Majors

Computer Science (A.B.)source 1 source 2

Courses

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COMPSCI 1: Great Ideas in Computer Science (4) intro

An introduction to the most important discoveries and intellectual paradigms in computer science, designed for students with little or no previous background. Explores problem-solving and data analysis using Python, a programming language with a simple syntax and a powerful set of libraries. This course covers basic data types and collections (lists, dictionaries, tuples, and sets), control flow, recursion, supervised machine learning via regression, visualization, information hiding and encapsulation using classes and objects, and introduces the analysis of program performance. Presents an integrated view of computer systems, from switching circuits up through compilers, and examines theoretical and practical limitations related to unsolvable and intractable computational problems. Other topics include the social and ethical dilemmas presented by such issues as software unreliability, algorithmic bias, and invasions of privacy.

COMPSCI 20: Discrete Mathematics for Computer Science (4) math

Widely applicable mathematical tools for computer science, including topics from logic, set theory, combinatorics, number theory, probability theory, and graph theory. Practice in reasoning formally and proving theorems.

COMPSCI 32: Computational Thinking and Problem Solving (4) intro

An introduction to computational thinking, useful concepts in the field of computer science, and the art of computer programming using Python. Significant emphasis is placed on class meetings and learning to use computers to solve complex, real-world problems. Concepts and techniques are introduced as they are needed to help solve the problems confronting us. Students will learn how to go from an ambiguous problem description to a running solution and will leave the class knowing how to instruct computers to do what they want them to do. Prior experience in computer science or computer programming is not necessary.

COMPSCI 37: Incentives in the Wild: from Tanking in Sports to Mining Cryptocurrencies (4) theory

How could it be that paving a new road might increase congestion for all drivers? Why would a professional sports team ever try not to score in a game that it wants to win? Why would any student rank high schools not in their order of preference when applying? And what are some incentive pitfalls that the designer of a cryptocurrency system should be aware of? In this course, we will examine seemingly strange social phenomena, use mathematical tools to model them and to analyze how and why distorted incentives give rise to them, and explore potential mechanisms to eliminate such phenomena.

COMPSCI 50: Introduction to Computer Science (4) intro

This is COMPSCI 50, Harvard University's introduction to the intellectual enterprises of computer science and the art of programming, for concentrators and non-concentrators alike, with or without prior programming experience. (More than half of COMPSCI 50 students have never taken CS before!) This course teaches you how to solve problems, both with and without code, with an emphasis on correctness, design, and style. Topics include computational thinking, abstraction, algorithms, data structures, and computer science more generally. Problem sets inspired by the arts, humanities, social sciences, and sciences. More than teach you how to program in one language, this course teaches you how to program fundamentally and how to teach yourself new languages ultimately. The course starts with a traditional but omnipresent language called C that underlies today's newer languages, via which you'll learn not only about functions, variables, conditionals, loops, and more, but also about how computers themselves work underneath the hood, memory and all. The course then transitions to Python, a higher-level language that you'll understand all the more because of C. Toward term's end, the course introduces SQL, via which you can store data in databases, along with HTML, CSS, and JavaScript, via which you can create web and mobile apps alike. Course culminates in a final project. See https://cs50.harvard.edu/college for advice, FAQs, syllabus, and what's new. Email the course's heads at heads@cs50.harvard.edu with questions.

COMPSCI 51: Abstraction and Design in Computation (4) intro

Fundamental concepts in the design of computer programs, emphasizing the crucial role of abstraction. The goal of the course is to give students insight into the difference between programming and programming well. To emphasize the differing approaches to expressing programming solutions, you will learn to program in a variety of paradigms -- including functional, imperative, and object-oriented. Important ideas from software engineering and models of computation will inform these different views of programming.

COMPSCI 61: Systems Programming and Machine Organization (4) sys

Fundamentals of computer systems programming, machine organization, and performance tuning. This course provides a solid background in systems programming and a deep understanding of low-level machine organization and design. Topics include C and assembly language programming, program optimization, memory hierarchy and caching, virtual memory and dynamic memory management, concurrency, threads, and synchronization.

COMPSCI 73: Code, Data, and Art (4)

A studio course where software is used as an artistic medium. The course is designed to expose students to current perspectives on the intersection of computer science and art, and to build skills that will allow them to express themselves creatively via software. An additional focus will be the role of data in modern artistic practice.

COMPSCI 91R: Supervised Reading and Research (4) special

Supervised individual study of advanced topics in computer science. A student wishing to enroll in Computer Science 91r must be accepted by a faculty member who will supervise the course work. Additional information and a form are available via https://harvardcs.info/forms/#cs-91r-form. The form must be filled out and signed by the student and faculty supervisor. Students writing theses may enroll in this course while conducting thesis research and writing.

COMPSCI 96: System Design Projects: Machine Learning for Social Impact (4) capstone

Student teams will work with real partner organizations to use machine learning techniques on a directly impactful project. Students will learn how to effectively explore data, create and iterate on real models, communicate and work with external partners, and incorporate ethics into their technical work. The class will include guest lectures from experts in various fields of the social impact tech space.

APCOMP 221: Critical Thinking in Data Science (4) impact

This course examines the wide-ranging impact data science has on the world and how to think critically about issues of fairness, privacy, ethics, and bias while building algorithms and predictive models that get deployed in the form of products, policy and scientific research. Topics will include algorithmic accountability and discriminatory algorithms, black box algorithms, data privacy and security, ethical frameworks; and experimental and product design. We will work through case studies in a variety of contexts including media, tech and sharing economy platforms; medicine and public health; data science for social good, and politics. We will look at the underlying machine learning algorithms, statistical models, code and data. Threads of history, philosophy, business models and strategy; and regulatory and policy issues will be woven throughout the course.

COMPSCI 229BR: Topics in the Foundations of Machine Learning (4) ai

This will be a graduate level course on recent advances and open questions in the foundations of machine learning and specifically deep learning. We will review both classical results as well as recent papers in areas including classifiers and generalization gaps, representation learning, generative models, adversarial robustness, out of distribution performance, and more. This is a fast-moving area and it will be a fast-moving course. We will aim to cover both state-of-art results, as well as the intellectual foundations for them, and have a substantive discussion on both the “big picture” and technical details of the papers. In addition to the theoretical lectures, the course will involve a programming component aiming to get students to the point where they can both reproduce results from papers and work on their own research. This component will be largely self-directed and we expect students to be proficient in Python and in picking up technologies and libraries such as pytorch/numpy/etc on their own (aka "Stack Overflow oriented programming").

