Splash Fall 2018 Course Catalog

Arts Engineering
Humanities Math & Computer Science
Science Miscellaneous
History

Arts

A787: Write Your Own Parody Full!
Difficulty: **
Teachers: Elizabeth Parizh

Have you ever wanted to take a song you know and make it your own? In this class, you can rewrite any song about something you actually know and care about. Or something you don't know or care about, it's all up to you!

A722: Postmodernism
Difficulty: **
Teachers: Michelle Chow

An examination of the Postmodern period in literature (generally considered as starting in the mid 20th century). We'll look at a few key authors and ideas as well as overarching concepts and contexts, such as the Canon and colonialism. Discussion will be encouraged!

A783: NYC Performing Arts Scene as Your Classroom Full!
Difficulty: *
Teachers: Vivian Tian

Interested in performing arts? Need to do some projects?
Come to this class to learn all the resources (and student discount programs) you can take advantage of.
City ballet, Philharmonic, Met opera, Carnegie Hal...

A780: Let's OULIPO (an introduction) Full!
Difficulty: **
Teachers: Lizka Vaintrob

Come explore OULIPO (“workshop of potential literature”) and try your hand at constrained writing or generating poems. Hopefully we’ll spend about half the class exploring cool poems/excerpts, then we can write some of our own—establish our laws and observe them.

Some classic constraints: palindromes, writing without the letter “e,” writing “snowball” poems—example below, etc.
Wacky generative techniques: N+7, Queneau’s 99 “Excercises in Style,” his One Hundred Thousand Billion Poems, etc.

I
am
now
post
haste
(sort of)
posting
new topic
to discuss.

do you enjoy
constraints?
does word play
are you confused?
This is a snowball,
A poetic form which
was created by those
who group themselves
with the name of Oulipo.
Every line contains one
(by John Newman)

Prerequisites

A810: How to Read Paintings and Sculpture
Difficulty: **
Teachers: Sameer Jain

This course will teach students how to look at a painting or piece of sculpture and make meaningful insights about the work. This course is intended for any students who has been to an art history museum and has felt completely lost and incapable of appreciating what they see. By the end of the course, the student should be able to go to an art museum and find value from the experience. There will be a focus on artwork in the Western tradition.

A753: Taiko Full!
Difficulty: *
Teachers: Kohtaro Yamakawa

Taiko is a Japanese drumming art that centers on movement and rhythm to create a dynamic performance. I have been playing for 10 years and will focus on not only the basics of playing but its importance and role in the emergence of Japanese-American culture in America. Taiko is not only a very fun sport but also leads to certain questions on modernity vs tradition, culture vs entertainment, and more.
If you've taken this course before, it is still worth taking again! This course will be more focused on what it means to play taiko, as opposed to exploring various forms of taiko.

Prerequisites
A willingness to learn, comfortable clothes, and a water bottle.

Engineering

E755: Intro to Space Exploration
Difficulty: **

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.

E776: Intro to Genome Engineering Full!
Difficulty: **
Teachers: Kelly Ryu

Genome editing is revolutionizing how we discover new therapies and study biological systems. If you've seen the recent movie, Rampage, you're probably wondering what CRISPR is and if it can really create monsters :) Come find out what the technology is and why it's been so revolutionary in biological research!

Prerequisites
Some knowledge about genetics (DNA, RNA, etc.) is useful but not required. We'll go slowly, assuming you don't know much about the material

E798: Intro to Space Exploration
Difficulty: **

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.

E747: Intro to Rocket Propulsion
Difficulty: ***

From the first Saturn V to the recent launch of the Falcon Heavy, people have always been awed by the enormous fireballs that propel these massive structures into space. In this class we'll be going over the the science and engineering that goes into the design of these rocket engines.
The first half of class will be devoted to understanding the physical design of rocket engines, including the various types of rocket engines, turbopump cycles, cooling systems, propellant choice, nozzles, injectors, tanking systems, and more.
The second half will be devoted to the physics and thus mathematics that are essential to the design of rocket engines. Depending on the class' interests, we may go over topics such as de Laval nozzle flow, the full engine thrust equation, combustion chamber cooling, injector dynamics, and more.

Prerequisites
Newtonian Physics Strong algebra background Basic calculus

Humanities

H767: Weird Laws and Cases
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.

