

The p-adics are an alternate metric completion of the rational numbers. Metric completions will be discussed as will the geometry of p-adic numbers.


Prerequisites
Basic algebra only but be ready to do some proofs.

The basics of number theory focusing on the divisor sum function, the greatest common divisor, and Bezout's identity. The class will culminate with the proof of the Euclid-Euler theorem which gives a correspondence between primes of the form $$2^p - 1$$ and perfect numbers.


Prerequisites
Basic algebra and arithmetic.

This class will be my attempt to do the entirety of an advanced undergraduate course in linear algebra in less than two hours. We will develop the theory of finite-dimensional vector spaces, starting with vectors, linear combinations, and bases. We'll talk about the kernel and image of linear transformations before moving onto isomorphisms and changes of basis. We will introduce eigenvectors, discuss inner products, linear functionals, and the dual space, and finish off with the self-adjoint operators and the spectral theorem.

The goal of the class is to show you a wild ride through linear algebra, and to "give away the trade secrets" of a beautiful subject.

After this class, consider taking my "All of Quantum Mechanics" sequence for a spectacular application of the ideas developed in this class.


Prerequisites
Be ready to move fast. The only strict prerequisite is the basic theory of sets and functions: know what injective, surjective, and bijective functions are. The more math you have seen, the better: mathematical maturity and experience are indispensable tools for appreciating its elegance. It also helps to know how to add.

Further topics in number theory focusing on Euler's phi function and multiplicative order. The class will culminate with the proof of the primitive root theorem which describes the multiplicative structure of modular arithmetic. Applications of the primitive root theorem such as quadratic equations in modular arithmetic and Carmichael numbers will be discussed if time permits.


Prerequisites
Basic algebra and arithmetic. The splash course: "The Most Integral Parts of Number Theory" is required.

In this introductory “math” class, we will “prove” some entirely false results in surprisingly convincing ways. For example, we'll show that 1 is the largest natural number, but that all natural numbers are equal to zero. Come find out why the Pythagorean theorem is a lot simpler than you thought (spoiler: $$c = a+b$$), how all functions integrate to zero, and as many proofs that $$1 = 2$$ as I have time for.

The emphasis will be as much on making math hilarious as on introducing the methods of “proof” that make these results tick—and why they’re wrong.

After this class, consider taking Theo's "Things you Think should be False but Aren't" for some more serious examples of the counterintuitive element in mathematics.


Prerequisites
Standard high-school mathematics up through differential and integral calculus, and familiarity with proof by induction. Come prepared with a confidence about mathematics ready to be shaken!

Using just a compass and straightedge (unmarked ruler), can one trisect a given angle? Construct a square with the same area as a given circle? Construct a cube with double the volume as a given cube? These three compass and straightedge construction problems perplexed the ancient Greeks. As it turns out, these tasks are impossible! In this class, we will find out why this is the case and formalize what constructions are possible.


Prerequisites
None, but knowing what a complex number is could be useful.

A classic joke goes that a topologist is someone who can't tell a coffee cup apart from a donut. We'll talk about what it means for two spaces to be "the same" to a topologist and how we can tell apart spaces that are actually different. We'll study tools like the Euler characteristic and the fundamental group and see how they can be used to study spaces.

Some cool applications of topology that I'll discuss include (but are not limited to!):

If you drop a map on the ground, some point on the map is on top of the point it represents.

There is some point on the Earth with the same temperature and humidity as the point directly opposite it.

Furthermore, there is a point on the Earth with no wind.


Prerequisites
Basic geometry, enough calculus to be comfortable with the word "continuous". A willingness to work with mathematical proofs. Knowing what a group is will be helpful but isn't required.

Mathematics isn't always as it seems. This class will be a melange of mathematical statements that seem utterly false but are indeed true, and others that seem so true but just aren't so.

Don't worry, we won't have any normie examples like Monty Hall or Banach-Tarski.


Prerequisites
David's "False Theorems and Fake Proofs" class would be a nice warmup. No formal prerequisites, but we will do math considerably more serious than the above description might suggest.

When most of us hear "cryptography", we think of code-breaking, spies, or maybe even cryptocurrency. But even though these are the most obvious applications, there are many interesting real-world problems we can solve with the theory of cryptography.

