Splash Spring 18
Course Catalog


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Arts Engineering
Humanities Lunch
Math & Computer Science Science
Walk-in Seminar Miscellaneous
History


Arts

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A620: When You Build It Will It Play?
Difficulty: **
Teachers: Genevieve Griffin

You are going to be a member of a team, and this team will design a game.
I will describe a problem, tell you how the success of the game will be judged, who your audience will be, and provide a few props. If enough people enroll there will be two teams and bit of competition.


Prerequisites
Love of math or science appreciated Team experience Have played Settlers of Catan, or something similar

A674: 100+ years of Crazy Artists
Difficulty: **
Teachers: Runyang Zhang

This class will be covering a series of 4 interconnected movements from the nineteenth to twentieth centuries: romanticism (think Frankenstein), symbolism (think nightmares), expressionism (think the Scream), and abstract expressionism (yes, you can finally learn more about Jackson Pollock!).
In summary, this course will cover some of the most neurotic, yet brilliant artists in the recent history of art.

A639: Short Introduction to Taiko: Japanese Drumming
Difficulty: *
Teachers: Kohtaro Yamakawa

Taiko is a Japanese art of drumming that emphasizes body movement and energy. I am an active player in Taiko, and have been playing for 9 years, having been trained by many great sensei including Hayashi Eitetsu, Kenny Endo, Ryouta Kataoka, and Yoko Nakahashi. We will be exploring the introductory types of Taiko, including all the different types of drums and songs and elements of Japanese culture. Students will be allowed to explore various elements of rhythm, sound, and culture in an overall fun experience! We will end the class with a performance from the group so that students will be able to see what an accumulation of all the different songs may amount to.


Prerequisites
Wear comfortable clothes, bring water bottle and perhaps ear plugs for sensitive ears (I will be loud, you will be loud, everything will be loud) Drums and bacchi (drum sticks) will be provided.

A660: Why Your Favorite Color Should Be Red
Difficulty: **
Teachers: Kristian Woerner

This course will cover a wide range of topics related to the color spectrum, including the etymology of color names, the meanings and implications of certain colors throughout history, the political associations with color, and the use of color as an artistic medium and design strategy. You'll feel blue if you miss this course!

A670: From Van Eyck to Van Gogh: All Northern Art
Difficulty: **
Teachers: Adam Elkhadem

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.


Engineering

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E693: Intro to Optimization
Difficulty: **
Teachers: Isabel Wang

Ever wondered what's the best way to model your system so that you can find a solution to maximize profit or minimize cost while sticking to your constraints? How should you design the best transportation network? Answering these kinds of questions is both an art and a science! If such problems pique your interest, this is the class for you.


Prerequisites
Pre-algebra

E619: Intro to Space Exploration

An interdisciplinary overview of aerospace, with a particular focus in astronautical engineering. Co-taught by members of Columbia Space Initiative.


Prerequisites
Some experience with physics, chemistry, algebra, geometry.

E634: Introduction to Civil Engineering

This course will offer an overview of civil engineering including the sub-disciplines of this field, roles and responsibilities of a civil engineer, and project considerations. The class will culminate with a mini-group activity in which students will take on the role of civil engineers.

E635: Lasers: A Materials Science Perspective
Difficulty: **
Teachers: Benjamin Miller

This course will bring to light how lasers work. Further, the history behind lasers will be illuminated. Finally, applications of lasers will be highlighted.

E712: Intro to Virtual Reality Full!
Difficulty: *
Teachers: Amita Shukla

Using Google Daydream devices and Unity, cover the basics of creating an Android app in virtual or augmented reality.


Prerequisites
None

E667: Introduction to Architectural Drawing
Difficulty: *
Teachers: Mackinley Wang-Xu

While the digital age has ushered in an era where architecture drafting is primarily performed on a computer. It is still important for aspiring architects to be able to draft by hand. This class will teach the basics in architectural drafting; You will learn different types of drawings such as plans, elevations, and sections. You will be thinking spatially like architects in no time!

E668: Introduction to Signal Processing
Difficulty: ***
Teachers: Lester Fan

This course aims to cover the key ideas of the signal processing techniques used to drive technologies such as WiFi, radio, and the Internet. To that end, the concept and applications of the Fourier Transform will be introduced, and supporting demonstrations will be given. Basic Python programming will also be covered to introduce students to a key programming language and so that students may play around with the material on their own.


Prerequisites
Knowledge of complex numbers. Some Calculus and Programming experience are recommended by not required.


Humanities

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H675: Color!!!
Difficulty: **
Teachers: Runyang Zhang

This course will discuss a few artists who made notable innovations in the artistic use of color: Turner, Blake, Monet, Van Gogh, Matisse, Kandinsky, Rothko, and Agnes Martin.

No prior knowledge necessary. Come see colorful pictures!

H662: (Lecture) Obsession and Dissatisfaction: Philosophy of Crushes, Voting, Poetry, Regret, and everything in between. Full!
Difficulty: **
Teachers: Emily Flahive

(This is the lecture version of this class. See "(Discussion)..." for the smaller, conversation-focused version)

Can we ever be satisfied?

We all have (seemingly irrational) obsessions from time to time:
- A “dream school”
- A crush you can’t get out of your head.
- A song you've been playing on a loop for hours.
- A belief that's unshakable, even when it seems irrational.

We try to justify ourselves, while feeling hopeless under an all-powerful idea that is holding us captive.

We will study the philosophy of Kant, Plato, Rousseau, Hobbes, and more, to try to answer questions like:

- Does "love at first sight" really exist?
- How is thinking different from and similar to feeling?
- Can you talk yourself into or out of love?
- Can we control what or whom we desire?
- Are we ultimately in love with ourselves?
- Am I falling in love with these philosophers (you might, honestly, and I'd be the *last* person to judge you), or the beauty of their words?