H760: The Zoo is Not For Animals
Difficulty: *
Teachers: Kristian Woerner

Join me for a discussion on the history, architecture, and ethical questions regarding zoos from an anthropocentric (human- centered) point of view! We will touch on animal rights, but the class will mainly focus on animal exhibits in context with colonialism and humanitarianism, as well as similarities between animal enclosures and human residential projects.
It will be wild!

H789: What is Philosophy? 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 thinking in the real world.

H754: A Brief History of the English Language
Difficulty: **
Teachers: Ben Zhang

The English language has a rich history dating back over a thousand years. In this class, we'll explore major events and trends that have shaped the language into what it is today. We'll combine British history and historical linguistics to answer question such as:

- Where does "Ye Olde" come from?
- Why is English pronunciation so inconsistent?
- Why meat from a deer called venison, and meat from a cow called beef?
- How come English doesn't have genders like French or German?

Everyone is welcome!

Prerequisites
None.

H752: Intro to Activism
Difficulty: *
Teachers: Julia Coccaro

Frustrated with the current political climate? Don't fully understand how elections work? Want to get involved with an issue(s) you're passionate about but don't know how? This class will go into depth about modern civics and the different avenues you can take to invoke change in your community.

H731: Horrible Histories: The Witch Hunts of Early Modern England and Scotland
Difficulty: **
Teachers: Amani Mohamed

You’re probably most familiar with the Salem Witch Trials of 1692-3, but to understand the witch hysteria, we must travel a hundred years farther, to Scotland, at the end of the 1500s...

Come along to my seminar to hear the full story, just in time for Halloween!

H813: Greek Mythology: A Timeline
Difficulty: **
Teachers: Ben Zhang

When did the Trojan War take place? Was Helen of Troy alive at the same time as Heracles? Who sailed with Jason on the Argo? Find out the answers to these questions, and more, in this class!

H737: How To Build A World Full!
Difficulty: *
Teachers: Gloriana Xia

Ever wanted to learn how to create a fantasy world from scratch? This course will walk you through the basics. If students have ongoing creative writing projects, time will be allotted for them to ask questions and get feedback. This course is intended for writers of all levels.

H728: Intro to American Sign Language (ASL) Full!
Difficulty: **
Teachers: Daniel Mitropolsky

Sign languages are sophisticated, natural, full-fledged languages that are entirely visual. Though there are many sign languages in the world, American Sign Language (ASL) is the native language to Deaf people and their families in North America. I have a lot of experience teaching ASL. After this class you'll know the basics of ASL, including the manual alphabet, basic sentence structure, and enough vocabulary and patterns to introduce yourself, ask/answer questions, and a base for continuing to learn sign. Learning sign language is EXTREMELY fun. You're not just learning a language, but you're learning how to think and communicate VISUALLY in a completely different language.

There's no talking at all in this class- from the second you walk in, we will be signing and communicating visually. You may have never experienced a setting like this, so embrace the challenge. Shut off your ears, open yours eyes, and focus on thinking and communicating visually.

Please learn the manual alphabet BEFORE class. We'll go over it quickly, but it is important that you learn the manual alphabet BEFORE coming to class so that we have time to learn the actual language and talk to each other in it! Please watch this video: https://www.youtube.com/watch?v=fXf4d23WqiA to learn the letters and practice spelling words BEFORE class.

Prerequisites
Please learn the manual alphabet BEFORE class. We'll go over it quickly, but it is important that you learn the manual alphabet BEFORE coming to class so that we have time to learn the actual language and talk to each other. Please watch this video: https://www.youtube.com/watch?v=fXf4d23WqiA to learn the letters and practice spelling words BEFORE class. If the link doesn't work search for "Learn ASL: The Fingerspelling Alphabet for Beginners" on Youtube, from the user ASLMeredith

H778: Philosophy for Scientists and Engineers
Difficulty: **
Teachers: Sameer Jain

The course will examine the roles and responsibilities of engineers in the context of civic life when creating new products and companies. This course will be an overview of three major ethical systems, Utilitarianism, Deontology, and Virtue Ethics in the context of various engineering disciplines. There will be an emphasis on modern problems in social media and free speech as well as data science.

Examples of questions that will be examined:

- What is the role of social media companies in our society given their ability to sell our information?

- What moral obligations do engineers posses when building bridges and other structures?

