Pre-College Programs

Math & Computer Science Courses (35)

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Introduction to Scientific Computing

For students in any discipline that may involve numerical computations. Includes instruction for programming in MATLAB. Applications discussed include solution of linear equations (with vectors and matrices) and nonlinear equations (by bisection, iteration, and Newton's method), interpolation, and curve-fitting, difference equations, iterated maps, numerical differentiation...

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Applied Ordinary Differential Equations

This course gives a comprehensive introduction to the qualitative and quantitative theory of ordinary differential equations and their applications. Specific topics covered in the course are applications of differential equations in biology, chemistry, economics, and physics; integrating factors and separable equations; techniques for solving linear systems of differential...

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Statistical Inference I

APMA 1650 begins an integrated first course in mathematical statistics. The first half of APMA 1650 covers probability and the last half is statistics, integrated with its probabilistic foundation. Specific topics include probability spaces, discrete and continuous random variables, methods for parameter estimation, confidence intervals, and hypothesis testing.Prerequisite:...

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Biomedical Informatics and Data Science for Biomedicine and Health Care

Modern health care relies on the ability to best interpret available data that may originate from a number of sources, including healthcare professionals, patients, and medical devices. Data science is the process of interpreting data for use within specific contexts. Biomedical informatics is the scientific discipline that is focused on transforming data for providing biomedical...

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Modeling Living Systems: The Principles of Life

Why can some cancer types elude treatments? How come we still haven't found a vaccine for HIV? Why do antibiotics sometimes work and sometimes don't? Adaptation, while providing quite a general answer to these questions, is not at all illustrative. This one simple principle governs many very different phenomena that we encounter in everyday life. The key to understanding...

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Computer Modeling of the Brain

The human brain is one of the most complicated and mysterious systems on the planet. In recent decades, a huge push has been made to understand the brain through computer modeling. A large number of scientists have been involved in the development of these models not only to advance our understanding and treatments of neurological and psychiatric illnesses, but also to help...

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Artificial Intelligence and Society

What is Artificial Intelligence (AI) and how will it shape the world in the decades to come? What ideas enable machines to see, use language, and reason, and how will these machines affect the world? In this course, we'll jointly explore the central ideas and anticipated societal impacts of Artificial Intelligence.The first week of the course we will focus...

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Introduction to Systems Thinking: Game Design and Learning

How do people learn, and how do games help people learn? In this workshop-based seminar, we will explore these questions by designing, reflecting upon, and critiquing our own games.Solving the complex problems of the 21st-century requires systems thinking- the “art of seeing the forest and the trees.” Yet, learning systems thinking as a decontextualized...

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Visualizing Your Data: Graphical Programming in R

We will use the statistical programming language R to graphically represent data. Students will be able to present their data in a compelling way. This will be useful for many fast-growing fields of study including public health and biomedical sciences.Advances in computing power have enabled scientists to amass huge amounts of data on everything from genetics to...

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Learn to Program in Five Days

This course is a whirlwind introduction to programming in Python. No programming experience is expected or required. By the end of the week, you will be able to design, execute, and debug your own code.The goal of this course is to learn how to program using Python, a highly popular, easy-to-learn programming language. Though the course is fast-paced, it assumes no...

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An Introduction to Game Theory

An Introduction to Game Theory is a three-week core course in behavioral economics. Game theory is the systematic study of strategic interactions that are present everywhere, not only in economics but in politics, sociology, law, computer science, and sports.The main goal of the course is to introduce students to the basic concepts and tools of game theory and to...

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Econometrics: Statistical Tools to Understand Economic Data

We are exposed to economic data and statistical analysis wherever we go: at the supermarket through prices and quantities of goods, at school through relative performance and GPAs, and in advertising through comparisons between the new iPhone 6 and a competitor’s model. Understanding the message is not an issue, but being a critical user of that information requires...

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Introduction to Behavioral Finance

The main goal of the course is to provide students with a broad idea of the ways in which psychological biases and heuristics influence our financial decisions.The course will focus on the biases and heuristics that have been documented in the behavioral literature. Students will relate these biases to news and to contemporary economic events. Students will thus read...

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Robotics - Programming and Innovation

Do you like LEGOs? Do you like robots? Do you want to learn to code? Have you ever wanted to make your LEGOs come to life? If you answered yes to any of these, come join us as we explore the fun and exciting world of robotics.This robotics course will feature fully customizable LEGO robotic creations as well as an introduction to the Arduino microcontroller. Students...

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Hack Your Space: Bringing J.A.R.V.I.S. Home

There are many reasons to envy Tony Stark, the Marvel character who created Ironman. He’s rich, good-looking, and can invent pretty much anything he wants. While the first two qualities are beyond the scope of this course, we can tackle the third. We want you to be able to build whatever you want, and this class will help you learn the skills.

First off, we won’t...

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Robot Rover Derby

Engineers design useful or desirable objects, employing scientific principles. In Robot Rover Derby you and your teammates will design, construct, and program a useful and desirable rover that will compete with other rover teams in a ladder tournament.Your rover can navigate autonomously by on-board computer signals. The rover will start remotely by 900MHz wireless...

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Engineering Your Own Smart Home: Custom Home Automation with Arduino

In what has been termed "The Second Industrial Revolution", millions of "makers" from around the world are collaborating via the internet to create amazing inventions using open source hardware and software. A major catalyst for this explosion of imagination is the Arduino platform, which includes a microcontroller and free software with which to program...

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The final frontier of the electromagnetic spectrum: the Terahertz Gap

The course will introduce students to one of the most fascinating and relatively new engineering research fields, namely, Terahertz (THz) Science & Technology; or in short, the THz field.