COMPSCI 229R: Topics in Theoretical Computer Science: Essential Coding Theory (4) theory

Introduces essential elements the theory of error-correcting codes. Focuses on the basic results in the area, taught from first principles. Special focus will be given on results of asymptotic or algorithmic significance. Principal topics include: 1. Construction and existence results for error-correcting codes 2. Limitations on the combinatorial performance of error-correcting codes 3. Decoding algorithms 4. Applications to other areas of mathematics and computer science. Lecture notes for this course from previous offerings give further details on the material covered. These may be found at http://madhu.seas.harvard.edu/courses/Spring2020 Notes: Instructor permission needed to enroll. Students interested in the course should write to the instructor explaining what their background is in CS and Math, and explaining why they are interested in the course. Note that the course is an advanced grad course and students are expected to have a strong math background in addition to the CS courses listed in Recommended Prep.

APCOMP 295: Topics in Applied Computation: Advanced Practical Data Science (4) ai

In this course we explore advanced practical data science practices. The course will be divided into three major topics: 1. How to scale a model from a prototype to the cloud. 2. How to use existing models for transfer learning. 3. Introducing intuitive visualization tools for investigating properties and diagnosing issues of models.

COMPSCI 1050: Privacy and Technology (4) impact

What is privacy, and how is it affected by recent developments in technology? This course critically examines popular concepts of privacy and uses a rigorous analysis of technologies to understand the policy and ethical issues at play. Case studies: database anonymity, research ethics, wiretapping, surveillance, and others. Course relies on some technical material, but is open and accessible to all students, especially those with interest in economics, engineering, political science, computer science, sociology, biology, law, government, philosophy.

COMPSCI 1070: Systems Development for Computational Science (4) softeng

This is a project-based course emphasizing designing, building, testing, maintaining, and modifying software for scientific computing and data sciences. The class is focusing on a thorough introduction of the Python programming language with discussion of core concepts in object-oriented programming as well as essential data structures useful in most programming tasks. Students will work in groups on a semester long project. Students will further learn how to work with SQL databases and how to integrate them in Python using SQLite3 and Pandas. After completion of this course, students will be able to adapt basic tools and techniques to design complex software systems aimed at solving computational and data processing problems in academic and industrial environments.

COMPSCI 1090A: Data Science 1: Introduction to Data Science (4) ai

Data Science 1 is the first half of a one-year introduction to data science. The course will focus on the analysis of messy, real life data to perform predictions using statistical and machine learning methods. Material covered will integrate the five key facets of an investigation using data: (1) data collection - data wrangling, cleaning, and sampling to get a suitable data set; (2) data management - accessing data quickly and reliably; (3) exploratory data analysis – generating hypotheses and building intuition; (4) prediction or statistical learning; and (5) communication – summarizing results through visualization, stories, and interpretable summaries. Part one of a two part series. The curriculum for this course builds throughout the academic year. Students are strongly encouraged to enroll in both the fall and spring course within the same academic year.

COMPSCI 1090B: Data Science 2: Advanced Topics in Data Science (4) ai

Data Science 2 is the second half of a one-year introduction to data science. Building upon the material in Data Science 1, the course introduces advanced methods for statistical modeling, representation, and prediction. Topics include multiple deep learning architectures such as CNNs, RNNs, transformers, language models, autoencoders, and generative models as well as basic Bayesian methods, and unsupervised learning. Students are strongly encouraged to enroll in both the fall and spring course within the same academic year. Part two of a two-part series.

COMPSCI 1200: Introduction to Algorithms and their Limitations (4) theory

An introductory course in theoretical computer science, aimed at giving students the power of using mathematical abstraction and rigorous proof to understand computation. Thus equipped, students will be able to design and use algorithms that apply to a wide variety of computational problems, with confidence about their correctness and efficiency, as well as recognize when a problem may have no algorithmic solution. At the same time, they will gain an appreciation for the beautiful mathematical theory of computation that is independent of (indeed, predates) the technology on which it is implemented.

COMPSCI 1210: Introduction to Theoretical Computer Science (4) theory

Computation occurs over a variety of substrates including silicon, neurons, DNA, the stock market, bee colonies and many others. In this course we will study the fundamental capabilities and limitations of computation, including the phenomenon of universality and the duality of code and data. Some of the questions we will touch upon include: Are there functions that cannot be computed? Are there true mathematical statements that can't be proven? Are there encryption schemes that can't be broken? Is randomness ever useful for computing? Can we use the quirks of quantum mechanics to speed up computation?

COMPSCI 1240: Data Structures and Algorithms (4) algs

Design and analysis of efficient algorithms and data structures. Algorithm design methods, graph algorithms, approximation algorithms, and randomized algorithms are covered.

COMPSCI 1260: Fairness and Privacy: Perspectives from Law and Probability (4) theory

Algorithms are mathematical objects with real life consequences. How do you say “fairness” and “privacy” in mathematics? How do existing theoretical computer science formulations mesh with legal privacy and nondiscrimination notions? Drawing on key concepts from differential privacy, the theory of algorithmic fairness, and crytography, the course focuses on the analysis and mitigation of privacy loss and unfairness in machine learning and data analysis. Through joint readings and weekly class meetings with the HLS course of the same name, students will develop disciplinary “bilingualism.”

COMPSCI 1270: Cryptography (4) theory

Cryptography is as old as human communication itself, but has undergone a revolution in the last few decades. It is now about much more than "secret writing" and includes seemingly paradoxical notions such as communicating securely without a shared secret, and computing on encrypted data. In this challenging but rewarding course we will start from the basics of private and public key cryptography and go all the way up to advanced notions such as fully homomorphic encryption and software obfuscation. This is a proof-based course that will be best appreciated by mathematically mature students.

COMPSCI 1360: Economics and Computation (4) theory

The course examines the interplay between economic thinking and computational thinking as it relates to the design of online platforms and societal decision-making mechanisms. The focus is on fundamental concepts, modeling, and mathematical analysis. Topics covered include game theory, incentive alignment, matching, social choice, fair division and social networks. Special attention is given to ideas that draw on both disciplines, such as worst-case bounds on the inefficiency of equilibria, voting rules that are computationally hard to manipulate, and approximation algorithms that discourage strategic behavior.

COMPSCI 1410: Computing Hardware (4) sys

This course delves into the design principles and practices of high performance digital computing systems that are cost effectively and reliably manufactured with billions of near atomic scale semiconductor components. Key abstractions and foundational concepts are emphasized as the course covers the basic operation of CMOS transistors and logic gates, combinational and sequential logic including Finite State Machines (FSMs), digital memory subsystems, and machine code culminating with the implementation of a MIPS processor. Lab assignments will focus on the practical aspects of digital hardware design by utilizing Field Programmable Gate Arrays (FPGAs), Verliog (Hardware Description Language) and advanced CAD tools for the design, simulation and verification of digital computing hardware.