- Does maximizing user's immediate happiness always lead to the best products for society at large?

- Why should STEM students study Philosophy in the first place?

H799: Why philosophers think everyone is wrong about everything - a biased look into ethics, mind, and freedom Full!
Difficulty: **
Teachers: Brennan McManus

Does free will exist? Do we have a soul, and what does it mean to be conscious Philosophers tend to offer radical and complicated answers to these questions. This course will focus on how to approach these questions, and how to draw upon these answers when shaping our own opinions.

H791: Linguistics of Pop Culture and the Internet
Difficulty: *

People may complain that the Internet is destroying language, but linguists know that's not true. The abbreviations we create, the jokes and memes we share, and the social media etiquette we use are just exciting new additions to a long tradition of language evolving to match the society around it. We'll discuss recent trends in the English language, learn about how online pop culture is changing the way we speak, and explore the larger phenomena that brought us here.

H744: Soccer and Politics
Difficulty: *
Teachers: Francesca Camahort

From the year Franco’s secret police bullied Barça players before El Clasíco to Xhaka and Shaqiri flashing Albanian eagles at the most recent World Cup, soccer has always been intertwined with politics. This course will explore prominent moments in history when politics and soccer collided head on, from soccer’s earliest origins to the present. If you are passionate about soccer as a sport and simultaneous reflection of society, come to this class!!

Prerequisites
Everyone is welcome except for Cristian Ronaldo fanboys.

H811: Human Behavior
Difficulty: **

Did you know that individuals are less likely to offer help to a victim when other people are present? Or that a mass shooting in the United States is followed by other mass shootings? This course will explain human behavior with psychological phenomena, such as the bystander effect and mass hysteria, and will discuss infamous behavioral experiments.

Math & Computer Science

M746: Lies, Damned Lies, and Statistics
Difficulty: *
Teachers: William Tong

Everything you need to know to make your numbers say what you want 'em to say :)

I'll take you on an intro tour through probability and statistics. We'll cover basic probability, core concepts of statistical inference, and the funky things people do to get results. If there's enough time and interest, we'll take a dive into deep waters and explore the hottest field in modern stats: machine learning.

Statistics is the fortune-telling of math. Learn this magic here.

Prerequisites
Being comfortable with math would be a big help, but the course is aimed to be understandable by anyone.

M742: A Tour of Turing
Difficulty: **
Teachers: Amanda Liu

A thrilling guided tour of Alan Turing's conception of the Universal Machine: the basis of the modern computer! Stops along the way include types of infinity, computability problems, the Entscheidungsproblem, and how real are real numbers actually?

M749: The Foundation Crisis in Mathematics
Difficulty: **
Teachers: Henry Williams

For centuries, mathematics was considered to be the most stable and deductive reasoning, which gives results with absolute certainty, it was
long believed that mathematical knowledge was beyond doubt. But at the end of the 19th century and the beginning of the 20th, several developments shook our faith in the unshakable nature of mathematical reasoning. The emergence
of non-Euclidean geometry undermined absolute acceptance of the theory
of space and shape that had reigned since classical Greece. Gregor Cantor’s work on the nature of infinity forced us to rethink our sense of numbers. And Kurt Gödel’s incompleteness theorem cast doubt on the possibility of a completely well-grounded notion of mathematical truth. In this class, we will explore the fundamental philosophical uncertainty in mathematics, and hopefully I will convince you that the math you have known and loved your whole life is built on shaky ground. This class will include discussions on the philosophy of math and whether it is grounded in the real world, or own minds, or somewhere far stranger.

Prerequisites
A heavy skepticism of mathematicians.

M793: Quantum Computing: What it is and what it isn’t Full!
Difficulty: ***
Teachers: Ryan Abbott

Quantum Computing is often explained as some mysterious, mythical computer which can do anything because of “quantum weirdness.” Going beyond these vague and sometimes misleading descriptions, I’ll dive into the actual math/physics underlying the weirdness, and give some concrete examples showing what Quantum Computing can and cannot do. Topics will include unitary time evolution, quantum gates, the Deutsch algorithm, and if time permits the full Deutsch-Jozsa algorithm.

Prerequisites
Knowledge of linear algebra and quantum mechanics would be appreciated, though the required topics will be reviewed during the class.

M773: 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!