My goal is not to tell you *what* to think, but to provide you with passages to meditate on and a space for you to practice exploring abstract ideas and questions.

H673: Impressionism and Paris
Difficulty: **
Teachers: Runyang Zhang

This course will be a survey over a few of the most well-known impressionists: Manet, Monet, Degas, Caillebotte, and Renoir.
We will discuss themes like new ways of seeing and new patterns of urban life in the city of Paris during the late nineteenth century.

No experience required. Come see colorful pictures:)

H711: What is Philosophy Anyways? Full!
Difficulty: *
Teachers: Hayden Kajercline

When most of us hear the word "philosophy" we think of mysterious bearded men from two thousand years ago. But philosophy is not just a historical artifact -- professional philosophers today continue to ask the hard questions, and do their best to answer them.

In this introductory course we will examine the sorts of questions philosophers ask, the methods of reasoning and argumentation they use, and the value of philosophical inquiry in the real world.

H690: From 'Attack on Titan' to 'Spirited Away': Religion in Japanese Pop Culture
Difficulty: **
Teachers: Sinai Cruz

This course will first introduce students to the basics and history of Japanese religious traditions, focusing on Buddhism, Shintoism, and Christianity. Then, students will study how aspects of these religions pop up in Japanese animation, comics, and video games. By the end of the course, students will become more knowledgeable consumers of Japanese pop culture. Whether you're a long-time fan of Japanese anime or manga, or whether you're just starting out, this course is for you!

H677: Surrealism
Difficulty: **
Teachers: Runyang Zhang

Do you want to know more about Surrealism than just Dali's Melting Clocks?

In this course we will explore Surrealist paintings by Dali, Ernst, Magritte, de Chirico, Miro, and Frida Kahlo (although she didn't really consider herself a surrealist). We will also look briefly at Surrealist film, photography, and sculpture.

No experience necessary, just come look at weird art:)

H691: Dead Poets Society
Difficulty: *
Teachers: Ali Keith

Carpe diem! Explore the intersection of music, language, and history through Latin poetry! Learn about various poetic forms and their place in ancient Rome and discover the relationship between meter and language processing that transcends time! (No Latin knowledge necessary)

H663: (Discussion) Obsession and Dissatisfaction: Philosophy of Crushes, Voting, Poetry, Regret, and everything in between. Full!
Difficulty: **
Teachers: Emily Flahive

(This is the smaller, conversation-focused version of this class. See "(Lecture)..." for the larger class.)

**Can we ever be satisfied?**

We all have (seemingly irrational) obsessions from time to time:
- A “dream school”
- A crush you can’t get out of your head.
- A song you've been playing on a loop for hours.
- A belief that's unshakable, even when it seems irrational.

We try to justify ourselves, while feeling hopeless under an all-powerful idea that is holding us captive.

We will study the philosophy of Kant, Plato, Rousseau, Hobbes, and more, to try to answer questions like:

- Does "love at first sight" really exist?
- How is thinking different from and similar to feeling?
- Can you talk yourself into or out of love?
- Can we control what or whom we desire?
- Are we ultimately in love with ourselves?
- Am I falling in love with these philosophers (you might, honestly, and I'd be the *last* person to judge you), or the beauty of their words?


This class is far from a lecture. My goal is not to tell you *what* to think, but to provide you with passages to meditate on and a space for you to practice exploring abstract ideas and questions. I provide just enough structure--with passages from different philosophers to give you ideas to think about--to facilitate a conversation.

H709: Theories of Justice: Intro to Moral Philosophy and Ethical Reasoning Full!
Difficulty: **
Teachers: Enrique Olivo

This course is an introduction to moral and political philosophy. It will briefly explore classical and contemporary theories of justice, and apply these theories to several "case studies" through a discussion-based lecture (or debate-based lecture depending on how you view it!). Authors we will discuss include John Rawls, Jeremy Bentham, and Plato.

The course invites students to subject their own views on certain moral controversies through these case studies.


Prerequisites
None - even if you didn't recognize any of the authors in the course description, this course is open to all students interested in the subject of moral philosophy.


Lunch

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L719: Lunch Period
Difficulty: None
Teachers:

Enjoy a break for lunch with your friends! Please register for at least one lunch period on each day of the program.


Math & Computer Science

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M664: Network Security: Malware overview & analysis Full!
Difficulty: **
Teachers: Crystal Ren

An overview of malware especially in the context of network security will be covered. Traffic analysis, how firewalls and ids work, types of malware commonly seen and analysis methods will be covered as well.


Prerequisites
Interest in security; preferably some knowledge of computer networks.

M623: How to (Mathematically) Guard an Art Gallery
Difficulty: ***
Teachers: Jessie Oehrlein

Suppose you had a polygonal art gallery with $$n$$ sides that you wanted to guard with 360-degree cameras at some of the polygon's vertices. What is the least number of cameras you could use? This is the classic art gallery problem, and it uses a lot of basic concepts in the mathematical field of graph theory. We'll cover some basic graph theory concepts and then tackle the art gallery problem!


Prerequisites
Comfort with use of variables.

M715: Quadratic Reciprocity
Difficulty: **
Teachers: Anton Wu

One of the crowning theorems of elementary number theory, the study of natural numbers, is quadratic reciprocity. It is a result about the remainders when you divide perfect squares by primes; it is among the most elegant I have ever seen. Fortunately, it also happens to be very accessible. We will sketch a proof of this theorem assuming no more than arithmetic.

M655: Fractal Fundamentals and Chaos Theory
Difficulty: **
Teachers: Amanda Liu

Come explore the both the visual and mathematical beauty behind fractals! Discover the basics of the laws that return order from chaos in the forms of strange attractors in dynamical systems.


