All Courses

This is a graduate course in operating systems. The course will consist of a reading/lecture/discussion component and a project component. The class will cover approximately 40 research papers. Some of these papers will introduce students to the basic principles on which modern operating systems and distributed systems are based. Others will cover more recent work to explore the state of the art and observe the evolution of these systems over time.

An advanced follow-on to 15-312 developing further ideas and results in the theory of programming languages.

Computing in the cloud has emerged as a leading paradigm for cost-effective, scalable, well-managed computing. Users pay for services provided in a broadly shared, power efficient datacenter, enabling dynamic computing needs to be met without paying for more than is needed. Actual machines may be virtualized into machine-like services, or more abstract programming platforms, or application-specific services, with the cloud computing infrastructure managing sharing, scheduling, reliability, availability, elasticity, privacy, provisioning and geographic replication This course will survey the aspects of cloud computing by reading about 30 papers and articles, executing cloud computing tasks on a state of the art cloud computing service, and implementing a change or feature in a state of the art cloud computing framework. There will be no final exam, but there will be two in class exams. Grades will be about 50 project work and about 50 examination results.

Computing in the cloud has emerged as a leading paradigm for cost-effective, scalable, well-managed computing. Users pay for services provided in a broadly shared, power efficient datacenter, enabling dynamic computing needs to be met without paying for more than is needed. Actual machines may be virtualized into machine-like services, or more abstract programming platforms, or application-specific services, with the cloud computing infrastructure managing sharing, scheduling, reliability, availability, elasticity, privacy, provisioning and geographic replication This course will survey the aspects of cloud computing by reading about 30 papers and articles, executing cloud computing tasks on a state of the art cloud computing service, and implementing a change or feature in a state of the art cloud computing framework. There will be no final exam, but there will be two in class exams. Grades will be about 50 project work and about 50 examination results.

This course is a comprehensive study of the internals of modern database management systems. It will cover the core concepts and fundamentals of the components that are used in large-scale analytical systems (OLAP). The class will stress both efficiency and correctness of the implementation of these ideas.

This course is a comprehensive study of the internals of modern database management systems. It will cover the core concepts and fundamentals of the components that are used in large-scale analytical systems (OLAP). The class will stress both efficiency and correctness of the implementation of these ideas.

In this course, students will learn the mathematical foundations of blockchains, including how to construct distributed consensus protocols and prove them secure, cryptography for blockchains, and mechanism design for blockchains. Students may also be expected to implement some consensus or cryptographic algorithms.

This course attempts to provide a deep understanding of the issues and challenges involved in designing and implementing modern computer systems. Our primary goal is to help students become more skilled in their use of computer systems, including the development of applications and system software. Users can benefit greatly from understanding how computer systems work, including their strengths and weaknesses. This is particularly true in developing applications where performance is an issue. 

15-744 is a doctoral course in computer networking research. The goals are: To understand the state of the art in network protocols, network architecture, and networked systems. To engage with systems research at a scholarly level through written and oral argument. To investigate novel ideas and make new scholarly arguments through a semester-long research project in computer networking.

Theoretical and practical aspects of building optimizing compilers that e¿ectively exploit modern architectures. The course will begin with the fundamentals of compiler optimization, and will build upon these fundamentals to address issues in state-of-the-art commercial and research machines.

Storage systems are among the most fascinating and the most important parts of computer systems. They often dominate the performance of a system, and failures of other components are frequently addressed by restarting from the data stored on them. Indeed, storage systems hold the crown jewels of most organizations: their information (from source code to Microsoft's software to the sales databases of every e-commerce site to the logs and indices driving the Big Data and ML revolution). There continues to be great demand for bright people and better solutions in this critical field of computer systems.

Computing has been dominated by von Neumann CPU architectures for seventy years. The von Neumann architecture is familiar and flexible, but it is also extremely inefficient, wasting upwards of 99% of energy. As computing is now energy-limited across all scales, from IoT to data center, von Neumann's inefficiency can no longer be tolerated. Recently, industry has adopted heterogeneous "accelerator" hardware to boost performance and efficiency. However, accelerators have limited programmability, sacrificing the main benefit of CPU architectures and putting future innovation at risk. This class will survey non-von Neumann general-purpose architectures, recent work on specialized hardware accelerators, and cutting-edge research on "programmable accelerators".