M733: Introduction to Applied Mathematics
Difficulty: **
Teachers: Lester Kim

This course will explore different topics in applied mathematics with examples from physics, economics, computer science, finance, and more. If you ever wondered how the math you learn in high school applies to the real world, this is the class for you.

Prerequisites
High school algebra

M769: Secret Sharing and Cryptography
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

M726: 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. This is intended to be a rudimentary introduction to an incredibly rich branch of modern mathematics.

M751: Fun with Fractals 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.

M804: Generating Functions
Difficulty: ***
Teachers: Anton Wu

Generating functions are a powerful tool to investigate properties of sequences. We'll look at how they are used to solve simple recurrences, to give easy solutions to combinatorics problems, and to study asymptotic properties of sequences.

Prerequisites
Familiarity with calculus and Taylor series will be assumed.

M748: Measure Theory and Vitali Sets
Difficulty: ***
Teachers: Benjamin Church

Given an arbitrary set of points in the real numbers, how do you measure its length? When the set is made from intervals this is quite clear but what about crazier sets like the rational numbers inside the reals. Can the notion of length be generalized to any number of dimensions? We will explore all these questions and develop the field of measure theory, the rigorous foundation for the study of size and probability. Along the way we will find that inevitably (up to choices for the axioms of set theory) any measure function, that is a choice for the length of each set, must fail to give a reasonable answer for some sufficiently nast set. We will give a description of a Vitali set which is an example of such an immeasurable set. If time permits, we will discuss the implications of immeasurable sets to the famed Banach-Tarski paradox which allows one sphere to be turned into two through cuts and rotations alone.

Prerequisites
No official prerequisites besides a love of abstract definitions and formal nonsense although one should be familiar with the basics of set theory

M732: Population Modeling
Difficulty: ***
Teachers: Jessie Oehrlein

Can trapping invasive crawfish save a newt population? How do regional or minority languages like Galician survive? When can two species with the same food sources coexist? In this class, we'll build mathematical models of populations to answer questions like these. In groups, you will mathematically describe different ways in which populations grow, decline, and interact. Each group's model will answer key questions about population behavior or control. We'll also discuss challenges and alternate methods for modeling.

Prerequisites
Comfort with thinking of a derivative as a rate of change

M807: 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

M770: Primes of the form x^2+ny^2
Difficulty: **
Teachers: Eli Fonseca

This course will explore which primes can be represented as $$x^2+ny^2$$ with $$x,y$$ integers and $$n$$ a natural number. Despite the questions simple appearance finding a complete answer is anything but simple as it requires a deep understanding of field class theory, modular functions, and complex multiplication. After introducing some basic preliminaries we will focus on the simpler case of $$n=1$$. I will present a constructive proof, due to Euler, which fully answers the question in this simpler case. Then we will turn our attention to the more general question by looking at a few more special cases and then present a theorem, due to Weber, that answers the general question without proof.

Prerequisites
Basic understanding of modular arithmetic would be useful but is not required. The only requirement is interest in crazy theorems about the representation of primes numbers.

M739: Godel's Incompleteness Theorems
Difficulty: ****
Teachers: Benjamin Church

Godel's Incompleteness Theorems are the most famous results in mathematical logic. These theorems prove the impossibility of David Hilbert's project of finding a set of formal axioms from which all of mathematics (specifically Godel consideres number theory) can be derived. The further requirement is to prove that these axioms are consistent i.e. cannot derive any contradictions. In a landmark paper, Kurt Godel proved both these projects are impossible. He showed that any reasonable (we will discuss what is required to make an axiom system reasonable) axiom system capable of expressing integer arithmetic must necessarily either be inconsistent i.e. derive a contradiction or incomplete i.e. cannot prove all true statements. We will dive into the murky depths of mathematica logic to discuss the proof of this remarkable theorem.

Prerequisites
There are no formal mathematical preliminaries required but a strong degree of comfort with complicated logical arguments is expected.

M772: 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 and linear combinations and moving on to linear transformations, isomorphisms, and the change of basis. Then we'll introduce eigenvectors and eigenvalues and discuss inner products as an excuse to define linear functionals and the dual space. Finally, we will finish off with the crowning glory of linear algebra, 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. Familiarity with sets and functions (e.g. injective, surjective, and bijective maps) is the only strict requirement; nevertheless, the more math you have seen, the better: mathematical maturity and experience are indispensable tools for appreciating elegance. It also helps to know how to add.