Prerequisites
Algebra. Calculus would help, but not necessary to follow along.

M678: Intro to Machine Learning Full!
Difficulty: *
Teachers: Amita Shukla

Intro to what ML is, and walkthrough of how to draw interesting conclusions from datasets with Microsoft Azure Machine Learning Studio, a free online tool.


Prerequisites
None

M643: Secret Sharing and Cryptography Full!
Difficulty: **

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

M669: Simply Symplectic (Geometry)
Difficulty: ***
Teachers: Theo Coyne

Symplectic geometry is a branch of differential geometry that has its roots in classical mechanics (specifically Hamiltonian mechanics) because of its usefulness in describing the phase space of a mechanical system. In this class, we will explain and motivate the basic notions of symplectic geometry, with a view towards the relevant physics. Time permitting, we will also cover some basic theory of symplectic embedding problems.


Prerequisites
Basic calculus (derivatives and integrals) is required. Some knowledge of Newtonian mechanics will be helpful, but is not required.

M666: Congruent Numbers and Elliptic Curves
Difficulty: ***
Teachers: Michael Tong

In an anonymous Arab manuscript from the year 927, the following question is posed: given a squarefree integer $$n$$, does there exist a rational number $$a$$ such that $$a-n, a, a+n$$ are all squares of rational numbers? The examples 5 and 6 were known to the Arabs, and later Fibonacci discovered that 7 was a congruent number. In the other direction, Fermat proved that 1 was not congruent -- this is equivalent to his famous Last Theorem in the special case that the exponent is 4. However, to this day, there is no algorithm for this problem in general.

Many advances on this problem were made using the theory of elliptic curves and, under the assumption that the Birch and Swinnerton-Dyer conjecture is true (a current Millenium Prize Problem), there is a fast algorithm to determine whether a given integer is congruent.

This class will first attack the congruent number problem using elementary methods, and then discuss how elliptic curves come in.


Prerequisites
Understanding of group theory (in particular, rank of finitely generated abelian groups). Familiarity with elliptic curves and power series will make you more comfortable, but are not strictly necessary.

M650: False Theorems and Fake Proofs
Difficulty: **
Teachers: David Grabovsky

In this introductory “math” class, we will “prove” some entirely false claims 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: $$c = a+b$$), why all functions are equal to zero, and why $$1 = 2$$. (I'll offer as many proofs of this "fact" as I have time for!)

The emphasis will be on making math ridiculous and funny, as well as on discovering what really makes standard methods of proof tick. Come ready to participate!


Prerequisites
Familiarity with proof by contradiction and by induction, as well as single-variable differential and integral calculus. Come prepared with a confidence about math ready to be shaken!

M676: P vs NP
Difficulty: **

With faster computers, better algorithms, and innovation in AI, machine learning, deep learning, and quantum computing, it seems like computation can instantly solve almost any problem in logistics, mathematics, and even society. But what if some problems are simply too time-consuming to solve?

Despite all the progress in computer science, we have failed to find fast algorithms for many interesting problems. However, some of these problems share an intriguing property: once you do find an answer, it is easy to verify. Does this help us solve them? Surprisingly, despite decades of work and a million dollar bounty, no one knows. This is the famous P vs NP problem.

In practice, we generally assume P != NP, so if P = NP, the computational world would be turned on its head. Though some useful tasks would suddenly become easier, encryption would be impossible. Even mathematics itself might be at risk. Come learn the basics of computational hardness and the surprising utility of hard-to-answer questions.

M631: Constructible Regular Polygons and Galois Theory
Difficulty: ***
Teachers: Benjamin Church

The ancient Greeks asked a simple question, what shapes could be geometrically constructed using nothing more than a compass and a straightedge? Quickly it was discovered that equilateral triangles, squares, regular pentagons, regular hexagons could all easily be constructed. But then progress came to a screeching halt. Constructing the regular heptagon eluded mathematicians for a thousand years until Gauss proved its impossibility in 1796. Better still, Gauss proved the incredible theorem: a regular n-gon can be constructed if and only if $$ n = 2^k \cdot p_1 \cdot p_2 \cdots p_r$$ where the numbers $$p_i$$ are primes of the form $$p_i = 2^{2^m} + 1$$ (known as Fermat primes). The proof of this fact will lead us to the development of Galois theory, one of the greatest developments in modern mathematics. This two millennium old problem will bring us face to face with an unsolved problem in modern mathematics: are there infinitely many Fermat primes? Equivalently, as Gauss showed, are there infinitely many constructable odd-sided regular polygons?


Prerequisites
Familiarity with complex numbers and Euclidean geometry. Knowing what a group and a field are would be helpful but is not required.

M654: Exploring Machine Learning in our Everyday Lives
Difficulty: **
Teachers: Monica Chan

Come join us for an engaging introductory workshop to machine learning, as we delve into a couple of examples from our everyday lives to explore the power of data science.


Prerequisites
Basic algebra and TONS of interest and excitement ;)

M649: All of Linear Algebra
Difficulty: ***
Teachers: David Grabovsky

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 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.


Prerequisites
Be ready to move fast. Be familiar with sets and functions: know what injective, surjective, and bijective maps 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.

M657: Counterexamples That Will Ruin Your Faith in Calculus
Difficulty: **
Teachers: Micah Gay

Coming up with a counterexample is one of the easiest ways to disprove a statement in mathematics (provided that it is, in fact, false). In this class, we will develop our arsenal of counterexamples to destroy ideas in calculus that you really wished were true, and try to salvage what we can.


Prerequisites
Knowledge of basic calculus will be very helpful

M610: Bayesian Statistics and Applications
Difficulty: ***
Teachers: Arnav Sood

Many interesting math problems aren't solved under certainty; for example, estimating asset returns, navigating a robot, and detecting spam email.