The course covers a broad set of topics in algorithms design and analysis. The goal is to cover tools and algorithms that give students the ability to (a) recognize which tool or method to apply to problems, (b) to become reasonably proficient at using these tools, and (c) to be able to reason about the correctness and performance of the resulting algorithms. The course webpage for this semester will list the tentative list of topics to be covered; these will include basic graph algorithms, randomized algorithms, hashing and streaming, flows and linear programming, convex optimization, and linear algebraic algorithms. Please refer to https://www.cs.cmu.edu/~csd-grad/courseschedules22.html for the most recent schedule updates.

This course will take a random walk through various mathematical topics that come in handy for theoretical computer science. It is intended mainly for students earlier in their graduate studies (or very strong undergraduates) who want to do theory research. The idea for the course comes from other courses by Arora (2002, 2007), Håstad (2004/05), Kelner (2007, 2009), and Tulsiani (2013). Students should have a solid undergraduate background in math (e.g., elementary combinatorics, graph theory, discrete probability, basic algebra/calculus) and theoretical computer science (running time analysis, big-O/Omega/Theta, P and NP, basic fundamental algorithms).

A graduate course on spectral graph theory: how to establish graph structure through linear algebra, and how to exploit this connection for faster algorithms

A graduate-level course on how to use randomization to design algorithms and data structures with strong provable guarantees.

This is a course giving a rigorous treatment of several topics in the theory of convex optimization. There will be a particular focus on developing intuition for how to analyze many convex optimization processes from first principles. Topics may include: gradient descent, interior point methods, linear regression, linear programming, sparsification, and more.

This course explores physics-based animations of solids and fluids, key in fields like visual effects, VR, and digital fashion. Central to this is solving partial differential equations (PDEs) using numerical methods, with applications in areas such as computational mechanics and 3D content creation. Through lectures and student presentations on research papers, we will cover the simulation of rigid bodies, deformable bodies, shells, rods, liquids, and smoke, from PDE discretization to solver implementation. A strong background in math and programming is recommended, as students will work on advanced numerical methods. The course also includes a project where students apply their knowledge to develop and test simulations. By the end, students will understand both classic and cutting-edge methods in solids and fluids simulation, along with the challenges of advancing these techniques in the broader field.

This course focuses on three-dimensional geometry processing, while simultaneously providing a first course in traditional differential geometry. Our main goal is to show how fundamental geometric concepts (like curvature) can be understood from complementary computational and mathematical points of view. This dual perspective enriches understanding on both sides, and leads to the development of practical algorithms for working with real-world geometric data. Along the way we will revisit important ideas from calculus and linear algebra, putting a strong emphasis on intuitive, visual understanding that complements the more traditional formal, algebraic treatment. The course provides essential mathematical background as well as a large array of real-world examples and applications. It also provides a short survey of recent developments in digital geometry processing and discrete differential geometry. Topics include: curves and surfaces, curvature, connections and parallel transport, exterior algebra, exterior calculus, Stokes' theorem, simplicial homology, de Rham cohomology, Helmholtz-Hodge decomposition, conformal mapping, finite element methods, and numerical linear algebra.Applications include: approximation of curvature, curve and surface smoothing, surface parameterization, vector field design, and computation of geodesic distance.

Real-time computer graphics is about building systems that leverage modern CPUs and GPUs to produce detailed, interactive, immersive, and high-frame-rate imagery. Students will build a state-of-the-art renderer using C++ and the Vulkan API. Topics explored will include efficient data handling strategies; culling and scene traversal; multi-threaded rendering; post-processing, depth of field, screen-space reflections; volumetric rendering; sample distribution, spatial and temporal sharing, and anti-aliasing; stereo view synthesis; physical simulation and collision detection; dynamic lights and shadows; global illumination, accelerated raytracing; dynamic resolution, "AI" upsampling; compute shaders; parallax occlusion mapping; tessellation, displacement; skinning, transform feedback; and debugging, profiling, and accelerating graphics algorithms.

Real-time computer graphics is about building systems that leverage modern CPUs and GPUs to produce detailed, interactive, immersive, and high-frame-rate imagery. Students will build a state-of-the-art renderer using C++ and the Vulkan API. Topics explored will include efficient data handling strategies; culling and scene traversal; multi-threaded rendering; post-processing, depth of field, screen-space reflections; volumetric rendering; sample distribution, spatial and temporal sharing, and anti-aliasing; stereo view synthesis; physical simulation and collision detection; dynamic lights and shadows; global illumination, accelerated raytracing; dynamic resolution, "AI" upsampling; compute shaders; parallax occlusion mapping; tessellation, displacement; skinning, transform feedback; and debugging, profiling, and accelerating graphics algorithms.

