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The following courses fulfill the Quantitative Reasoning with Data (QRD) requirement

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APCOMP 209A: Data Science 1: Introduction to Data Science

Semester: 

Fall

Offered: 

2023

APCOMP 209A/CS 109A/STAT 109A is an interdisciplinary course that relies on the data science process; the course equips students with computational, mathematical, and statistical methods for analyzing data, making inferences, and predicting outcomes, covering subject matter including tech, medicine, and pop culture. The course emphasizes not only theoretical understanding but also the practical application of these methods to real-world datasets, helping students recognize the value and impact of data in diverse fields. While no strict prerequisites are required, a fundamental...

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APCOMP 209B: Data Science 2: Advanced Topics in Data Science

Semester: 

Spring

Offered: 

2024

APCOMP 209B/COMPSCI 109B/STAT 109B is a direct continuation of APCOMP 209A/COMPSCI 109A/STAT 109A that will cover topics such as smoothing and additive models, unsupervised learning, Bayesian analysis, deep learning including convolutional neural networks, recurrent neural networks, language models, generative models and deep reinforcement learning. The course aligns with the QRD criteria by teaching methods for analyzing data, drawing statistical inferences, and making predictions applied to real data sets. Prerequisites: APCOMP 209A/COMPSCI 109A/STAT 109A.

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APMTH 101: Statistical Inference for Scientists and Engineers

Semester: 

Spring

Offered: 

2024

APMTH 101 is an introductory statistics course for students in engineering and the sciences that covers probability, statistical inference, and regression modeling. Students are expected to diligently read prior to class, such that sessions can be weighted towards performing in-class problem solving and lecturing can be reserved for the nuanced points of the material. A comprehensive understanding of multivariable calculus is required, however computational software (MATLAB) is leveraged to dedicate more attention on the application of statistical methods.

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APMTH 10: Computing with Python for Scientists and Engineers

Semester: 

Fall

Offered: 

2023

Students will learn to code in Python to solve mathematical and statistical problems in science and engineering, using real data such as epidemiological data for predicting the spread of the SARS-Cov-2 virus, financial data for risk assessment, and climate time series for calculating global trends. Students will learn to analyze and fit real data, calculate and propagate uncertainty, extract parameter values from data, and explore how the sampling of data affects inferences and prediction, while being aware of numerical approximation errors, overfitting, and model limitations. Students...

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APMTH 120: Applied Linear Algebra and Big Data

Semester: 

Spring

Offered: 

2024

APM120 teaches basic big-data analysis methods, all demonstrated using real-world examples, that based on student feedback are very often then used by students in their summer internships/career. Many methods for analyzing data are covered, and there is an emphasis throughout on motivating these methods with real problems and real data, in both lectures and homework assignments. Prerequisites: Math 21a and 21b or equivalent; and CS50 or APM10, or equivalent.

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APMTH 205: Advanced Scientific Computing: Numerical Methods

Semester: 

Fall

Offered: 

2023

This course covers the mathematical foundations of well-established numerical algorithms that are used for both modeling and data analysis. The algorithms will be explored through a range of real-world examples drawn from a variety of fields. Requires familiarity with linear algebra and calculus, as well as some programming experience at the level of COMPSCI 50 and above.

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APMTH 207: Advanced Scientific Computing: Stochastic Methods for Data Analysis, Inference and Optimization

Semester: 

Fall

Offered: 

2023

 

This class presents methodologies to model, analyze and optimize, physical systems using stochastic processes. We use data to develop and evaluate models and in turn algorithms that link models with data. We discuss advantages aan limitations of these processes and link them to computational thinking. Course prerequisites include a good level of probabilities and statistics, programming skills, as well as knowledge of partial differential equations.

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APMTH 22A: Solving and Optimizing

Semester: 

Fall

Offered: 

2023

This course covers concepts from linear algebra and multivariate calculus with a view towards data analysis, computation, and optimization. The course covers both the underlying mathematical theory as well as the practical tools needed for application to real world data. Students should already be comfortable with the material from Math 1ab.

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APMTH 231: Decision Theory

Semester: 

Spring

Offered: 

2024

APMTH 231 teaches statistical inference and estimation from a signal processing perspective. The courses aims to teach students a) to think about probabilistic models of data, b) how to develop estimation and inference algorithms, and c) how to apply it to real data. The course emphasizes the entire pipeline from writing a model, estimating its parameters and performing inference utilizing sports data, neuroscience data, geyser eruption data and other sources. The course also teaches students how to assess the goodness of fit of models to data, diagnostic tools to detect lack of fit, and...