COMPSCI 1411: Computer Architecture (4) sys

Review of the fundamental structures in modern processor design. Topics include computer organization, memory system design, pipelining, and other techniques to exploit parallelism. Discussion of modern topics including GPU architectures, datacenter architecture, mobile/embedded SoC architectures, and machine learning acceleration as time permits. Emphasis on a quantitative evaluation of design alternatives and an understanding of performance and energy consumption issues.

COMPSCI 1430: Computer Networks (4) sys

Computer networking has enabled the emergence of mobile and cloud computing, creating two of the most significant technological breakthroughs in computing. Computer networks have become even more critical these days since remote activities have become a new norm. We expect several focuses in the coming years. First, we will witness the emergence of 5G wireless mobile networks, which have already begun to replace the current 4G networks. Second, cybersecurity and privacy will receive unprecedented attention from the industry. Third, blockchain technology, which underlies Bitcoin, creates a new trusted network infrastructure for many new distributed applications. Fourth, distance learning and virtual meetings will push the limits of current multicast and network management technologies. In this course, students will learn basic networking protocols as well as these timely topics.

COMPSCI 1450: Networking at Scale (4) sys

This course studies computer network topics including Layer 2/Layer 3 topology, routing, transport protocols, traffic engineering, network functions, programmable switches, and software-defined networking. Modern networks have grown to large scale (connecting millions of servers) and high speed (terabits per second) to meet the needs of cloud applications in business and society. Thus, in addition to learning the conventional concepts in networking, we will also discuss how to adapt these concepts to large-scale networks. These discussions will hopefully help deepen our understanding of networking technologies. This course includes lectures and system programming projects.

COMPSCI 1520: Programming Languages (4) pls

Comprehensive introduction to the principal features and overall design of both traditional and modern programming languages, including syntax, formal semantics, abstraction mechanisms, modularity, type systems, naming, polymorphism, closures, continuations, and concurrency. Provides the intellectual tools needed to design, evaluate, choose, and use programming languages.

COMPSCI 1530: Compilers (4) pls

Implementation of efficient interpreters and compilers for programming languages. Associated algorithms and pragmatic issues. Emphasizes practical applications including those outside of programming languages proper. Also shows relationships to programming-language theory and design. Participants build a working compiler including lexical analysis, parsing, type checking, code generation, and register allocation. Exposure to run-time issues and optimization.

COMPSCI 1610: Operating Systems (4) sys

This course focuses on the design and implementation of modern operating systems. The course discusses threads, processes, virtual memory, schedulers, and the other fundamental primitives that an OS uses to represent active computations. An exploration of the system call interface explains how applications interact with hardware and other programs which are concurrently executing. Case studies of popular file systems reveal how an OS makes IO efficient and robust in the midst of crashes and unexpected reboots. Students also learn how virtualization allows a physical machine to partition its resources across multiple virtual machines. Class topics are reinforced through a series of intensive programming assignments which use a real operating system.

COMPSCI 1650: Data Systems (4) sys

We are in the big data era and data systems sit in the critical path of everything we do. We are going through major transformations in businesses, sciences, as well as everyday life - collecting and analyzing data changes everything and data systems provide the means to store and analyze a massive amount of data. This course is a comprehensive introduction to modern data systems. The primary focus of the course is on the modern trends that are shaping the data management industry right now: column-store and hybrid systems, shared nothing architectures, cache conscious algorithms, hardware/software co-design, main-memory systems, adaptive indexing, stream processing, scientific data management, and key-value stores. We also study the history of data systems, traditional and seminal concepts and ideas such as the relational model, row-store database systems, optimization, indexing, concurrency control, recovery and SQL. In this way, we discuss both how and why data systems evolved over the years, as well as how these concepts apply today and how data systems might evolve in the future. We focus on understanding concepts and trends rather than specific techniques that will soon be outdated - as such the class relies largely on recent research material and on a semi-flipped class model with a lot of hands-on interaction in each class.

COMPSCI 1710: Visualization (4) graphics

An introduction to key design principles and techniques for visualizing data. Covers design practices, data and image models, visual perception, interaction principles, visualization tools, and applications. Introduces programming of web-based interactive visualizations.

COMPSCI 1750: Computer Graphics (4) graphics

This course covers the fundamentals of 3D computer graphics using a modern shader-based version of OpenGL. Main topics include: geometric coordinate systems and transformations, keyframe animation and interpolation, camera simulation, triangle rasterization, material simulation, texture mapping, image sampling and color theory. The course also touches on ray tracing, geometric modeling and simulation-based animation.

COMPSCI 1780: Engineering Usable Interactive Systems (4) humans

In this course, students learn critical techniques, concepts, and technologies for building usable interactive systems, alone and in pairs. Assignments provide hands-on experiences with different modern frameworks, platforms, and libraries while conceptual commonalities and distinctions are annotated and explained. Lectures cover relevant basic and advanced topics, such as human cognitive capabilities, iterative prototyping, and human-AI interaction. The final project will require both front-end and back-end development, iterative prototyping with humans, and a final evaluation with target users. Designed for advanced undergraduates.

COMPSCI 1810: Machine Learning (4) ai

Introduction to machine learning, providing a probabilistic view on artificial intelligence and reasoning under uncertainty. Topics include: supervised learning, ensemble methods and boosting, neural networks, support vector machines, kernel methods, clustering and unsupervised learning, maximum likelihood, graphical models, hidden Markov models, inference methods, and computational learning theory. Students should feel comfortable with multivariate calculus, linear algebra, probability theory, and complexity theory. Students will be required to produce non-trivial programs in Python.

COMPSCI 1820: Artificial Intelligence (4) ai

Artificial Intelligence (AI) is already making a powerful impact on modern technology, and is expected to be even more transformative in the near future. The course introduces the ideas and techniques underlying this exciting field, with the goal of teaching students to identify effective representations and approaches for a wide variety of computational tasks. Topics covered in this course are broadly divided into search and planning, optimization and games, and uncertainty and learning. Special attention is given to ethical considerations in AI and to applications that benefit society. For more information please see the course website.

COMPSCI 1840: Introduction to Reinforcement Learning (4) ai

Modern AI systems often need the ability to make sequential decisions in an unknown, uncertain, possibly hostile environment, by actively interacting with the environment to collect relevant data. Reinforcement Learning (RL) is a general framework that can capture the interactive learning setting and has been used to design intelligent agents that achieve high-level performance in challenging applications such as Go, computer games, robotic manipulation, health care, and education. This course provides an introduction to reinforcement learning covering a range of problem formulations, algorithms, and theory. The four main themes of the course are (1) Markov decision processes (Bellman equations/optimality, planning, UCB, unknown environments, linear quadratic control, exploration, imitation learning), (2) bandits (epsilon-greedy, UCB, Thompson sampling, contextual bandits, linear bandits, exploration in MDPs), and (3) methods for large-scale systems (policy gradient methods, deep RL, Monte Carlo tree search, Q-learning). There will also be an Embedded Ethics lecture on ethical issues arising in reinforcement learning. The assignments will focus on a mix of algorithmic and statistical principles, along with their programming implementations.