This course provides a broad perspective on AI, covering (i) classical approaches of search and planning useful for robotics, (ii) integer programming and continuous optimization that form the bedrock for many AI algorithms, (iii) modern machine learning techniques including deep learning that power many recent AI applications, (iv) game theory and multi-agent systems, and (v) issues of bias and unfairness in AI. In addition to understanding the theoretical foundations, we will also study modern algorithms in the research literature.

This course provides a broad perspective on AI, covering (i) classical approaches of search and planning useful for robotics, (ii) integer programming and continuous optimization that form the bedrock for many AI algorithms, (iii) modern machine learning techniques including deep learning that power many recent AI applications, (iv) game theory and multi-agent systems, and (v) issues of bias and unfairness in AI. In addition to understanding the theoretical foundations, we will also study modern algorithms in the research literature.

In AI and beyond, systems of multiple agents are naturally modeled using game theory. From game theory, we know that sometimes, when each agent pursues its own objectives, the outcome may be one that is bad for all agents (e.g., the Prisoner's Dilemma). Learning algorithms can indeed converge to such bad equilibria. What can be done to prevent such bad outcomes, and how should we think about designing agents in such contexts? In this course, we will approach this question from a variety of angles, ranging from traditional approaches in game theory to novel ones that fit AI better than humans.

In this advanced machine learning seminar class, we tackle the typical struggle in using the modern machinery including large language models and other foundation models: what works and why? How do we make things more reliable and robust? We build a conceptual understanding of deep learning and foundation models through several different angles: standard in-distribution generalization, out-of-distribution generalization, self-supervised learning, data curation, scaling laws, alignment etc. We will read papers that contain a mix of theoretical and empirical insights with a focus on making connections to classic ideas, identifying recurring themes, and discussing avenues for future developments. The class aims to equip students with the ability to critically reason about and build a more principled understanding of current advances which will hopefully spark their own research.

An advanced follow-on to 15-312 developing further ideas and results in the theory of programming languages.

This course is broadly focused on full-stack system security and will cover the foundations of building secure systems and cryptography. During the course we will cover hardware, system software, and cryptographic primitives for building secure systems, both within the datacenter environment and in the decentralized setting. The course will focus on the cross-cutting security requirements of systems and how to bolster their security guarantees using a combination of systems and cryptographic techniques. The lectures will cover fundamental security concepts (e.g., threat models, trusted computing base), and do a deep dive into state-of-the-art attacks and defenses (e.g., speculative execution attacks). The course will span a set of hardware security topics including trusted execution environments, side-channels, hardware attacks (e.g., Meltdown, Spectre, Rowhammer), software systems such as blockchains, anonymous messaging, and secure machine learning.

This course is broadly focused on full-stack system security and will cover the foundations of building secure systems and cryptography. During the course we will cover hardware, system software, and cryptographic primitives for building secure systems, both within the datacenter environment and in the decentralized setting. The course will focus on the cross-cutting security requirements of systems and how to bolster their security guarantees using a combination of systems and cryptographic techniques. The lectures will cover fundamental security concepts (e.g., threat models, trusted computing base), and do a deep dive into state-of-the-art attacks and defenses (e.g., speculative execution attacks). The course will span a set of hardware security topics including trusted execution environments, side-channels, hardware attacks (e.g., Meltdown, Spectre, Rowhammer), software systems such as blockchains, anonymous messaging, and secure machine learning.

This course aims to give implementation motivated perspectives on some algorithmic ideas that fall outside of the scopes of typical algorithms courses. It is intended for graduate students, as well as undergraduate students who have high grades in 15-451, and 15-259 or 21-325. The first half of the course will discuss floating point precision, numerical approximation schemes, heuristic search, usage of optimization packages, and vectorization. The second half will provide high-level surveys of 2-D range update & query data structures, proactive propagation, and iterative methods. Evaluations will consist of about 30 auto-graded coding tasks, plus either participation in the ICPC NAEast Programming Contest, or presentations of problem-solving reports from various OI team selections.