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APMTH 50: Introduction to Applied Mathematics

Semester: 

Spring

Offered: 

2024

This course provides an introduction to the problems and issues of applied mathematics, focusing on areas where mathematical ideas have had a major impact on diverse fields of human inquiry. The course is organized around two-week topics drawn from a variety of fields, and involves reading classic mathematical papers in each topic. We will build mathematical and statistical models of real life problems such as spread of disease and option pricing, use computational methods to calculate predictions of our models, and test these predictions on real data. Mathematics 1b is a prerequisite,...

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APPHY 50A: Physics as a Foundation for Science and Engineering, Part I

Semester: 

Fall

Offered: 

2023

The AP50A/B sequence is a team- and project-based introduction to physics designed for engineering and physics concentrators focusing on the application of physics to real-world problems. It is equivalent in content and rigor to a standard calculus-based introductory physics course sequence (A: mechanics and waves; B: electromagnetism and optics). Through, hands-on and collaborative learning activities you will hone your scientific reasoning, estimation, and open-ended problem-solving skills. In addition, the activities in the course are designed to help you grow your capacity for self-...

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ASTRON 2: Celestial Navigation

Semester: 

Fall

Offered: 

2023

Students have described Celestial Navigation as “the most hands-on course at Harvard.” Teaching is almost entirely experienced in a laboratory setting with constant day and night climbs to the roof for data collection and culminating with a day on the water navigating eastward until Boston sinks below the horizon. Using a quantitative approach, we will construct and use maps to inform us, build quantitative models to predict how objects in the sky move, and explore the development of instruments and methods that resonant in current technologies...

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COMPSCI 109A: Data Science 1: Introduction to Data Science

Semester: 

Fall

Offered: 

2023

APCOMP 209A/CS 109A/STAT 109A is an interdisciplinary course that relies on the data science process; the course equips students with computational, mathematical, and statistical methods for analyzing data, making inferences, and predicting outcomes, covering subject matter including tech, medicine, and pop culture. The course emphasizes not only theoretical understanding but also the practical application of these methods to real-world datasets, helping students recognize the value and impact of data in diverse fields. While no strict prerequisites are required, a fundamental...

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COMPSCI 109B: Data Science 2: Advanced Topics in Data Science

Semester: 

Spring

Offered: 

2024

APCOMP 209B/COMPSCI 109B/STAT 109B is a direct continuation of APCOMP 209A/COMPSCI 109A/STAT 109A that will cover topics such as smoothing and additive models, unsupervised learning, Bayesian analysis, deep learning including convolutional neural networks, recurrent neural networks, language models, generative models and deep reinforcement learning. The course aligns with the QRD criteria by teaching methods for analyzing data, drawing statistical inferences, and making predictions applied to real data sets. Prerequisites: APCOMP 209A/COMPSCI 109A/STAT 109A.

...

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COMPSCI 10: Elements of Data Science

Semester: 

N/A

DS10 takes a holistic approach to helping students understand the key factors involved, from data collection and exploratory data analysis to modeling, communication, and effective teamwork. DS10 is aligned with all of the QRD criteria, teaching students computational, and statistical methods for analyzing real data, drawing inferences, and making predictions to answer questions, and understanding the limitations of these methods. DS10 has no prerequisites and is open to students from varied backgrounds, concentrations, and interests.

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COMPSCI 181: Machine Learning

Semester: 

Spring

Offered: 

2024

CS 181 provides a broad and rigorous introduction to machine learning, probabilistic reasoning and decision making in uncertain environments. Students will derive the mathematical underpinnings for many common methods, work computationally, applying machine learning to challenges with real data, and give consideration to the ethical implications of machine learning. The material is aimed at an advanced undergraduate level and students should be comfortable with writing non-trivial programs, have a background in probability theory, and familiarity with calculus and linear algebra.

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COMPSCI 1: Great Ideas in Computer Science

Semester: 

Spring

Offered: 

2023

COMPSCI 1 is a broad introduction to some of the most important principles and practices of functional and object-oriented software development using a methodology that places a high value on programs that are easy to read, maintain and modify.  Most of the programming will be done using Python, through which fundamental data structures and their algorithms will be investigated. Lectures and problem sets include visualization techniques using real-world data sets, linear regression, variance, and both formal and empirical analysis of execution time. This course is designed for...