M750: All of AP Calculus BC in 2 hours Full!
Difficulty: ***
Teachers: Henry Williams

Watch me do in 120 minutes what took Newton his entire lifetime. I'm not joking, we will (attempt to) cover the entirety of this high school course in the period of two hours. AP Calculus is a lot of dumb formulas and bad presentations of really interesting and simple concepts. I hope that in this session you gain enough to excel if and when you are forced to take it. In addition, I hope you leave with an appreciation of what is ACTUALLY interesting about this really terribly designed course that many of us have suffered through.

Prerequisites
You should know most of the topics in a typical Algebra II course with a few extras from Precalc (trig functions, polynomials, VERY comfortable with basic algebra, limits, difference quotients, logarithms). However, this course is absolutely open to those who have not taken a Precalculus course.

M806: MATHEMAGIC - mindblowing math concepts and problems
Difficulty: **
Teachers: Henrique Monteiro

Forget calculus! In this class, you will (1) solve graph theory problems that puzzled people for generations, (2) understand the incredible equation that made Euler believe he found the proof for the existence of God, (3) know the truth and the tricks behind the famous Fibonacci sequence, (4) learn how to calculate the digits of pi on your own and (5) understand some of the most famous problems in the history of math and how you can get \$1,000,000 solving one of them.

BONUS: you will learn how to prove to your friends that the sum of all integers is -1/12 (no joke, this is a real Math result).

Prerequisites
Bravure, imagination, and lots of curiosity

Science

S729: Chemophobia: What's a Chemical? Full!
Difficulty: **
Teachers: Benjamin Rudshteyn

This class gives an overview of the phenomenon of chemophobia, the fear of chemicals (not of organic chemistry as a class!). It will define the terminology of chemicals, including the difference between natural and artificial chemicals and how one is not necessarily better than the other.

Prerequisites
High school level chemistry

S808: Canonical Quantization
Difficulty: ***
Teachers: Shantanu Deshmukh

We will start with an altogether too fast introduction to Lagrangian and Hamiltonian Mechanics (poetry for physicists would be a good class to take for a more in depth presentation). Then, we will explore the movement from classical to quantum theory under what the process of canonical quantization. Using canonical quantization, we will "prove" Schrodinger's equation and work out some simple problems in quantum mechanics. We will demonstrate how to derive the uncertainty principle and how it is hidden within classical mechanics itself. Finally, if time permitting, we will extend our notion of quantization to quantum field theory.

Prerequisites

S777: 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 (because they're boring), and we'll spend most of the class discussing two beautiful reformulations of classical mechanics. Among our poetic vistas will be Hamilton's least-action principle, the Euler-Lagrange equations of motion, Noether's theorem relating symmetries to conservation laws, canonical conjugate momenta, Hamilton's equations of motion, Poisson brackets, and Liouville's theorem. Time permitting, we may also discuss classical field theory or symplectic geometry.

At the end of class, I will try to convince you that classical and quantum physics are really the same, and that commutators, Heisenberg's uncertainty principle, and path integrals are all really part of the same poetic physical structure.

Prerequisites
As much math as possible: multivariable calculus and linear algebra will be very helpful, though strictly speaking flexibility with single-variable calculus should suffice. In particular, integration by parts and the product rule are absolutely essential. No physics is strictly required beyond knowing what $$F = ma$$ means, but the more you have seen, the better. If you have ever seen a Lagrangian, this class will be full of them! It also helps to be familiar with energy.

S730: Introduction to Solar Fuels Full!
Difficulty: **
Teachers: Benjamin Rudshteyn

Introduction to the use of solar fuels to solve pressing climate change problems. Topics of interest include climate change, solar cells, conversion of water to hydrogen, conversion of carbon dioxide to fuels, conversion of nitrogen to ammonia,, and how chemistry, particularly computational chemistry, are used to solve these challenge

Prerequisites
High school level chemistry

S738: Einstein's Annus Mirabilis
Difficulty: **

In this class we will investigate the four groundbreaking papers published all within one year (the miraculous year) which took Albert Einstein from a nobody patent clerk to a household name. In these papers, Einstein proved the existence of atoms, laid the groundwork for quantum mechanics, and unveiled his special theory of relativity.

Prerequisites
A critical eye and insatiable hunger for knowledge. Introductory calculus will also be helpful but is not required.