The THz field deals with the generation, detection, and manipulation of electromagnetic waves in the THz frequency range. THz waves bridge the gap between microwaves and light-waves,...

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Spy Training 101: How to Encode and Decode Messages like an Expert

The course provides an introduction to the history and mathematics behind cryptography. From Julius Caesar's encoded messages to his generals and Thomas Jefferson's wooden cipher to modern day encryption systems, codes have always been used to protect important or personal information. In this course we study the mathematical concepts behind encoding and decoding...

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Million Dollar Mathematics

Although not all open problems in mathematics come with a million dollar prize, some definitely do! Math is a changing and growing subject and new discoveries are being made all the time. Through experimentation and with the help of computers, we will discover how research mathematicians draw their conclusions. If we are lucky, we may even solve a million dollar problem!This...

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Number Theory: An Introduction to Higher Mathematics

"Mathematics is the queen of the sciences and number theory is the queen of mathematics." Carl Friedrich Gauss

Number theory, the study of the integers, is a vibrant area of mathematical research that many students do not have the opportunity to study in high school. The objectives for this course are to expose students to this beautiful theory, to understand...

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Applied Statistics

“For Today’s Graduate, Just One Word: Statistics.” Such was the title of a New York Times feature and the motivation behind this course. While the field of statistics is growing daily, the most critical aspects of the subject are accessible to high school students. This course will explain how, where, and why statistics is used to solve...

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How Big Is Infinity? And Other Math Questions

Have you ever wondered how many numbers there really are or how big infinity is? Many mathematicians have asked these questions, and the answers can be fascinating . . . and sometimes quite strange. This course will be a journey through the mathematical concepts that have helped answer such questions, and along the way, you'll get a taste of what pure mathematics is...

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Logic & Paradox

Logic is a system of rules upon which human reasoning is based. It is a tool that we deploy routinely in our everyday lives. It pervades every academic discipline, from mathematics to the sciences to the humanities. To philosophers, however, logic is a deep and complex subject of study in its own right. This course is devoted in part to exploring this system of rules, which...

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Combinatorics: Why Counting Counts, or How to Count Without Counting

Imagine putting a random group of people in a room: how many do you need so the probability that two of them have the same birthday is at least one half? Something like 182 or about 365/2, right? Wrong! In fact, the probability is already greater than one half with a random collection of only 23 people! At its core, this is a question about counting; in this course, we study...

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Probability and Its Applications

Don’t let them fool you! You hear people talking about probabilities all the time. 80% chance of rain? Well, what does that even mean? If a medical test gives the correct answer with 99% probability, does a positive test result mean you have a 99% chance of being sick? It does not. And when you hang out with your friends playing poker, wouldn’t you like to know...

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Bridging the Gap Between Math Class and the Real World

More often than not, the things we learn in math class seem to have no other use except in math class: the quadratic formula, finding domain and range, the Pythagorean Theorem... Yet these very techniques can give us a deep understanding of the world around us and even enable us to do things like create basic computer animation and predict the weather. This course will offer...

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Probability: Indispensable Tool, Philosophical Mystery

Suppose you roll two dice. Of course, you can’t say exactly what you will get. But there are some things you can say. You can say, for example, that it is less likely for the dice to land “snake eyes” (two ones) than to not land snake eyes. You can say that getting a sum of two is as likely as getting a sum of twelve. And you can say that...

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The Grand Tour: Our Solar System Up Close and Personal

Strange worlds exist within our solar system. On Saturn’s moon Titan, methane falls instead of rainwater. Mars is home to both the deepest canyon and the tallest mountain. Pluto has mountains made of ice that may still be actively forming today.

Humans have explored the Earth and our moon, but the other planets are millions of miles away. How do we learn about...

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From the Solar System to the Universe: An Introduction to Astrophysics and Cosmology

The Solar System. Black holes. Galaxy clusters. Quasars. The closer we look at these and other astrophysical objects, the more mysteries we uncover. This course will provide an introduction to topics of active research in astrophysics and cosmology, traveling from our galaxy to the furthest reaches of the Universe. Along the way, we will explore objects like black holes,...

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From Newton to String Theory: A History of Physics

We all know how a falling apple helped Newton discover the laws of gravitation, but did you know that playing bongos in the desert helped Richard Feynman untangle quantum field theory? Or that every famous physicist who studied thermodynamics eventually went crazy?This is a course for people who want to understand what physics is all about. We will discuss the equations...

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Decision Theory: Where Math and Philosophy Meet

Suppose you are offered a game: you flip a fair coin. If the coin comes up heads, you win $5. If the coin comes up tails, you lose $1. Playing the game is free. Is it rational to play this game? To many, the obvious answer is “yes.” Though the chances of losing and winning are the same, you stand to win much more money than you stand to lose. Decision...

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A new study shows.....How to handle conflicting evidence

Have you ever read an article that relies on a scientific study to draw conclusions, only to learn of another study with contradicting results? One day eating chocolate is good for you, the next it is not. How do we reconcile these conflicting messages - or are they conflicted at all? This course will help students critically assess and synthesize evidence to inform decision-making...

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A Data-Centric Introduction to Programming

An introduction to computer programming with a focus on skills needed for data-intensive applications. Topics include core constructs for processing both tabular and structured data; decomposing problems into programming tasks; data structures; algorithms; and testing programs for correct behavior.

This course is not intended for CS concentrators. In particular, it...

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Introductory Calculus, Part I

An intensive course in calculus of one variable including limits, differentiation, maxima and minima, the chain rule, rational functions, trigonometric functions, and exponential functions. Introduction to integration with applications to area and volumes of revolution. MATH 0090 and 0100, or AP Calculus BC score 4 or 5 are recommended for all students intending to concentrate...

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