This course is a hands-on exploration of the most challenging problem in computer science: database query optimization. It will cover the classical and state-of-the-art methods and algorithms for converting SQL statements into physical query plans. Additional topics include cost models, feedback mechanisms, and adaptive query optimization. All class projects will be in the context of an open-source query optimizer service using real-world queries. The course is appropriate for graduate students in software systems and advanced undergraduates with nasty programming skills that are pursuing a database-centric lifestyle.

This course number is used by the department for approved alternate electives for doctoral students.

This number is used internally by the department to transfer approved courses for elective credit.

This course number is used by the department for approved alternate electives for doctoral students.

This course number is used for internal course transfer for approved electives outside CSD

This lecture course introduces the foundational concepts and techniques of programming language semantics. The aim is to demonstrate the utility of a scientific approach, based on mathematics and logic, with applications to program analysis, language design, and compiler correctness. We introduce the concepts and techniques associated with the most well established and generally applicable frameworks for semantic description: the denotational, operational, and axiomatic styles of semantic description. We use semantics to analyze program behavior, guide the development of correct programs, prove correctness of a compiler, validate logics for program correctness, and derive general laws of program equivalence. We will discuss a variety of imperative and functional languages, sequential and parallel, as time permits.

The course studies the theory of type systems, with a focus on applications of type systems to practical programming languages. The emphasis is on the mathematical foundations underlying type systems and operational semantics. The course includes a broad survey of the components that make up existing type systems, and also teaches the methodology behind the design of new type systems.

Automated reasoning has become a powerful technology with applications ranging from verification of hardware and software to solving long-standing open problems in mathematics. This course covers several state-of-the-art automated reasoning techniques and provides hands-on experience with research questions in this area.

The course covers the implementation of compilers for higher-order typed languages such as ML and Haskell and gives an introduction to type-preserving compilation. Core topics include type checking and inference, elaboration, closure conversion, garbage collection, and translation to a low-level imperative language. Other topics may vary from year to year and include phase splitting, CPS conversion, typed assembly language, substructural and adjoint type systems, intersection types, and variable lifetimes.

TBA

This is a course exploring research issues in mobile computing and its close relative, pervasive computing (aka "Internet of Things (IoT)"). Many traditional areas of computer science and computer engineering are impacted by the constraints and demands of mobile and pervasive computing. The course will offer significant hands-on experience: students will work in small groups under the guidance of a mentor on a project. Each student will present a research paper from the literature in a conference-style 30-minute talk. In teams of two, students will present a short (30 minutes) overview of the commercial landscape for one of the topics covered in class. There will a brief quiz at the start of each class, based on the readings for that class. Prerequisites Knowledge of operating systems, distributed systems, and computer architecture. If in doubt, check with one of the instructors before registering.

The course covers advanced algorithms for learning, analysis, data management and visualization of large datasets. Topics include indexing for text and DNA databases, searching medical and multimedia databases by content, fundamental signal processing methods, compression, fractals in databases, data mining, privacy and security issues, rule discovery, data visualization, graph mining, stream mining.

In this course, you will learn the mathematical foundations of distributed consensus as well as how to construct consensus protocols and prove them secure. We will motivate distributed consensus with a modern narrative, and yet we will cover the classical theoretical foundations of consensus.

An intensive graduate course on the design and analysis of algorithms.

With the growing number of massive datasets in applications such as machine learning and numerical linear algebra, classical algorithms for processing such datasets are often no longer feasible. In this course we will cover algorithmic techniques, models, and lower bounds for handling such data. A common theme is the use of randomized methods, such as sketching and sampling, to provide dimensionality reduction. In the context of optimization problems, this leads to faster algorithms, and we will see examples of this in the form of least squares regression and low rank approximation of matrices and tensors, as well as robust variants of these problems. In the context of distributed algorithms, dimensionality reduction leads to communication-efficient protocols, while in the context of data stream algorithms, it leads to memory-efficient algorithms. We will study some of the above problems in such models, such as low rank approximation, but also consider a variety of classical streaming problems such as counting distinct elements, finding frequent items, and estimating norms. Finally we will study lower bound methods in these models showing that many of the algorithms we covered are optimal or near-optimal. Such methods are often based on communication complexity and information-theoretic arguments.

With the growing number of massive datasets in applications such as machine learning and numerical linear algebra, classical algorithms for processing such datasets are often no longer feasible. 