COMPSCI 1870: Introduction to Computational Linguistics and Natural-language Processing (4) ai

Natural-language-processing applications are ubiquitous: Alexa can set a reminder, or play a particular song, or provide your local weather if you ask; Google Translate can make documents readable across languages; ChatGPT can be prompted to generate convincingly fluent text, which is often even correct. How do such systems work? This course provides an introduction to the field of computational linguistics, the study of human language using the tools and techniques of computer science, with applications to a variety of natural-language-processing problems such as these. You will work with ideas from linguistics, statistical modeling, machine learning, and neural networks, with emphasis on their application, limitations, and implications. The course is lab- and project-based, primarily in small teams, and culminates in the building and testing of a question-answering system.

COMPSCI 1910: Classics of Computer Science (4) special

Papers every computer scientist should have read, from all areas of the field and dating from its origins to the present.

COMPSCI 1960: Designing K-12 Computer Science Learning Experiences (4) softeng

From computational thinking to workforce arguments, there is considerable interest in and excitement about including computer science education for all K–12 students. Yet, unlike other disciplines with a much longer history in formal schooling, the interest in computer science education is not yet supported by commensurate attention to research and teacher practice. In this course, we will examine the state of K–12 computing education: questioning its value, examining its history, and imagining and contributing to its potential. The course will be organized as both a reading group and a lab, building a community of people who are committed to K–12 CS education. Each week you will read classic and current research, and write accompanying memos to document your evolving understandings of the field. Throughout the course, either individually or with partners, you will develop an independent project that explores the design of K–12 computer science learning experiences. Some examples of possible projects include: designing CS-standalone or cross-curricular learning activities and curriculum, building a programming language for novices, developing an annotated bibliography, critically analyzing policy documents such as curriculum frameworks and standards from around the world, or contributing to current K–12 CS education research initiatives.

COMPSCI 1970: AI Research Experiences (4) ai

Learn the practical skills required for applied deep learning work, including hands on experience with method development, model training at scale, and error analysis. You will learn the technical writing skills required for applied AI research, including experience composing different elements of a full research paper. Through structured assignments, you will tackle a scoped-out research project in a small team from conception to co-authoring a manuscript.

COMPSCI 2050: High Performance Computing for Science and Engineering (4) sys

With manufacturing processes reaching the limits in terms of transistor density on today’s computing architectures, efficient modern code must exploit parallel execution to maintain scaling of available hardware resources. The use of computers in academia, industry and society is a fundamental tool for solving (scientific) problems while the 'think parallel' mindset of code developers is still lagging behind. The aim of this course is to introduce the student to the fundamentals of parallel programming and its relationship on computer architectures. Various forms of parallelism are discussed and exploited through different programming models with focus on shared and distributed memory programming. The learned techniques are tried out by means of homework, lab sessions and a term project.

COMPSCI 2080: Applied Privacy for Data Science (4) ai

The risks to privacy when making human subjects data available for research and how to protect against these risks using the formal framework of differential privacy. Methods for attacking statistical data releases, the mathematics of and software implementations of differential privacy, deployed solutions in industry and government. Assignments will include implementation and experimentation on data science tasks.

COMPSCI 2210: Computational Complexity (4) theory

A quantitative theory of the resources needed for computing and the impediments to efficient computation. The models of computation considered include ones that are finite or infinite, deterministic, randomized, quantum or nondeterministic, discrete or algebraic, sequential or parallel.

COMPSCI 2231: Quantum Computation and Quantum Complexity (4) theory

An introduction to the quantum view on a variety of disciplines: algorithms, complexity, cryptography and information. Course will elucidate the source of quantum advantage in computation, ties of quantum computation with physics, and the power of entanglement.

COMPSCI 2241: Algorithms at the Ends of the Wire (4) algs

Covers topics related to algorithms for big data, especially related to networks and database systems. Themes include sketch-based data structures, compression, graph and link information, and information theory. Requires a major final research-based project.

COMPSCI 2242: Probabilistic Analysis and Algorithms (4) algs

Probabilistic techniques and tools for the design and analysis of algorithms. Designed for all first-year graduate students in all areas.

COMPSCI 2243: Algorithms for Data Science (4) algs

This is a graduate topics class on algorithmic challenges in modern machine learning and data science. We will touch upon a number of domains (generative modeling, deep learning theory, robust statistics, Bayesian inference) and frameworks for algorithm design (spectral/tensor methods, moment methods, message passing, diffusions), focusing on provable guarantees. The theory draws upon a range of techniques from stochastic calculus, harmonic analysis, statistical physics, algebra, and beyond. We will also explore the myriad modeling challenges in building this theory and prominent paradigms (semi-random models, smoothed complexity, oracles) for going beyond traditional worst-case analysis.

COMPSCI 2260: Topics in Theory for Society: Differential Privacy (4) theory

Differential Privacy is a mathematically rigorous definition of privacy that has become the de facto standard for statistical analysis of large datasets. Differential privacy provides a concrete measure of privacy loss, and differentially private algorithms are equipped with a parameter for controlling this loss. A signal property of differential privacy is closure under composition, meaning that we can understand and control the cumulative privacy loss as the data are subjected to multiple analyses. In consequence, differential privacy is 'programmable:' one can combine simple differentially private computational primitives in creative ways to obtain privacy-preserving algorithms for complex analytical tasks. The course will cover (1) the basics of differential privacy: the definition and its properties, computational primitives, and composition theorems; (2) selected advanced differentially private algorithms drawn from the literature and a wide range of application areas from industry to the US Census; and (3) lower bounds: limits on what differential privacy – or any privacy technology – can offer.

COMPSCI 2270: Cryptography (4) pls

Cryptography is as old as human communication itself, but has undergone a revolution in the last few decades. It is now about much more than 'secret writing' and includes seemingly paradoxical notions such as communicating securely without a shared secret, and computing on encrypted data. In this challenging but rewarding course we will start from the basics of private and public key cryptography and go all the way up to advanced notions such as fully homomorphic encryption and software obfuscation. This is a proof-based course that will be best appreciated by mathematically mature students.

COMPSCI 2280: Computational Learning Theory (4) theory

Possibilities of and limitations to performing learning by a computational process. Computationally feasible generalization and its limits. Topics include computational models of learning, polynomial time learnability, learning from examples and from queries to oracles. Applications to Boolean functions, languages and geometric functions. Darwinian evolution as learning.