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COMPSCI 32: Computational Thinking and Problem Solving

Semester: 

Spring

Offered: 

2024

COMPSCI 32 is an introduction to computational thinking, useful concepts in the field of computer science, and the art of computer programming using Python. Each class meeting and assignment focuses on learning to use computers to gain insights about the world around us and solve real-world problems, often using real-world data. The material assumes no prior experience in computer science or computer programming.

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E-PSCI 100: The Missing MATLAB Course: A Practical Intro to Programming and Data Analysis

Semester: 

Fall

Offered: 

2023

This hands-on course aims to empower students for solving problems using computer programming.  This involves learning the programming language (syntaxes) but more importantly, how to break down a problem into small pieces that can individually be solved easily.  A significant part of this course will be spent on solving problems and discussing various approaches with which they can be analyzed.  No previous experience in computer programming is necessary but students must be comfortable with vector/matrix calculations.

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E-PSCI 101: Global Warming Science 101

Semester: 

Spring

Offered: 

2024

E-PSCI/ESE 101 teaches climate change science from a quantitative perspective, so that students can understand the exact mechanisms behind changes often discussed in the news, as well as the mathematical or statistical methods used to analyze them. Many methods for analyzing climate data and simple climate modeling are covered, and the students will be involved in in-class climate data analysis during every lecture. Prerequisites: Basic calculus and ordinary differential equations, as covered for example by Math 1b, Math 19a, Math 21b. Basic programming experience is assumed (not...

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E-PSCI 102: Data Analysis and Statistical Inference in the Earth and Environmental Sciences

Semester: 

Fall

Offered: 

2023

Students will become familiar with techniques in statistical inference, deterministic and stochastic models of data, regression, time series analysis, bootstrap and Markov Chain Monte Carlo methods, and receive a brief introduction to machine learning. The course emphasizes hands-on learning: all examples we use are real data sets drawn from current research in the Earth, atmospheric, and planetary sciences. Familiarity with single variable calculus is required while multivariable calculus is recommended, but not required. 

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E-PSCI 131: Introduction to Physical Oceanography and Climate

Semester: 

Spring

Offered: 

2024

EPS/ESE131 teaches ocean physics from a quantitative perspective, so that students can understand the dynamics behind ocean circulation and waves and their role in climate and climate change. The course is math-based, and involves analyzing ocean data, and simple ocean and climate models; the students will be involved in in-class small-group collaborative work during lectures, developing and deriving the physical and mathematical foundations of ocean dynamics and complementing lecture materials. Basic calculus and ordinary differential equations as covered for example by Math 21b, and...

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E-PSCI 139: Paleoclimate as Prologue

Semester: 

Spring

Offered: 

2024

In this course we will quantitatively assess past events in Earth's history involving temperature, precipitation, and sea level, and leverage these past phenomena to inform about future changes in climate. Topics include inferring temperature from instrumental, dendrochronological, ice-core, and marine proxy records over the Medieval Warm Period, Little Ice Age, and post-industrial epochs; exploring variations in sea level recorded by tide gages and coral records over the Holocene and Last Interglacial; assessing precipitation variability using modern instrumental records and late-...

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ECON 1123: Introduction to Econometrics

Semester: 

Fall

Offered: 

2023

This course introduces state-of-the-art methods for answering important public policy questions, such as quantifying the causal effect of incarceration on recidivism or measuring the causal effect of unemployment insurance on unemployment durations. Students will learn how to develop, evaluate, and implement their own research designs to answer these types of questions and quantify uncertainty associated with such estimates. The class concludes with time series forecasting and financial econometrics. Most students will have taken one prior course in statistics or probability theory, such...

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ECON 1126: Quantitative Methods in Economics

Semester: 

Fall

Offered: 

2023

ECON 1126 is an advanced econometrics class that focuses on the analysis of empirical quantitative models that are commonly used in applied economics. We focus first on studying the mathematical and statistical foundations of using linear models. This includes approximating conditional expectations, forming predictions, studying omitted variables bias,  and most importantly analyzing requirements for causal interpretations. The class uses real world data as a vehicle to illustrate the theoretical concepts. Applications include the demand and supply model of simultaneous causality,...

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ECON 50: Using Big Data to Solve Economic and Social Problems

Semester: 

Spring

Offered: 

2024

This course will show how "big data" can be used to understand and address some of the most important social and economic problems of our time. In empirical projects and weekly labs, students will work with real data to learn how the methods discussed in the course can be implemented in practice. The course will give students an introduction to frontier research and policy applications in economics and social science in a non-technical manner that does not require prior coursework in economics or statistics, making it suitable both for students exploring economics for the first time, as...

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