Consider this problem: everyone knows you need two officers with two different keys in order to launch a nuclear weapon. But in the 21st century, no one wants to carry a physical key. So the military goes out and buys a password-protected system to secure the weapons. Unfortunately, the system only requires a single password. How do we "split" or "share" the secret password in a way that both officers are needed to launch the weapon?

Cryptographers call this problem "secret sharing" and with a little bit of math, we can implement it in a provably secure and correct way. We will learn about polynomials over finite fields, Gaussian elimination, the Shamir Secret Sharing scheme, and applications of secret sharing.


Prerequisites
high school algebra

Students will be introduced to the chemical basis of biological processes, with a focus on protein structure and function. Finally, students will learn how protein structures can be used to design novel therapeutic compounds in the fields of pharmacology and synthetic biology.


Prerequisites
High school level biology

The nervous system is a complex network of electrical systems all working in sync with one another. Understanding the signaling and encoding methods that these networks use is the key to unlocking the secrets of the brain's computational power. By tapping into the neural pathways that transmit sensory information, it is possible to influence the actions of the host. In this class demonstration, a cyborg roach is created by implanting electrodes into the roach's antenna nerves. This allows the experimenter to control the movement of the roach via a wireless phone uplink. If you're interested in any branch of neuroscience (or you just want to see a cool experiment), this is the class for you!


Prerequisites
There are live roaches in the experiment, so be forewarned. There is a handout provided containing the ethics statement of altering the roach's nervous system, in case you have any concerns.

Interesting things happen when you are moving really quickly.

In this talk, we will examine Albert Einstein's special theory of relativity (STR). In a nutshell, STR postulates that, depending on your point of view, when moving __very__ quickly (fractions of the speed of light), time slows down and length/distance actually contracts!

In this class, we will prove these ideas out with some basic thought experiments and simple math (elementary algebra / euclidean geometry). By the end of the talk, it should be clear (mathematically) why it is impossible for anything in this universe to travel faster than the speed of light.


Prerequisites
Basic algebra, Basic geometry. $$ v = \frac{\Delta x}{\Delta t} $$

Can the Earth really fit into the Sun more than a million times? How far did New Horizons fly to reach Pluto? Why isn't Pluto a planet?
These are some questions that you will hopefully not only know the answers to by the end of class, but truly comprehend the scales that we have no reference to here on Earth. In one hour, each one of you will create a scale model of the solar system that will give you a new perspective on how you view the solar system. If time allows, we will also discuss how our solar system compares to others nearby and in the grand scheme that is the entire universe.


Prerequisites
A readiness to get your mind blown

A brief introduction to Feynman diagrams for particle physics. Learn how to use Feynman diagrams and their purpose in Particle physics. Learn how, by using fairly simple pictures we can reduce a problem of the form
$$ \int e^{-p_x^2-p_y^2-x^2-y^2 + \Sigma \lambda x^n y^n} dy dx $$
to a few diagrams and a vertex counting schema.


Prerequisites
Don't freak out when you see math, don't worry we wont be doing anything harder than addition

Have you ever been stumped by some of the things that people do? Have you ever wanted to catch your friend lying? Do you want two senior psychology majors to ramble at you for an hour? If yes, then come join us for an introduction to the science and theory of psychology!

Freud once had a theory. Someone told him it was science. It kind of wasn't. We're going to tell you why. Along the way, you'll probably learn some actual psychology.

What do ghosts, astrology, lizard people, mind reading, and alien abductions have in common? They are all strange beliefs that aren't backed by science! But that doesn't mean that your weird aunt who does palm readings is crazy; quite the opposite, actually. There are plenty of reasonable explanations for why people believe in strange things, and we are here to tell you all about them!


Prerequisites
Understand that psychology is a thing that exists.

An intense introduction to the mathematics of relativistic quantum mechanics. This class will introduce Lorentz transformations, relativistic mass-energy, the Klien-Gordon equation (and why it fails), and finally the magnificent Dirac equation. We will show that the odd phenomenon of spin is a necessary consequence of including relativity in quantum mechanics.