COMPSCI 2281R: Topics in the Foundations of Machine Learning (4) ai

This will be a graduate level course on recent advances and open questions in the foundations of machine learning and specifically deep learning. We will review both classical results as well as recent papers in areas including classifiers and generalization gaps, representation learning, generative models, adversarial robustness, out of distribution performance, and more. This is a fast-moving area and it will be a fast-moving course. We will aim to cover both state-of-art results, as well as the intellectual foundations for them, and have a substantive discussion on both the 'big picture' and technical details of the papers. In addition to the theoretical lectures, the course will involve a programming component aiming to get students to the point where they can both reproduce results from papers and work on their own research. This component will be largely self-directed and we expect students to be proficient in Python and in picking up technologies and libraries such as pytorch/numpy/etc on their own (aka 'Stack Overflow oriented programming').

COMPSCI 2370: Economic Analysis as a Frontier of Theoretical Computer Science (4) theory

How can we use tools from statistical learning theory to design better auctions? Can we use cryptography to better implement matching mechanisms? And how should we approach formally proving that welfare in Nash equilibria for many games is not 'much worse' than in the social optimum? This course explores the application of diverse ideas, techniques, and solution aesthetics from theoretical computer science to derive meaningful new insights into classic economic problems. The three main themes are approximation theorems (including bounding the loss in revenue or welfare due to lack of information, to strategic behavior, or to impracticality of the optimal mechanism); various notions of complexity (including computational complexity, communication complexity, and sample complexity); and cryptographic tools (including cryptographic commitments, multiparty computation, and zero-knowledge proofs). Economic applications mostly include analysis of equilibria, pricing, and mechanism design.

COMPSCI 2380: Optimized Democracy (4) theory

The course examines the mathematical and algorithmic foundations of democracy, running the gamut from theory to applications. The goal is to provide students with a rigorous perspective on, and a technical toolbox for, the design of better democratic systems. Topics include computational social choice (identifying optimal voting rules), fairness in political redistricting (avoiding gerrymandering) and apportionment (allocating seats on a representative body), sortition (randomly selecting citizens assemblies), liquid democracy (transitively delegating votes), and weighted voting games (analyzing legislative power through cooperative game theory).

COMPSCI 2411: Advanced Computer Architecture (4) sys

COMPSCI 2420: Computing at Scale (4) ai

Specialized AI accelerators enable efficient AI computations for a variety of tasks at various scales using a wide range of parallel, distributed, and embedded computing platforms. For example, in generative AI applications such as ChatGPT and Stable Diffusion, these accelerators allow for (1) distributed model training and low-latency, high-throughput inference serving in the cloud, and (2) efficient private training and inference using local knowledge on resource-constrained edge devices. In this course, students will learn systematic methods for implementing parallel computations for computer vision and language models on numerous computing cores or nodes. They will also learn techniques for co-designing machine learning models, data curation methods, computing algorithms, and system architectures. Upon successful completion of this course, students will be equipped to tackle the challenging tasks of designing and utilizing energy-efficient, high-performance AI accelerators.

COMPSCI 2430: Advanced Computer Networks (4) sys

This is a graduate-level course on computer networks. This course offers an in-depth exploration of a subset of advanced topics in networked systems. We will discuss the latest developments in the entire networking stack, the interactions between networks and high-level applications, and their connections with other system components such as compute and storage. In this year's edition, we will use machine learning as a prime example to understand its unique requirements and challenges in the context of networking. As machine learning applications increasingly rely on larger models and faster accelerators, the demand for enhanced networking capabilities becomes imperative. Throughout this course, we will study cutting edge networking solutions and principles for co-designing networks with compute and storage, to meet the evolving needs of machine learning applications. The course will include lectures, in-class presentations, paper discussions, and a research project.

COMPSCI 2470R: Advanced Topics in Computer Architecture (4) sys

Seminar course exploring recent research in computer architecture. Topics vary from year to year and will include subjects such as multi-core architectures, energy-efficient computing, reliable computing, and the interactions of these issues with system software. Students read and present research papers, undertake a research project.

COMPSCI 2490R: Tiny Machine Learning (4) ai

Tiny machine learning (TinyML) is defined as a fast-growing field of machine learning technologies and applications including hardware (dedicated integrated circuits), algorithms and software capable of performing on-device sensor (vision, audio, IMU, biomedical, etc.) data analytics at extremely low power, typically in the mW range and below, and hence enabling a variety of always-on use-cases and targeting battery-operated devices. The pervasiveness of ultra-low-power embedded devices, coupled with the introduction of embedded machine learning frameworks like TensorFlow Lite for Microcontrollers, will enable the mass proliferation of AI-powered IoT devices. The explosive growth in machine learning and the ease of use of platforms like TensorFlow (TF) make it an indispensable topic of study for modern computer science and electrical engineering students.

COMPSCI 2520R: Advanced Topics in Programming Languages (4) pls

Seminar course exploring recent research in programming languages. Topics vary from year to year. Students typically read and present research papers, undertake a research project.

COMPSCI 2540: Formal Methods for Computer Security (4) theory

This course explores formal methods for computer security, including formal security models, relationships between security properties/policies and enforcement mechanisms, principled techniques and tools to specify, analyze, and construct secure computer systems. Specific topics include properties, hyperproperties, side channels, reasoning about cryptographic protocols, information flow, authorization logics, and verification techniques. Assessment will include homeworks and/or small projects during the semester as well as a final, larger project that is open-ended and driven by student interests.

COMPSCI 2610: Research Topics in Operating Systems (4) sys

An introduction to operating systems research. Paper-based seminar course that introduces students to the state of the art in systems research through historical and quantitative lenses. Students will read and discuss research papers and complete a final research project.

COMPSCI 2620: Introduction to Distributed Computing (4) sys

An examination of the special problems associated with distributed computing such as partial failure, lack of global knowledge, asynchrony and coordination of time, and protocols that function in the face of these problems. Emphasis on both the theory that grounds thinking about these systems and in the ways to design and build such systems.

COMPSCI 2630: Systems Security (4) sys

This course explores practical attacks on modern computer systems, explaining how those attacks can be mitigated using careful system design and the judicious application of cryptography. The course discusses topics like buffer overflows, web security, information flow control, and anonymous communication mechanisms such as Tor. The course includes several small projects which give students hands-on experience with various offensive and defensive techniques; the final, larger project is open-ended and driven by student interests.

COMPSCI 2650: Big Data Systems (4) sys

Big data is everywhere. A fundamental goal across numerous modern businesses and sciences is to be able to utilize as many machines as possible, to consume as much information as possible and as fast as possible. The big challenge is how to turn data into useful knowledge. This is a moving target as both the underlying hardware and our ability to collect data evolve. In this class, we discuss how to design data systems, data structures, and algorithms for key data-driven areas, including relational systems, distributed systems, graph systems, noSQL, newSQL, machine learning, and neural networks. We see how they all rely on the same set of very basic concepts and we learn how to synthesize efficient solutions for any problem across these areas using those basic concepts.