S801: Documenting Endangered Languages: What, Why, and How?
Difficulty: **
Teachers: Brennan McManus

Research suggests that a vast majority of the languages spoken around the world today will be gone by the end of the century. The languages with the highest risk of disappearing are called endangered languages, the focus of the field of linguistics known as documentation linguistics. This class will first focus on describing endangered languages, where they tend to be found, and why preserving their features (and their use!) is important. The latter half will focus on methodology field linguists use to study these languages, as a practically-motivated introduction to core areas of linguistic study.

S803: A Narrative Approach to Bioethics
Difficulty: **
Teachers: Anthony Chesebro

Doctors and scientists are often taught to be objective, to view the world as a collection of facts awaiting analysis. One of the most important skills for any medical professional, however, is the ability to empathize with a patient's subjective experience, the story that they have lived that has left them in need of care. This class will talk about the insights that narrative medicine, or the telling of patients' stories, can bring to understanding new issues in bioethics. This course is geared towards students who are interested in either STEM fields or the humanities, as it combines approaches from both.

S790: Philosophy of Science
Difficulty: **
Teachers: Hayden Kajercline

We've all heard about the scientific method, but let's go deeper. What is the foundation of 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'll focus on David Hume's problem of induction, and Karl Popper's theory of falsification.

Prerequisites
No prior experience with philosophy is expected. However, if you are interested, I am teaching a 2 classes earlier in the day -- one called "What is Philosophy" and the other called "Introduction to Logic" -- both of which could help contextualize the topics of this class.

S740: Natural Medicines Full!
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 your meds, in this class designed for all eager minds!

S784: Why Science Research?
Difficulty: *
Teachers: Yarim Lee

This course is for PASSIONATE high school scientists looking to succeed in high school, college, and science fairs.

There are 2 parts to this course.
A. For all young scientists
B. For students who are looking for tips on succeeding at science research fairs

As a alumna of science research fairs, a lack of passion was observed among contestants.
Your very passion is not only the key to success in science fairs, but also in college.
In this course the following will be discussed:

A.
1. Science in society
2. Why science: What scientific passion can do for you

B.
2. The science fair

If you have any questions, please email me: yarim.lee@columbia.edu

Prerequisites
A passion and interest in science (Background in science research)

S785: How to read a science research article
Difficulty: **
Teachers: Yarim Lee

As intimidating as they appear to be, science articles that publish incredible data does not have to be impossible to read. In this course, we will be reviewing one of the groundbreaking research articles in stem cell research titled, "Induction of Pluripotent Stem Cells from Adult Human Fibroblasts by Defined Factors" (Yamanaka et. Al 2007) By the time you walk out the door, you will have some background knowledge on developmental biology/stem cell biology and feel more confident in tackling research papers for your future endeavors!

S761: Crash Course Carbonyl Chemistry Full!
Difficulty: **
Teachers: Eva Farkas

This class will aim to develop in students an intuitive understanding for the mechanisms that drive some important organic and biological reactions. We'll start with fundamental concepts in organic chemistry (like electronegativity and resonance) and work our way up to diagramming specific reaction mechanisms (including examples from amino acid synthesis and metabolism).

Prerequisites
Enthusiasm for understanding how the biological world works!

S741: Animal Intelligence - neuroscience of non-human brains
Difficulty: **

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.

Taught by Columbia MD+PhD and JD students.

Prerequisites
Biology

S758: Navigating by the Stars
Difficulty: *
Teachers: John Pederson

Feeling lost and adrift? Or maybe you're actually lost and adrift - either way, this class is for you! Navigating by the stars is a tradition both ancient and modern, and can help you find your way anywhere on Earth. In this class, you'll learn the surprisingly simple theory behind star navigation, and explore historical and modern techniques of wayfinding – from the Age of Exploration to the modern castaway. You'll come out of this class able to find your latitude and longitude with nothing but a watch, a calculator, and a protractor!

S763: Spectroscopy & Analytical Methods
Difficulty: **
Teachers: Eva Farkas

Have you ever wondered how scientists determine the arrangement of bonds in an organic molecule or how the sequence of primary structure of a protein is determined? Or how biological species are analyzed and purified? If you've ever pondered these questions, or just want to learn more about experimental methods, take this class to survey a number of historical and contemporary analytical methods in chemistry and the biological sciences. Topics will include, nuclear magnetic resonance spectroscopy, ultraviolet-visible light spectroscopy, mass spectrometry, chromatography techniques, gel electrophoresis and more!