One way to approach these problems is with a class of methods named for Thomas Bayes, which give us a rigorous way to work with uncertainty and new information (which may itself be of variable or unknown quality).

We'll study those methods and applications in this class.


Prerequisites
Curiosity is the main one. The class will be easiest for those who know some probability and statistics, and who are used to following math arguments. It'll probably be really hard for people who don't know algebra.

M656: Painless Differential Equations
Difficulty: ***
Teachers: Amanda Liu

Diffeq doesn't have to be diffeqult! Together we'll explore different cases, concepts, and problems. Come learn to solve linear differential equations the quick and dirty way.


Prerequisites
Calculus

M698: The Most Important Theorem in Math: The Fourier Inversion Formula
Difficulty: ***

We start by building intuition and proving formulae for Fourier series as well as the Fourier transformation and the Fourier inversion theorem. We then use our intuition to generalize our notion of the Fourier transform. Then, we delve into the numerous applications of the Fourier transform, including solving differential equations, signal processing, and the Riemann-Zeta function. We culminate with an exploration of the fundamentality of the Fourier transform to the Uncertainty Principle and Quantum Field Theory.


Prerequisites
Single Variable Calculus (know it very well). It will be also helpful to have familiarity with Complex Variables and Linear Algebra

M629: Dynamical Systems
Difficulty: ***
Teachers: Dean Parker

A dynamical system is a group of equations which an be used to describe a variety of physical events, such as motion or population. The defining feature of these is that the change over time is dependent on other factors (for example, birth rate is dependent on the current population). The best part is that these complex equations cannot always be solved, but a lot of information can still be taken from them! If nothing else, come look at the neat pictures these systems generate when graphed.


Prerequisites
Algebra, Knowledge of matrices, Calculus would make things easier, but can be explained when needed

M688: Knot Theory: An Introduction
Difficulty: **
Teachers: Yi Wang

Knot theory is a burgeoning branch of mathematics which has numerous applications to modern topological and geometric problems. In this class, I will define a mathematical knot, draw numerous examples of knots, define what makes a knot the "same" as another knot, and introduce some ways of distinguishing knots from others.

M687: Why the Earth is Flat: An Introduction to Manifolds
Difficulty: ***

In the past couple years, the "flat earth" conspiracy theory has seen a rise in publicity. In a way, this theory is actually true! Locally, the Earth is "the same" as a flat plane. In this class, we will introduce students to concepts of topology, continuity, homeomorphism, and finally define and give numerous examples of manifolds.


Prerequisites
A grasp of set theory and knowledge of algebra (particularly of continuous functions). Calculus will be helpful, but is not required.

M697: Intro programming (newb friendly) Full!
Difficulty: *
Teachers: Nathan Bendich

Stuff they don't teach until too late in college, made simple

Come learn how to 1) get a job, 2) make things other people like


Science

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S612: The Gut Microbiome
Difficulty: **

Students will be introduced to recent discoveries on the impact of the gut microbiome on human metabolism. We will go over basic techniques to assess the microbiome, and explore current efforts in scientific research to take advantage of this emerging area. This will include synthetic biology, cell biology, and bio-engineering.


Prerequisites
High school level biology

S651: Why People Believe Weird Things: An Introduction to Anomalistic Psychology
Difficulty: **

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.

S659: Superfluid Helium
Difficulty: ***
Teachers: Noah Miller

I probably shouldn't teach this class, but what the heck. I'll try to explain some of the awesome properties of super fluid helium starting from first principles. It's a liquid at absolute zero, for starts, and can flow without any viscosity! And that's not even mentioning the quantized vortex lines...

If you know about calculus and complex numbers, that'd be very helpful. I don't expect you to know quantum mechanics, but that would awesome if you did. Hopefully this course should be fun, but take it at your own risk.


Prerequisites
Knowledge of calculus and complex numbers would be quite nice

S645: Autism Spectrum Disorders 101
Difficulty: **
Teachers: Stella Kyprianou

Discuss what is Autism Spectrum Disorder, what are the characteristics, possible causes and current interventions. Most importantly we will discuss how we can create a society of awareness and acceptance!


Prerequisites
n/a

S695: Debunking Toxins: Therapeutic Powers of Venom
Difficulty: **

What do you think of when you hear the word “toxins”? For some it makes them cry in fear and others may think of the “detox cleanse diet.” In reality, however, toxins are much more than just harmful. In this class we will explore the medicinal use of toxins, which include treating chronic pain, hypertension, diabetes, and cancer. We will also explore the many types of venomous and poisonous animals and hear about the current research done in the field of medicinal toxins!


Prerequisites
Basic understanding on cells and neurons is helpful, but not required. Excitement about science is heavily encouraged.

S653: The Evolution of the Universe: From Galaxies to Planets
Difficulty: **

In this course we will explore the physical mechanisms that drive both galaxy and planet formation, albeit on different scales. We will look at physical theory, astronomical observation, and, of course, some stunning pictures, to help paint a story about how the universe evolved to look like how it does today. At the end of the course, we will have all learned just a bit more about our place in this magnificent universe.


Prerequisites
No formal prerequisites, however, the more advanced knowledge of physics, and math that you have, the more you will be able to get from the lecture. We will keep the material on an intermediate level but will accept questions on all levels.

S717: Modern Neuro Crash-Course: The Senses
Difficulty: ***
Teachers: Rachel Mikofsky

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: optogenetics, mouse genetic engineering and fluorescent proteins.

There will be some overlap with the other Modern Neuro course.


Prerequisites
Basic (non-AP) biology, including genetics, any neuroscience is a bonus.