COMPSCI 2780: Conceptualizing, Building, and Evaluating Usable Novel Interactive Systems (4) humans

Students learn critical techniques, concepts, and technologies for building usable novel interactive systems, alone and in teams. Assignments provide hands-on experiences with different modern frameworks, platforms, and libraries while conceptual commonalities and distinctions are annotated and explained at multiple levels, from the programming environments to the interfaces users interact with. Discussions grounded in readings will also cover human cognitive capabilities, iterative prototyping, and human-AI interaction. The final research project requires iteratively designing and building a novel interactive system informed by pilot user studies and a final evaluation with target users. Designed for PhD students interested in HCI or using interactive systems as tools for discovery in other fields.

COMPSCI 2790R: Research Topics in Human-Computer Interaction (4) humans

Students will read, write about, prepare presentations about, and discuss human-computer interaction (HCI) and HCI-relevant work with a focus on papers about interfaces and automation that work especially well with (or clash against) human cognitive capabilities. Papers will primarily be on the building and evaluation of novel systems, as well as theories of and studies characterizing human cognition relevant to human-AI interaction scenarios. As a semester-long final project, students will pursue a research project of their own design in self-organized groups and present their findings in writing and orally in a conference-style format, as means to understand more deeply the processes behind HCI research.

COMPSCI 2810: Advanced Machine Learning (4) ai

Advanced statistical machine learning and probabilistic data analysis. Covers discrete and continuous probabilistic modeling and computational inference. Topics include: Bayesian modeling, probabilistic graphical models, latent variables and unsupervised learning, deep learning, time series models, variational inference, and sampling. Requires a final project.

COMPSCI 2821R: Topics in Machine Learning: Interpretability and Explainability (4) ai

As machine learning models are increasingly being employed to aid decision makers in high-stakes settings such as healthcare, finance, and law, it becomes important to ensure that the decision makers correctly understand and consequent trust the functionality of these models. This graduate level course aims to familiarize students with the recent advances in the emerging field of explainable ML. In this course, we will review seminal position papers of the field, understand the notion of model interpretability from the perspective of various kinds of end users (e.g., doctors, ML researchers/engineers), discuss in detail different classes of interpretable models and model explanations (e.g., case/prototype based approaches, sparse linear models, rule-based techniques, saliency maps, generalized additive models, and counterfactual explanations), and explore the connections between model interpretability and fairness, robustness, and privacy. The course will also emphasize the unique opportunities and challenges that arise when interpreting and explaining the functionality of foundation models (e.g., language models such as GPT-3, diffusion models such as DALLE etc.)The course will comprise of a mix of lectures by the instructor, paper presentations by students, and guest lectures by researchers who have authored seminal papers in this area. This course has a significant research component in the form of a course project that students will be expected to work on throughout the semester. All in all, this course is geared towards those students who are interested in diving deep and conducting research in the field of interpretable and explainable ML.

COMPSCI 2822R: Topics in Machine Learning: Computational Properties in Interpretable Machine Learning (4) ai

There has been growing interest in recent years for machine learning systems that are somehow transparent about their inner workings -- whether it be that the entire system is inherently interpretable, or that a single decision can somehow be explained. However, the question of what approach is best for what context remains elusive. In this course, we will focus on computational properties of interpretable machine learning methods, such as faithfulness or stability. Assessing methods with respect to these properties may allow us to rule out poorly-performing approaches without the need for expensive user studies. By categorizing methods by their computational properties, we will also be able to start thinking about which methods might be useful for a specific context. After a few initial assignments, the course will be focused on reading papers, discussion, and a semester-long project.

COMPSCI 2831: Advanced Computer Vision (4) ai

Vision as an ill-posed inverse problem: image formation, two-dimensional signal processing; feature analysis; image segmentation; color, texture, and shading; multiple-view geometry; object and scene recognition; and applications.

COMPSCI 2860: Multi-Robot Systems: Control, Communication, and Security (4) ai

The ability to connect devices over long distances, via the internet, changed our world. The second phase of this revolution, that we are still living in today, came about when these devices became wireless. Now we are at the cusp of a new phase of this evolution where devices are connected, wireless, and controlled – i.e. the robot revolution.Multi-robot systems are becoming more pervasive; from future autonomous vehicle fleets, to drones, to manufacturing robots. As a result, the question of how to control, coordinate, and secure these systems has been a growing topic in the robotics literature in recent years. In this seminar-style course we will do a deep dive into this topic by reviewing classic and recent results in multi-agent planning and control literature. We will cover a wide gamut of applications from control of groups of flying drones, to decision making in autonomous car networks, to space exploring CubeSats.This class will treat both the theory and the practical applications behind multi-robot systems. Students with mathematical inclinations and exposure to graph theory, probability theory, linear algebra, and algorithms will derive the most benefit from this course.

COMPSCI 2880: AI for Social Impact (4) ai

Recent years have seen AI successfully applied to societal challenge problems. Indeed, recognizing the potential of AI for tremendous social impact in the future, 'AI for social impact' is growing as a subdiscipline within AI. In this course, we will discuss successful case studies of use of AI for public health, environmental sustainability, public safety and public welfare. Simultaneously, we will discuss key foundations of the area of AI for social impact. To that end, among other topics, we will focus on challenges in AI for Social Impact, what makes projects successful, how to investigate project impact in the field and ethical considerations for such projects. A key part of this course will be AI4SI projects with non-profits.

COMPSCI 2890: Biologically-inspired Multi-agent Systems (4) ai

Surveys biologically-inspired approaches to designing distributed systems. Focus is on biological models, algorithms, and programming paradigms for self-organization. Topics vary year to year, and usually include: (1) swarm intelligence: social insects and animal groups, with applications to networking and robotics, (2) cellular computing: including cellular automata/amorphous computing, and applications like self-assembling robots and programmable materials, (3) evolutionary computation and its application to optimization and design.

COMPSCI 2901: Seminar on Effective Research Practices and Academic Culture (4) talks

This is a reading and discussion-based seminar designed for entering Computer Science Ph.D. students. This course prepares students to manage the difficult and often undiscussed challenges of Ph.D. programs through sessions on research skill building (e.g. paper reading, communication), soft skill building (e.g. managing advising relationships, supporting your peers), and academic culture (e.g. mental health in academia, power dynamics in scientific communities), as well as research and professional-oriented discussions. This is a full-year, 4-unit course, meeting once a week in each of the fall and the spring. Students must complete both terms of this course (COMPSCI 2901 and COMPSCI 2902) within the same academic year to receive credit.

COMPSCI 2902: Seminar on Effective Research Practices and Academic Culture (4) talks

COMPSCI 2990R: Special Topics in Computer Science (4) special

Supervision of experimental or theoretical research on acceptable problems in computer science and supervision of reading on topics not covered by regular courses of instruction.