Prerequisites
Calculus. Knowing what a partial differential equation is would be helpful. Linear algebra is also essential please take David's courses "All of Linear Algebra" and "All of Quantum Mechanics" if you want an excellent foundation for this class. Some knowledge of basic relativity is helpful but not required.

This course will provide students with a broad overview of the role bacteria have played in human disease and infection. More than that, facets of microbiology which study bacteria in a more holistic sense just might change your mind about this entire class of model organism!


Prerequisites
An interest in learning about biology beyond just human beings!

Have you ever wondered how you get cold sores or why they keep returning? Ever been bitten by a mosquito and thought you could have contracted dengue? Or just curious about whether viruses are dead or alive? Then here's the virus crash course for you! We'll be talking a lot about viruses, their reproduction, vaccines, your immunity against them and how you can prevent viral-related pathology.


Prerequisites
a curious mind and interest in viruses!

Part I of an intense introduction to one of the most ridiculous and ridiculously beautiful physical theories ever invented.

We will cover Hilbert space and quantum states, Dirac's bra-ket notation, observables and hermitian operators, quantum measurement and collapse, the spectral theorem, probabilities and the Born rule, and commuting observables. We will conclude with the Stern-Gerlach experiment as a stunning demonstration of the quantum formalism.


Prerequisites
Linear algebra--the more of it, the better. My Splash class "All of Linear Algebra" should provide good preparation for the math I'll be discussing. No previous experience in physics will be assumed, although it certainly helps to have exposure to some quantum mechanics. Above all, be prepared to move fast.

Part II of an intense introduction to one of the most ridiculous and ridiculously beautiful physical theories ever invented.

We will start with the double-slit experiment, cover quantum wavefunctions, position and momentum eigenstates, the canonical commutator identity, and conclude with a derivation of the Schrodinger equation.

This class is not to be taken without first taking Part I of this sequence! After this class, consider taking Ben Church's and Ryan Abbott's "Relativistic Quantum Theory" for a serious introduction to relativity of quantum mechanics.


Prerequisites
Linear algebra and single-variable integral and differential calculus, plus some familiarity with complex exponentials. My Splash class "All of Linear Algebra" should provide good preparation for the math I'll be discussing, and Part I of my "All of QM" sequence provides all of the quantum-mechanical prerequisites I'll be assuming. Be prepared to move fast and to have your mind blown.

What's the deal with spin? How can an electron only be "spin up" or "spin down" when space is three dimensional? In this class we will cut past the confusing analogies and jump right into the math! We'll talk about spin states, Schrödinger's equation, Pauli matrices, and the dank topology lurking right beneath the surface! Bring paper and pencils!


Prerequisites
Absolutely must know about complex numbers, including Euler's formula. Knowledge of matrices will be very helpful, but not required.

The Milky Way Galaxy is a complex system of stars, gas, dust and dark matter. How many stars are there? What does the Milky Way do with all its gas? What the heck is dark matter? And where the heck did it all come from! The answers to these questions work together in a fantastic and mesmerizing way to eventually create a system capable of supporting life. Come and learn about all the things that keep the Milky Way shining and spinning!


Prerequisites
Basic algebra and an understanding of some physics and higher math will lead to a deeper understanding but isn't necessary to get something from the material.

Remember the movie GATTICA from biology class? Gene-editing and personalized medicine are rapidly moving forward. This class will focus on what CRISPR Cas9 is, and its applications in modern medicine.


Prerequisites
Basic knowledge of genetics would be helpful, but not required

Ever seen the ingredients in Diet Coke and wondered what potassium benzoate was used for? Or why Subway eventually phased out azodicarbonamide in their bread? You'll find out in this class!


Prerequisites
Basic knowledge of chemistry and biology.

This course will review some of the basics of neuroscience. We'll focus on how the senses work. Then we'll cover some of the more modern findings and techniques in neuroscience. Including: addiction, learning, movement, optogenetics, mouse genetic engineering and fluorescent proteins.


Prerequisites
Basic (non-AP) biology, including genetics and neuroscience is desired.