S680: Organic Chemistry through the Lens of Rings Full!
Difficulty: ***
Teachers: Justin Wong

This lecture introduces students to the language of Organic Chemistry through an in-depth discussion of ring structures. Specifically, we will explore pericyclic reactions (sigmatrophic rearrangement, electrocyclic., and cycloaddition). Students should expect to gain a deeper understanding of molecular orbital theory, and the principles and methods used in organic synthesis


Prerequisites
AP Chemistry or the equivalent: contact instructor with any questions.

S624: Way Too Much General Relativity to Fit in 3 Hours
Difficulty: ****

A mathematically rigorous introduction to general relativity, Einstein's legendary theory of gravity. This class will explore the motivation behind geometric curvature and its connection to gravity. Topics will include: the basic theory of manifolds and differential geometry, geodesics, the Einstein Field Equations, Black Holes, Gravitational Waves, and (time permitting) the cosmological constant and models of the universe. Get ready to learn about this beautifully geometric theory and the bizarre consequences of Einstein's elegant field equations connecting energy to space-time curvature, $$R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu} $$


Prerequisites
Basic calculus is ABSOLUTELY required. Some knowledge of multivariable calculus would be helpful as well.

S706: Light in Astronomy
Difficulty: ***

Light is a vital tool in astronomy but we can do more with it than just take pretty pictures. In this class we will learn how astronomers split light into the electromagnetic spectrum, what that is, and what that can tell us about various objects throughout the universe. There will be an interactive demonstration to help students understand the physics behind why splitting light emitted from celestial objects creates useful scientific data. Once we know how the data is collected, we will connect it to current research topics in astronomy.


Prerequisites
Some physics knowledge recommended but not required

S633: Signals, Screening, and Lemons: A Brief Introduction to Information Economics
Difficulty: ***
Teachers: Arnav Sood

Many papers have been written (and many Nobel prizes have been won) about the role of information in economic stories. The idea is that what people believe, and what learning constraints they face, are major forces in the economy.

Examples of questions these stories can answer are "why don't health insurers just charge elderly people more?" (Akerlof, 1970), and "how does education distinguish between job applicants?" (Spence, 1970). In one paper (Veldkamp, 2004), we see the argument that rebuilding the economy usually takes longer than crashing it, because "economic activity generates higher-precision information about productivity," so people are more uncertain about the economic state in bad times.

We'll examine these and other questions in this class.


Prerequisites
Curiosity is the main one! But: a good math background (algebraic manipulations, understanding how probability works, some calculus is good for rigor) and some basic economics (demand, supply, equilibrium, etc.) is good.

S617: A Brief Tour of the Stratosphere
Difficulty: **
Teachers: Jessie Oehrlein

We live in the layer of the atmosphere called the troposphere, where nearly all weather happens. But the stratosphere, just above the troposphere, is also important for climate! We'll talk about the ozone layer, why the direction of the winds in the tropics switches every 28 months, and what a scientist actually observed when he noticed an "explosion-like warming" over the Arctic. (One of these warmings just happened in mid-February, and it's causing the cold spell in Europe!)

S658: Special Relativity
Difficulty: **
Teachers: Noah Miller

In this class, I'll cover the basics of Einstein's theory of special relativity! (That's the theory of light, space, and time. Not the one about gravity, that's general relativity.)

S644: Bacterial Biotechnology
Difficulty: **
Teachers: Ben Zhang

Bacteria do much more than just causing infections and spoiling food! In this class, you'll learn about how we can engineer bacteria to do all sorts of cool things - from cleaning up oil spills to making plastic, and even producing medications!


Prerequisites
Basic understanding of cells and DNA. Biology and chemistry classes would be helpful but not required.

S636: Electron Microscopy
Difficulty: **
Teachers: Benjamin Miller

This course explores the principles behind and the uses of electron microscopy.

S720: DNA Fingerprinting: from CSI to Candy Culprit
Difficulty: **

Interested in learning about DNA? Do you like solving crimes? If you said yes, then sign up! You will learn about the latest forensics techniques and how to identify the culprit.

S615: Protein Biochemistry
Difficulty: **

Organisms use proteins to accomplish nearly everything. This course will first go
over protein structure and function. This will include protein related disorders and their subsequent treatments. Finally, we will learn traditional and modern techniques in protein research.


Prerequisites
High school level biology

S630: Chemistry of Cooking
Difficulty: **
Teachers: Julian Maceren

What exactly happens when you put those cookies in the oven? Why do foods have a distinct flavor that we describe as "baked". What reactions produce flavor?There is so much chemistry behind cooking and baking that is often unexplored, and this class aims to unite chemical concepts in order to understand the chemistry behind food. Many reactions incorporate organic chemistry concepts, so this class also serves as a great introduction to organic chemistry and other college-level chemistry courses. If you're an aspiring chemist, an avid cook, or simply a food enthusiast, then this class is for you!


Prerequisites
No major prerequisites but a good background in chemistry is recommended. Many of the reactions discussed in this course are simple organic reactions.

S638: Introduction to Topological Insulators
Difficulty: ****
Teachers: Kohtaro Yamakawa

I will begin with basic band theory,Bloch states, and elementary point set Topology and go straight into what Topological Insulators are and including where the current research is going. While rigorous understanding of topology is not required, having an understanding of a topological invariant is key in understanding topological insulators.


Prerequisites
Basic Calculus Basic Quantum Mechanics

S681: Tensors, 4-Vectors, and Special Relativity
Difficulty: ***
Teachers: Ryan Abbott

This class will cover the basics of tensors without going deep into abstract definitions. We will then apply this to 4-vectors and special relativity - a topic made far more elegant by the introduction of tensors.