MIT 9.19: Computational Psycholinguistics (4) ai

Introduces computational approaches to natural language processing and acquisition by humans and machines, combining symbolic and probabilistic modeling techniques. Covers models such as n-grams, finite state automata, and context-free and mildly context-sensitive grammars, for analyzing phonology, morphology, syntax, semantics, pragmatics, and larger document structure. Applications range from accurate document classification and sentence parsing by machine to modeling human language acquisition and real-time understanding. Covers both theory and contemporary computational tools and datasets. Students taking graduate version complete additional assignments.

MIT 6.1060: Software Performance Engineering (4) softeng

Project-based introduction to building efficient, high-performance and scalable software systems. Topics include performance analysis, algorithmic techniques for high performance, instruction-level optimizations, vectorization, cache and memory hierarchy optimization, and parallel programming.

MIT 6.5210: Advanced Algorithms (4) algs

First-year graduate subject in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Surveys a variety of computational models and the algorithms for them. Data structures, network flows, linear programming, computational geometry, approximation algorithms, online algorithms, parallel algorithms, external memory, streaming algorithms.

MIT 6.5410: Advanced Complexity Theory (4) theory

Current research topics in computational complexity theory. Nondeterministic, alternating, probabilistic, and parallel computation models. Boolean circuits. Complexity classes and complete sets. The polynomial-time hierarchy. Interactive proof systems. Relativization. Definitions of randomness. Pseudo-randomness and derandomizations. Interactive proof systems and probabilistically checkable proofs.

MIT 6.5660: Computer Systems Security (4) sys

Design and implementation of secure computer systems. Lectures cover attacks that compromise security as well as techniques for achieving security, based on recent research papers. Topics include operating system security, privilege separation, capabilities, language-based security, cryptographic network protocols, trusted hardware, and security in web applications and mobile phones. Labs involve implementing and compromising a web application that sandboxes arbitrary code, and a group final project.

MIT 6.5940: TinyML and Efficient Deep Learning Computing (4) ai

Introduces efficient deep learning computing techniques that enable powerful deep learning applications on resource-constrained devices. Topics include model compression, pruning, quantization, neural architecture search, distributed training, data/model parallelism, gradient compression, on-device fine-tuning. It also introduces application-specific acceleration techniques for video recognition, point cloud, and generative AI (diffusion model, LLM). Students will get hands-on experience accelerating deep learning applications with an open-ended design project.

MIT 6.7900: Machine Learning (4) ai

Principles, techniques, and algorithms in machine learning from the point of view of statistical inference; representation, generalization, and model selection; and methods such as linear/additive models, active learning, boosting, support vector machines, non-parametric Bayesian methods, hidden Markov models, Bayesian networks, and convolutional and recurrent neural networks.

MIT 6.8200: Sensorimotor Learning (4) ai

Provides an in-depth view of the state-of-the-art learning methods for control and the know-how of applying these techniques. Topics span reinforcement learning, self-supervised learning, imitation learning, model-based learning, and advanced deep learning architectures, and specific machine learning challenges unique to building sensorimotor systems. Discusses how to identify if learning-based control can help solve a particular problem, how to formulate the problem in the learning framework, and what algorithm to use. Applications of algorithms in robotics, logistics, recommendation systems, playing games, and other control domains covered. Instruction involves two lectures a week, practical experience through exercises, discussion of current research directions, and a group project.

MIT 6.8611: Quantitative Methods for Natural Language Processing (4) ai

Introduces the study of human language from a computational perspective, including syntactic, semantic and discourse processing models. Emphasizes machine learning methods and algorithms. Uses these methods and models in applications such as syntactic parsing, information extraction, statistical machine translation, dialogue systems. Instruction and practice in oral and written communication provided. Students taking graduate version complete additional assignments.

MATH MA: Introduction to Functions and Calculus I (4) math

The study of functions and their rates of change. Fundamental ideas of calculus are introduced early and used to provide a framework for the study of mathematical modeling involving algebraic, exponential, and logarithmic functions. Thorough understanding of differential calculus promoted by year long reinforcement. Applications to biology and economics emphasized according to the interests of our students.

MATH 1A: Introduction to Calculus (4) math

The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium. This course will help you see why by introducing: how differential calculus treats rates of change; how integral calculus treats accumulation; and how the fundamental theorem of calculus links the two. These ideas will be applied to problems from many other disciplines.

MATH 1B: Integration, Series and Differential Equations (4) math

Speaking the language of modern mathematics requires fluency with the topics of this course: infinite series, integration, and differential equations. Model practical situations using integrals and differential equations. Learn how to represent interesting functions using series and find qualitative, numerical, and analytic ways of studying differential equations. Develop both conceptual understanding and the ability to apply it.

MATH 21B: Linear Algebra and Differential Equations (4) math

Matrices provide the algebraic structure for solving myriad problems across the sciences. We study matrices and related topics such as linear transformations and linear spaces, determinants, eigenvalues, and eigenvectors. Applications include dynamical systems, ordinary and partial differential equations, and an introduction to Fourier series.

MATH 22A: Vector Calculus and Linear Algebra I (4) math

MATH 22 covers multivariable calculus and linear algebra for students interested in mathematical sciences. It covers the same topics as Mathematics 21, but does so with more rigor. Students are taught techniques of proof and mathematical reasoning. The workload and content is comparable with the Mathematics 21 sequence. But unlike the latter, the linear algebra and calculus are more interlinked. The content of Math 22a is mostly aligned with Math 21b (linear algebra), and the content of Math 22b is mostly aligned with Math 21a (multivariable calculus).

APMTH 22A: Solving and Optimizing (4) math

This course covers a combination of linear algebra and multivariate calculus with an eye towards solving systems of equations and optimization problems. Students will learn how to prove some key results, and will also implement these ideas with code.Linear algebra: matrices, vector spaces, bases and dimension, inner products, least squares problems, eigenvalues, eigenvectors, singular values, singular vectors.Multivariate calculus: partial differentiation, gradient and Hessian, critical points, Lagrange Multipliers.

MATH 23A: Linear Algebra and Real Analysis I (4) math

Linear algebra: vectors, linear transformations and matrices, scalar and vector products, basis and dimension, eigenvectors and eigenvalues, including an introduction to the R scripting language. Single-variable real analysis: sequences and series, limits and continuity, derivatives, inverse functions, power series and Taylor series. Multivariable real analysis and calculus: topology of Euclidean space, limits, continuity, and differentiation in n dimensions, inverse and implicit functions, manifolds, Lagrange multipliers, path integrals, div, grad, and curl. Emphasis on topics that are applicable to fields such as physics, economics, and computer science, but students are also expected to learn how to prove key results. Notes: Students are expected to watch videos of the lectures from Fall 2015 before attending class. Weekly two-hour classes will consist of a one-hour seminar in which students present key definitions and proofs and a one-hour activity-based session in which students work in small groups to solve problems. Students are expected to continue in either MATH 23B (recommended for students who are thinking of concentrating in mathematics, the physical sciences, or engineering) or MATH 23C (recommended for students who are not sure of their concentration, or who are thinking about a concentration in the social sciences, economics, computer science, life sciences or data science). Either alternative will provide a solid foundation for a concentration in mathematics or any field that uses mathematics.