Prerequisites
A curiosity for the natural world on a molecular scale!

S768: An Introduction to Special Relativity
Difficulty: ***
Teachers: Aidan Reddy

Even if you know nothing about physics, you've certainly heard of Albert Einstein, and know that he is largely considered one of the greatest geniuses to ever have lived. Have you ever wondered why? If so, this class if for you. We will explore one of Einstein's most disruptive contributions to our understanding of universe. We will learn about the conceptual and mathematical relationship between space and time.

Prerequisites
A strong grasp of high school algebra and familiarity with basic physical concepts. An ability to revise your prior understanding of the relationship between space and time. Many will probably not be able to keep up with everything, but that is okay. All will at least gain a basic conceptual understanding of special relativity.

S802: Applied Neuroscience: Remotely Controlling a Roach's Actions
Difficulty: **
Teachers: Anthony Chesebro

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.

S812: The Origin of Life on Earth
Difficulty: **
Teachers: Ben Zhang

How did something as complex as life originate on planet Earth? Nobody knows for sure, but we'll discuss several theories and experiments in this class, including panspermia, the RNA World, and the primordial soup hypothesis.

Prerequisites
Some biology and chemistry background (do you know what an amino acid is? What is DNA made of?)

S766: Microbiology: Crazy Things Cells Do
Difficulty: **
Teachers: Allison Hung

Microbes are organisms that live on a microscopic level. They live EVERYWHERE, and affect the world as we know it.
This class will review the fundamental concepts of microbiology and look at how cells do the crazy things they do to thrive. Then we will explore current areas of research - astrobiology, cell engineering, host-pathogen interactions, and more!

S764: Vital Signs & Their Physiological Foundations Full!
Difficulty: **
Teachers: Eva Farkas

This class will cover not only how to take blood pressure, respiratory rate and heart rate readings but also an overview of the biology and physiology that explain the medical significance of these techniques.

Prerequisites
None, though previous experience with general chemistry and/or biology material may be helpful.

S757: A Brief Tour of the Stratosphere
Difficulty: ***
Teachers: Jessie Oehrlein

What is the ozone hole, and when will it recover? What did a scientist actually observe when he noticed an "explosion-like warming" over the Arctic? Why did 1883 and 1908 data show tropical winds going in opposite directions? All of these questions are about phenomena that happen in the stratosphere, the layer of the atmosphere about 10-50 km above us. In groups, you'll explore questions like these, the related stratospheric phenomena, and their impacts on us. We'll put them all together to create a coherent picture of the stratosphere.

S800: Breaking the universe: physics of the very small, the very fast, and the very large Full!
Difficulty: **
Teachers: Brennan McManus

Classical physics is wonderful. It is a way of understanding the universe that is clear, elegant, even beautiful. It applies from the simple force of a hammer blow to the whirling motion of the stars. And it is also, of course, very wrong. But why is it wrong? And what strange things happen when our universe stops working?

Miscellaneous

X765: Twists and Twangs: The History of Accents
Difficulty: **
Teachers: Maha Khan

Are you an accent aficionado? Curious why we say Houston and not Houston? Why does Brazilian Portuguese sound so musical? Learn about how accents came to be in not only the English-speaking world but also in Portuguese, Spanish, and more.

X759: Careers in Medicine and Health Sciences
Difficulty: *
Teachers: Ben Zhang

"Nobody knew healthcare could be so complicated" - 45th President of the United States

But it does't have to be that way! In this class, we'll go over the various careers and jobs available in healthcare, ranging from phlebotomy to nursing to surgery. For each position, we'll talk about things like basic job responsibilities, the education and training required, and average incomes. Additionally, we'll talk about what you can do right now to prepare to enter this growing and high-demand field!

Prerequisites
None

X774: Rubik's Cube Workshop
Difficulty: *

Sick of peeling off the stickers? Want to learn the first steps in solving the Rubik's Cube? Want to solve it faster?

In this hands on work-shop, we will teach you the first steps in Solving the Rubik's cube! You'll also learn a little bit about the World Cube Association and Speedcubing, and all of the events - ranging from the classic 3x3, to the massive 5x5, to solving the Rubik's cube blindfolded ... or with your feet? We'll have demonstrations, cool videos, and of course, the hands-on workshop!