Prerequisites
Calculus

S716: Problems in the Philosophy of Science
Difficulty: **
Teachers: Hayden Kajercline

We've all heard about the scientific method, but let's go deeper. What are the aims of science and how does it achieve them? What justifies scientific reasoning? What distinguishes scientific branches of inquiry from non-scientific ones -- for example, astronomy from astrology? These (and many others) are the questions of philosophy of science.

In this course we will look at some important problems and theories in the philosophy of science. In particular, we will focus on David Hume's problem of induction, and Karl Popper's theory of falsificationism.

Come with an open mind, and expect to leave with more questions than you arrived with.


Prerequisites
Some acquaintance with philosophy is recommended but not required. I am teaching another course earlier in the day called "What is Philosophy Anyways" which would be a useful introduction for those less familiar with philosophy.

S679: The Chemistry of Color

Come learn about some of the awesome chemical structures that color the world around us. We'll be exploring transition metal complexes, the organic dye lycopene, and what gives butterfly wings their color.


Prerequisites
General Chemistry Knowledge

S700: Bathroom Chemistry
Difficulty: **
Teachers: Ben Zhang

Have you ever forgotten to bring your phone to the bathroom, and ended up bored enough to read through the ingredients list on a shampoo bottle? Curious about what those ingredients do? Look no further than this class - we'll go over critical components of everyday items like toothpaste, shampoo, soap, and bleach!


Prerequisites
Basic understanding of chemistry (atoms, covalent/ionic bonds, polarity).

S647: Vital Signs Full!
Difficulty: ***

This class will be an introductory course on the fundamental clinical measurements that help assess a patient's essential body functions. We will do a brief overview of the underlying biology of all the measurements and then proceed to learn how to take heart rate, respiration rate and blood pressure.

S641: Cancer Pathology!
Difficulty: **
Teachers: Andrea Jurado

Ever wonder how cancer looks like from the cellular point of view? Well, look no further because in this class, we'll look through different slides of tumors-- both benign and malignant -- and discuss their pathology!


Prerequisites
Basic Biology

S626: Natural Medicines
Difficulty: **
Teachers: Stephanie Siegmund

Have you ever wondered where we get all of our medicines, from the pills we take every day to the expensive regimens administered in the ICU of hospitals? Why are some medicines "natural" and others not? And are "natural" medicines really any different, or better for us?

Come learn about meds, in this class designed for all eager minds! We will begin by covering key examples of medications and health care practices, and will then spend the remaining time discussing the implications.

S682: What is Psychology?
Difficulty: *
Teachers: Abby Feinberg

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!

S718: Modern Neuroscience: Neuropsychiatric Illness
Difficulty: ***
Teachers: Rachel Mikofsky

This course will review some of the basics of neuroscience. We'll focus on the modern techniques in neuroscience (optogenetics, mouse genetic engineering and fluorescent proteins). Then we'll cover what we know about the neuroscience of psychiatric illness. How does it change the brain? How is it caused? We'll specifically cover schizophrenia, depression, anxiety and if we have time we'll cover bipolar disorder and OCD.

There will be some overlap with the other Modern Neuro course.


Prerequisites
Basic (non-AP) biology, including genetics, any neuroscience is a bonus.

S661: The Origins of Human Life Full!
Difficulty: **
Teachers: Neeraj Sakhrani

Want to learn more about our early ancestors and the emergence of human life on Earth? From evolution to migration, this class will investigate some of the major archaeological discoveries and fossil dating techniques used by scientists today to uncover the history of human life millions of years ago. While many people are familiar with Carbon-14 dating, I will discuss the limitations of this method. I will also discuss my research in the area of Electron Spin Resonance, a relatively new fossil dating technique, and the results I have found that could potentially change our earliest known ages for human migration patterns.

S685: Introduction to Statistical Mechanics
Difficulty: ***
Teachers: Benjamin Church

In introductory physics classes, one spends a lot of time thinking about the motions of a small number of particles. But in real life, things aren't made of one or two particles, they are made of at least a trillion trillion atoms. How can a physicist ever hope to understand the properties of real materials and objects given this complexity? The answer is statistical mechanics, asking not what a material will do but rather what is the most probable state to find it in. In this class we will introduce the methods of statistical physics, understand fundamental quantities such as entropy and pressure from the viewpoint of statistical ensembles and, time permitting, apply these ideas to the problem of spontaneous magnetization in magnetic materials.


Prerequisites
Calculus is ABSOLUTELY required. You will not understand anything if you do not know what a derivative is. Know what the following forms of energy are, kinetic, potential, and heat. Some basic understanding of probability would also be helpful.

S652: Poetry for Physicists
Difficulty: ****
Teachers: David Grabovsky

In this class, I will wax poetic on the beauty of physics by writing down an inordinate number of equations. Forgoing technical derivations in favor of physical argument, I will try to describe the glorious apparatus of modern theoretical physics, from classical mechanics to the quantum theory of fields.

We will start by scrapping Newton's laws and postulating a principle of stationary action to govern the dynamics of classical particles. After writing down the Euler-Lagrange equations of motion, we will discuss the truly poetic theorem of Noether relating symmetries to conservation laws. We will then rewrite mechanics in the Hamiltonian formalism and pause to discuss phase space. Next, we will change gears and give the basic postulates of quantum mechanics. We will solve the harmonic oscillator, and then discuss unitary dynamics in the Schrödinger and Heisenberg pictures.

Having laid down our "basic" formalism, we will start the second hour by making the transition to classical field theory, where Noether's theorem reappears more powerful than ever. We will embark on the project of quantizing the free scalar field, which will turn out to satisfy the Klein-Gordon equation. Time permitting, I will also talk about interacting quantum field theories, Feynman diagrams, and the path integral formulation of QFT.