We can model lots of things in the world as a collection of particles -- air, magnets, and even light! Statistical mechanics is a tool physicist use to understand complex systems from the air around us and stars to Bose-Einstein condensates and Fermi gases. We'll go through the microcanonical and canonical ensemble models and try to derive basic thermodynamics, the ideal gas law, and the Stefan-Boltzmann law!


Prerequisites
Solid understanding of algebra required. Exposure to calculus, probability, high school chemistry, high school physics recommended.

OPTION PLAY is a card game that helps players transition to college, but can also be a tool for players to learn about social cues and tolerance.


Prerequisites
Enjoy playing games.

Discussion on Marriage/Relationships from Old & New Testament


Prerequisites
Smiles and Interest

If you’re going through a tough time, dealing with a mental illness, or struggling with any problem, it’s important to be able to cope in healthy ways. This class will give you a chance to learn some new, healthy coping skills or strengthen the ones you already have. We’ll talk about *and try* things like mindfulness and yoga, making art, laughing, helping others, writing, socializing, and reaching out to resources. (note: these might not be the exact things we do) There are many ways to take care of yourself in a positive way, and this class will cover just a few. Not every technique will work for everyone, but hopefully you’ll come away from this class with a new skill to add to your toolkit! (Note: participation in all activities is optional, and I would never force you to do something that's uncomfortable for you!)

“Did you hear that?”
“No, what?”
“That sound, like an authority figure trying to tell me what to do.”
“Are you okay?”
“How can I be okay when the world is conspiring against me!?”
Have you ever felt like you were being lied to or cheated by the government? Have you been called crazy by your friends for sharing with them your entirely valid concerns? Do you not believe in any conspiracy theories but find them interesting/thought-provoking/hilarious? Then this is the class for you! We will go over a bunch of mainstream (and far off the mainstream) conspiracy theories, but be mindful; not all the theories we’ll talk about are real, so listen carefully to pick out the internet favorites from the ones we just made up! We will also bring food, because, as we all know, handing out free food is the best way to make people listen to you (just add a colosseum and it will be like Ancient Rome). So come learn what the people screaming on the streets are all about! Or maybe we’ll just drain your souls and use your bodies as puppets to serve our own nefarious purposes -- you really can’t be sure.

Yay! This is the third semester that the Marvel-series will be taught. This means we've completed a "trilogy" :)

This time, we won't be watching clips or discussing science. We also won't be discussing "ideas" and the abstract morals of the Marvel Universe. This is the real deal. This class is a jeopardy game meant to show-off your Marvel skills.

Scope: from Phase I - Phase III. May include recent releases of Inhumans, Sony-related Marvel movies and Netflix-owned Marvel shows (Daredevil, JJ, Luke Cage and the Immortal Iron Fist, sworn defender of Kun-lun)

*Jeopardy will be done in pre-assigned groups* (8 groups of 5)


Rewards include bragging rights!

If you've been a previous student, please, please consider joining the class!

In Newark, it's illegal to sell ice cream after 6pm without a doctor's note.
Silly string is illegal in Marlborough.
Arkansas man head-butted his mother. Twice.

In this class, you can learn all about weird laws like this, which exist in cities everywhere in the country. And then we might talk about some criminals that have gotten into some... unlucky situations. People are fascinating creatures, after all.

Break down the enormous concept of "public health": What is it? What factors affect it? Who are the key players? What does it mean for the public to be healthy? What are our biggest public health problems in the U.S.? Most of all, how do we go about trying to fix them?

The book, not the movie

The average person will spend 80,000 hours of their adult like working. That is a lot of time that could be put to good use for yourself, your community, and the world. The website 80000hours.org has collected extensive research and interviews to determine what makes people happy with their job choices and their impact on the world. We'll go over that work to help you think about how you want to spend your 80,000 hours.

Fountain pens may seem like a thing from the days of yore, but they are making a real comeback! Whether it’s about being steampunk, #calligraphy on Instagram or whatever you kids do these days, a myriad of benefits come with using a fountain pen. It can not only help you have neater handwriting but some evidence even shows it can help your self-esteem and raise your academic performance. In class, we will cover the basic parts of a fountain pen, the common variations you might come across and some writing techniques. I will provide some cheap fountain pens for you to try out and play around with.


Prerequisites
Absolutely no prior experience necessary!