X782: What Happens in a Trade War
Difficulty: **
Teachers: Blaine Helleloid

Do you wonder why everyone keeps talking about tariffs and trade? Have you questioned why countries impose tariffs? Or are you interested in economics?

Learn about the economics of trade, tariffs, and how a trade war impacts companies and consumers. Along with learning the concepts of trade, we will explore real-world examples of why different trade policies influence the decisions of companies.

X786: Introduction to Video Game Design
Difficulty: *
Teachers: Layne Britton

What makes a good video game fun? What makes a bad video game bad? How do you teach your player how to play your game? How do you make a game be just challenging enough to feel fair? In this class we will explore these questions to learn about the core of designing video games. We will look at examples of video games, both good and bad, to begin answering these questions.

Prerequisites
No official perquisites besides an interest in the design of video games!

X756: Practical Philosophy: Stocisim in the Modern World
Difficulty: **
Teachers: Joshua Elias

We live in a world where we constantly hear negative news, have trouble coping with stress, and are looking for fulfillment in an often empty world. Whether it be mindful meditation, yoga, or seeing a therapist there are so many ways one can help themselves feel centered in the chaos. Stoicism is another ancient tool that anyone can apply to their daily lives.
Stoicism is not the cold, apathetic attitude many attribute it to today but the mastery of our mindset. It's about being present and grateful. Learning to grow and embrace the obstacles in front of us rather than crumble under their weight. It's about finding peace in our lives.

X792: Introduction to Logic Full!
Difficulty: *
Teachers: Hayden Kajercline

Want to be better at reasoning? Better at persuading people?

Logic is the science of correct reasoning, and lies at the heart of mathematics, philosophy, computer science, and other fields.

In this course we'll look at how logic uncovers the mathematical structures underlying language, and how it is put to use in various fields.

X794: Investing in the stock market
Difficulty: ***
Teachers: Canwen Xu

Interested in the stock market? Learn how to invest in public equities from two asset management interns! No experience/knowledge required.

X781: Japanese- Basics
Difficulty: *
Teachers: Gregory Ginsburg

If you're interested in Japanese but haven't had lessons, learn about the alphabet and basic phrases in this beginners' Japanese class.

X723: 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.

X734: Adulting 101: 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

Y788: India and Indians in the First World War
Difficulty: ***
Teachers: Sami Raza

Over a million men from the Indian subcontinent served all over the world during the First World War, but their contribution has been mostly forgotten, even in the subcontinent itself. This course will be a brief introduction to both the military and social history of India during the period focusing mainly on the Indian Army and Independence Movement. It will use the Indian experience of the war as a lens into British India.

Prerequisites
Some knowledge of World War One and basic knowledge of Indian history will help, but is not essential.

Y743: History of Ballet: 1900-Present
Difficulty: **
Teachers: Jessie Oehrlein

This class will discuss the past century of ballet, focusing on the westward spread of Russian-style classical ballet, the establishment of new major ballet traditions in England and the United States, and the rise of contemporary ballet. Along the way, we'll look at photos and video to see how different techniques and styles emerged in different parts of the world. We'll also talk about where ballet is headed now.

Y771: The Protestant Reformation: 1517 -
Difficulty: **
Teachers: Amani Mohamed

The Protestant Reformation changed the face of Western Europe and would influence the history of the entire world until the Present day. This class will provide a basic introduction for explaining the course, allure, and progress of Protestantism in Western Europe.

Prerequisites
Some knowledge of European history.

Y745: The History of You: Discovering Digital Genealogy Full!
Difficulty: *

Here in New York City, we are blessed to be surrounded by many vibrant cultures, but have you ever wondered about your own heritage? The days of genealogy as a paper-based pastime for exclusively geriatric populations are long gone: welcome to family history in the digital age, where millions of records from around the globe are available to you with the click of a button—and often, for free!

In this class, we will learn the basics of genealogy using free digital resources, discuss ways to bring your family's history to life, and explore the resources available to you in New York City as you continue on your genealogy journey!

Whether you don't know your parents or come from a family of genealogists, I hope you'll be able to use this class as a springboard in discovering your personal history through rigorous and accurate genealogical methods.