Prerequisites
As much math as possible: multivariable calculus, linear algebra, and some Fourier analysis are essential. The following words should warm your heart and bring joy to your soul: integration by parts, Taylor series, complex exponentials, Fourier transforms, vector spaces, eigenvalues, inner products, hermitian and unitary operators. No physics is strictly required, but experience with basic quantum mechanics is highly recommended. The more you know about the harmonic oscillator, the better.

S708: Philosophy and Physics Full!
Difficulty: **
Teachers: Sahar Khan

Why do electrons behave the way they do? How does quantum mechanics satisfy or dissatisfy our intrinsic expectations? In this lecture, we explore the behavior of electrons in experiments. We will talk about superposition and locality.

S625: Animal Intelligence - neuroscience of non-human brains
Difficulty: **
Teachers: Stephanie Siegmund

What makes the human brain so unique? What aspects of human thought differentiate our intelligence from that of all other species on Earth? And how do our conclusions change when we learn that dolphins possess complex language, that New Caledonian crows can solve puzzles, and that octopuses can predict the future? Finally, how can neuroscientists use seas slugs, mice and rats to make so many conclusions about the human mind? In this two-hour class, we will spend our first hour discussing recent scientific research uncovering amazing feats of animal intelligence, and the second hour discussing the implications of these findings for our lives.


Prerequisites
Biology


Walk-in Seminar

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W714: Batman is Lawful Good
Difficulty: *

An introduction to D&D alignments through your favorite characters. Participate in an open forum debate dissecting the morals and motivations of pop culture icons, such as Series of Unfortunate Event's Lawful Evil Count Olaf or Brooklyn Nine-Nine's Chaotic Neutral Gina Linetti (played by Columbia alum Chelsea Peretti).

W618: Entropy in Our Political Climate
Difficulty: **
Teachers: Chloe Li

Entropy is known in the science world as the degree of disorder in a system. As a concept, the idea is that all systems gradually decline into chaos. Now, a daily look at our media will reveal that our political climate matches this description perfectly. We will discuss the connection between this scientific concept, and the state of the world's political atmosphere.

W622: Get Started Early -- Play a Game
Difficulty: *
Teachers: Genevieve Griffin

Are you an 11th grader in the midst of taking tests and trying to figure out which colleges you should look at? Take a moment and play a game!
OPTION PLAY has scenarios based on situations that college freshman are actually having. You are not going to college yet so it is all a fun, competitive game. And, you will have something to talk about with the 12th graders in your life.

W642: Marvel Talks with Marvel fans Full!
Difficulty: *
Teachers: Andrea Jurado

HYPE! Marvel Infinity Wars is right around the corner, and we'll give you a taste of how humanities seminars are run here at Columbia, by discussing hot topics on the MCU. We'll have guests who will join our debates on who's going to die, Cap or Iron Man? Where is the soul stone? Who is the White Wolf?


Prerequisites
Have seen Marvel movies or willing to discuss past Marvel movies to be able to contribute to discussion.

W621: Are You Going to College? Play OPTION PLAY
Difficulty: *
Teachers: Genevieve Griffin

Are you a 12th grader headed to college this fall? Congratulations! You worked hard to get in, and now going will become real. You are so lucky because you can play OPTION PLAY, and get a glimpse of what will probably happen while you at college. Will you have the most points at the end of the round? Can you sell your idea of how to deal with the scenarios?


Prerequisites
Desire to talk about going to college with other people like you. Desire to think about things you might want to do to get ready to go to college


Miscellaneous

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X648: Soccer Ads #goalz
Difficulty: *
Teachers: Francesca Camahort

Do you enjoy soccer? Do you like watching inspirational videos that are subtly selling you products? This might be the class for you! We will embark on a journey through mostly Nike and Adidas commercials from the early 2000s to the present. Enjoy the beautiful game through advertising and fierce debates about the great players of the past two decades.


Prerequisites
Not being a Real Madrid fan. Just kidding! All are welcome.

X703: Weird Laws and Cases Full!
Difficulty: *
Teachers: Elizabeth Parizh

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.

X628: How to Succeed in High School and Beyond!
Difficulty: **
Teachers: Katie Curran

Students will learn: PSAT/SAT/ACT tips, academic course planning and advice for thriving in extracurricular activities all in a fun and welcoming setting.

X671: Keep the Hive Alive!
Difficulty: **
Teachers: Adam Elkhadem

You might have heard that bees are dying at an alarming rate. What you didn't probably know is that there is something being done about it right here at Columbia. In this class you'll learn about the plight of the honey bee and what needs to be done about it, and what me and some friends are currently working on: a board game that will raise awareness and money to help the bees.

X694: Game Theory: Cheating, Negotiations, and Trust
Difficulty: **
Teachers: Justinas Grigaitis

From chess and dating, to war and climate change, ideas from Game Theory appear in our everyday life more often than we realize. Created by math geniuses solving puzzles in their free time, it has now become a point of reference to solving problems in almost every discipline.

Come play games, analyze the Dark Knight, and learn why countries do not cooperate in reducing CO2 emissions!

X713: When is it "Just a Joke"?
Difficulty: *
Teachers: Eileen Wong

Have you ever wondered how a casual conversation could be so serious? How could a small comment lead to a huge impact? How could a joke be dangerous?
Through the lens of psychology, explore the theories behind the evolution of prejudice throughout history and how they can be applied today.

X627: The Economics of Energy in America
Difficulty: **
Teachers: Stephanie Siegmund

Learn about how energy is generated in America, where we stand compared with other countries in the world, and what steps we have taken (if any) to respond to the growing threat of Climate Change.

X665: Entrepreneurship 101 Full!
Difficulty: *

Got good ideas? Ever thought of starting your own business? Come and join entrepreneurship 101 Splash version - specially designed for motivated high school students like you. We will introduce entrepreneurship through a fun, dynamic and collaborative game. You will grasp the fundamentals of starting a business after this class and learn how to conduct elevator pitches to investors. Yep, like Shark Tank.