MATH 23C: Mathematics for Computation, Statistics, and Data Science (4) math

Proof strategies and logic. Sets, countability, sigma fields, and axiomatic foundations of probability. Summation of series and evaluation of multiple integrals, with emphasis on calculation of expectation and variance. Abstract vector spaces and inner product spaces, with applications to analysis of large datasets. Key functions and theorems of mathematical statistics. A brief introduction to classical vector calculus as used in electromagnetic theory. Students will learn to use some of the statistical and graphical display tools in the R scription language.

MATH 25A: Theoretical Linear Algebra and Real Analysis I (4) math

A rigorous treatment of linear algebra. Topics include: Construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors, determinants and inner products. Metric spaces, compactness and connectedness.

MATH 55A: Studies in Algebra and Group Theory (4) math

A rigorous introduction to abstract algebra, including group theory and linear algebra. This course covers the equivalent of Mathematics 25a and Mathematics 122, and prepares students for Mathematics 123 and other advanced courses in number theory and algebra. (A course in analysis such as Mathematics 25b or 55b is recommended for Spring semester.)

MATH 101: Sets, Groups and Real Analysis (4) math

This course provides an introduction to conceptual and axiomatic mathematics, the writing of proofs, and mathematical culture, with sets, groups and real analysis as the main topics.

APMTH 107: Graph Theory and Combinatorics (4) math

Topics in combinatorial mathematics that find frequent application in computer science, engineering, and general applied mathematics. Specific topics taken from graph theory, enumeration techniques, optimization theory, combinatorial algorithms, and discrete probability.

STAT 110: Introduction to Probability (4) math

A comprehensive introduction to probability. Basics: sample spaces and events, conditional probability, and Bayes' Theorem. Univariate distributions: density functions, expectation and variance, Normal, t, Binomial, Negative Binomial, Poisson, Beta, and Gamma distributions. Multivariate distributions: joint and conditional distributions, independence, transformations, and Multivariate Normal. Limit laws: law of large numbers, central limit theorem. Markov chains: transition probabilities, stationary distributions, convergence.

APMTH 115: Mathematical Modeling (4) math

Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problems without the prejudice of trying to apply a particular method of solution. Topics drawn from biology, economics, engineering, physical and social sciences.

MATH 152: Discrete Mathematics (4) math

An introduction to finite groups, finite fields, quaternions, finite geometry, finite topology, combinatorics, and graph theory. A recurring theme of the course is the symmetry group of the regular icosahedron. Taught in a seminar format: students will gain experience in presenting proofs at the blackboard.

MATH 154: Probability Theory (4) math

An introduction to probability theory. Discrete and continuous random variables; distribution and density functions for one and two random variables; conditional probability. Generating functions, weak and strong laws of large numbers, and the central limit theorem. Geometrical probability, random walks, and Markov processes.

STAT 185: Introduction to Unsupervised Learning (4) math

An introductory course in unsupervised learning with an emphasis on dimensionality reduction and clustering. Topics include principal component analysis, nonnegative matrix factorization, and spectral clustering. In this course we will study these techniques and others with a focus on high-dimensional geometry and insights provided by linear algebra. Numerous data example will be included throughout the course.

MATH MB: Introduction to Functions and Calculus II (4) math

Continued investigation of functions and differential calculus through modeling; an introduction to integration with applications; an introduction to differential equations. Solid preparation for MATH 1B.

ENGSCI 143: Computer Vision (4) engr

An introduction to the mathematical, optical, and computational foundations of computer vision, with a focus on applications in augmented reality and robotic perception. Topics include: camera optics, digital color photography pipelines, multi-camera geometry, image processing and manipulation, simultaneous localization and mapping, lighting and material estimation, and 3D scanning. Emphasis on combining mathematical modeling with robust algorithms for solving ill-posed problems.

ENGSCI 150: Probability with Engineering Applications (4) engr

This course introduces the fundamentals of probability theory for parameter estimation and decision making under uncertainty. It considers applications to information systems as well as other physical and biological systems. Topics include: discrete and continuous random variables, conditional expectations, Bayes’ rules, laws of large numbers, central limit theorems, Markov chains, Bayesian statistical inferences, and parameter estimations.

PHYSICS 123B: Laboratory Electronics - Digital Circuits (4) sci

A lab-intensive introduction to digital electronic circuit design. Develops circuit intuition and debugging skills through hands-on lab exercises, each preceded by class discussion, with minimal use of mathematics and physics. After a short introduction to the basics of electronic circuits and MOSFET switches, we move onto digital devices including logic families, Boolean arithmetic, combinatorial and sequential circuits including finite state machines. We continue with analog-digital interfacing, the use of microcontrollers in embedded systems and programmable logic devices (FPGAs). We will also discuss data conversion techniques

ECON 2070: A Computer Science Toolbox for Modern Economic Theory (4)

How can we use tools from machine learning theory to design better auctions? Can we use cryptography to better implement matching mechanisms? And how should we approach formally proving that welfare in Nash equilibria for many games is not 'much worse' than in the social optimum? This course explores the application of diverse ideas, techniques, and solution aesthetics from theoretical computer science to derive meaningful new insights into classic economic problems. The three main themes are approximation theorems (including bounding the loss in revenue or welfare due to lack of information, to unpriced externalities, or to restricting the functional form of mechanisms); various notions of complexity (including computational complexity, communication complexity, and machine-learning sample complexity); and cryptographic tools (including cryptographic commitments, multiparty computation, and zero-knowledge proofs). Economic applications mostly include analysis of equilibria, pricing, and mechanism design. No prior knowledge in computer science is required.

MIT 21M.387: Fundamentals of Music Processing (4) math

Analyzes recorded music in digital audio form using advanced signal processing and optimization techniques to understand higher-level musical meaning. Covers fundamental tools like windowing, feature extraction, discrete and short-time Fourier transforms, chromagrams, and onset detection. Addresses analysis methods including dynamic time warping, dynamic programming, self-similarity matrices, and matrix factorization. Explores a variety of applications, such as event classification, audio alignment, chord recognition, structural analysis, tempo and beat tracking, content-based audio retrieval, and audio decomposition. Students taking graduate version complete different assignments.