X646: What Makes War?
Difficulty: **
Teachers: Jamie Withorne

This will be an introductory course to basic International Relations and concepts that create our national security. We will define and discuss basic phenomenon (such as power, rising powers, diplomacy, institutions, and the military power) in order to better understand the anatomy of inter-state conflict.

X699: Design Thinking and Empathy
Difficulty: *
Teachers: Raphael Owino

BUILD - a human-centred design thinking approach that stands for Believe, Understand, Invent, Listen, and Deliver BUILD Labs are organized as project-based learning modules in which experiential learning is maximized so that our students can become “agile thinkers who take a systemic, iterative approach to develop innovations that address the root causes of challenges”


Prerequisites
None

X701: Behavioral Economics: Lotteries, Gym, and High Expectations
Difficulty: *
Teachers: Justinas Grigaitis

Why do we fail New Year's resolutions and buy lottery tickets, overpay for food and undervalue our time? No surprise that in many situations people make irrational decisions or have unreasonable expectations. Good that at least I don't...or do I? Let's discuss how we make choices and rationalize our behavior.

Learn about the concepts of rationality, opportunity cost, choices under uncertainty, and future discounting through the examples from everyday life.

X684: Diagramming Sentences and Grammar Fun!
Difficulty: **
Teachers: Eva Farkas

Learn about how parts of speech come together to make beautiful sentences! We'll go over some clever computational linguistics tidbits, fun grammar facts and tips for writing.


Prerequisites
None!

X705: Public Speaking 101 Full!
Difficulty: *
Teachers: Enrique Olivo

This course aims to introduce students to a practical, hands-on approach to effective public speaking. Our focus is on developing a personal style of speaking that is confident, expressive, and present. Through exercises and speech presentations, the course is aimed at anyone who would like to improve their ability to speak in front of small or large groups, regardless of experience - and for those who simply want to build confidence in the way they speak.


Prerequisites
Have an interest in learning to command a room with your voice!

X710: How College Can Impact Your Mental Health
Difficulty: *
Teachers: Eileen Wong

How does a mood or anxiety disorder develop? Is there a relationship between symptoms of mood or anxiety disorders and stress? What data has been collected from American universities, and what can we infer from them?
This course will open a conversation on how life in university impacts its students, as well as introduce theories and models from psychology and sociology that aim to answer the questions above.

X683: It's a Conspiracy! From Aliens to the XYZ Affair
Difficulty: *

“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! 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 circus 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.

X686: Starting A Cult For Fun And Profit Full!
Difficulty: *

Want to be part of an exclusive group? Want to discover the secrets of the universe? Want to learn how to live forever? Then come join our cult -- or make your own!

In this class, we will be covering the essentials of how cults arise/are maintained and how they are perceived in society. We will also look into the history of some of the biggest cult groups in America.


Prerequisites
Maturity to deal with some of the more serious aspects of cults.

X702: How To Be An Adult: From Taxes to Job Applications
Difficulty: *
Teachers: Ben Zhang

Most schools don't teach you real-life skills like how to file your taxes, what your credit score is, and how to write a resume and apply for jobs, so come learn them here!


Prerequisites
None


History

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Y632: History of Ballet
Difficulty: **
Teachers: Jessie Oehrlein

This class will follow how ballet developed and spread around the world, starting in Renaissance Italy and moving forward to the present. Along the way, we'll look at paintings, photos, and video clips to see how different techniques and styles emerged in different parts of the world. If we have time, we'll talk about where ballet is headed now.

Y616: Lessons from Great Leaders
Difficulty: **
Teachers: Omar Khedr

Students will learn about some of the great leaders of history and how they thought about leadership and problem solving.

Y707: Profiles of Radicals
Difficulty: **
Teachers: Mehrzad Farnoosh

We will discuss several figures in the history of radicalism, from around the world from the ancient era until the present. Basic knowledge of world history is helpful but not required.

Y640: German History, 1806-2018
Difficulty: **
Teachers: Daniel Shao

How could the same nation that gave birth to Beethoven, Goethe, and Kant have been the source of the some of the worst atrocities in all of human history? How could a seemingly insignificant and infinitely divided number of small principalities unite into a state that threatened the balance of world power not only once, but twice in the 20th century? Through this course, I hope to provide an introduction to the most important developments in German history over the past two centuries, and examine the role that Germany and the Germans played in shaping not only the political and economic order of the world today, but also European and American intellectual and cultural life. I will discuss both the political, social, and military developments that are taught in standard history courses and also subjects like classical music and philosophy that are often excluded from standard high school courses. While I hope to move at a quick pace, I will also leave plenty of time during and after the lecture for questions, and will not presume that students have a high degree of familiarity with 19th and 20th century European history.


Prerequisites
Basic knowledge of European history recommended, but no specific knowledge needed.

Y689: Alternate History and Counterfactuals Full!
Difficulty: **

An alternate history imagines a different present or future originating in a point of separation from our actual history—a branching point in the past. Counterfactuals, of which alternate history is a subtrope, is anything relating to that which has not happened. Alternate History and counterfactuals are an increasingly popular form of fiction, and, despite the ire of many, increasingly accepted (or at least, decreasingly disreputable) as an analytical tool in history and social sciences.

The class will first explain the definition of alternate history, examine theories and controversies regarding it, and look at real examples from literature and social science. The class will then break into groups, create their own examples, and then discuss them with the class and each other..


Prerequisites
Some knowledge of world history is necessary to fully appreciate examples in class and participate in the in-class discussions. Encyclopedic knowledge of history is by no means required, but more is more.