In this course we will cover algorithmic techniques, models, and lower bounds for handling such data. A common theme is the use of randomized methods, such as sketching and sampling, to provide dimensionality reduction. In the context of optimization problems, this leads to faster algorithms, and we will see examples of this in the form of least squares regression and low rank approximation of matrices and tensors, as well as robust variants of these problems. In the context of distributed algorithms, dimensionality reduction leads to communication-efficient protocols, while in the context of data stream algorithms, it leads to memory-efficient algorithms. We will study some of the above problems in such models, such as low rank approximation, but also consider a variety of classical streaming problems such as counting distinct elements, finding frequent items, and estimating norms. Finally we will study lower bound methods in these models showing that many of the algorithms we covered are optimal or near-optimal. Such methods are often based on communication complexity and information-theoretic arguments.

TBD

This course is aimed as an introduction to modern cryptography. This course will be a mix of applied and theoretical cryptography.

This course focuses on three-dimensional geometry processing, while simultaneously providing a first course in traditional differential geometry. Our main goal is to show how fundamental geometric concepts (like curvature) can be understood from complementary computational and mathematical points of view. This dual perspective enriches understanding on both sides, and leads to the development of practical algorithms for working with real-world geometric data. Along the way we will revisit important ideas from calculus and linear algebra, putting a strong emphasis on intuitive, visual understanding that complements the more traditional formal, algebraic treatment. The course provides essential mathematical background as well as a large array of real-world examples and applications. It also provides a short survey of recent developments in digital geometry processing and discrete differential geometry. Topics include: curves and surfaces, curvature, connections and parallel transport, exterior algebra, exterior calculus, Stokes' theorem, simplicial homology, de Rham cohomology, Helmholtz-Hodge decomposition, conformal mapping, finite element methods, and numerical linear algebra.Applications include: approximation of curvature, curve and surface smoothing, surface parameterization, vector field design, and computation of geodesic distance.

This course is geared to cover advanced topics in cryptography. The course will have a theory focus and cover trending topics in cryptography (that might change depending on the year). The course is meant for students who are either already doing research in cryptography or considering research in the area. In the Spring 2025, we will cover advanced topics such as homomorphic crypto-systems, multi-party computation, zero-knowledge proofs and obfuscation.

The Monte Carlo method uses random sampling to solve computational problems that would otherwise be intractable, and enables computers to model complex systems in nature that are otherwise too difficult to simulate. This course provides a first introduction to Monte Carlo methods from complementary theoretical and applied points of view, and will include implementation of practical algorithms. Topics include random number generation, sampling, Markov chains, Monte Carlo integration, stochastic processes, and applications in computational science. Students need a basic background in probability, multivariable calculus, and some coding experience in any language.

Computational photography is the convergence of computer graphics, computer vision and imaging. Its role is to overcome the limitations of the traditional camera, by combining imaging and computation to enable new and enhanced ways of capturing, representing, and interacting with the physical world. This advanced undergraduate course provides a comprehensive overview of the state of the art in computational photography. At the start of the course, we will study modern image processing pipelines, including those encountered on mobile phone and DSLR cameras, and advanced image and video editing algorithms. Then we will proceed to learn about the physical and computational aspects of tasks such as 3D scanning, coded photography, lightfield imaging, time-of-flight imaging, VR/AR displays, and computational light transport. Near the end of the course, we will discuss active research topics, such as creating cameras that capture video at the speed of light, cameras that look around walls, or cameras that can see through tissue. The course has a strong hands-on component, in the form of seven homework assignments and a final project. In the homework assignments, students will have the opportunity to implement many of the techniques covered in the class, by both acquiring their own images of indoor and outdoor scenes and developing the computational tools needed to extract information from them. For their final projects, students will have the choice to use modern sensors provided by the instructors (lightfield cameras, time-of-flight cameras, depth sensors, structured light systems, etc.).

Textile artifacts are -- quite literally -- all around us; from clothing to carpets to car seats. These items are often produced by sophisticated, computer-controlled fabrication machinery. In this course we will discuss everywhere code touches textiles fabrication, including design tools, simulators, and machine control languages. Students will work on a series of multi-week, open-ended projects, where they use code to create patterns for modern sewing/embroidery, weaving, and knitting machines; and then fabricate these patterns in the textiles lab. Students in the 800-level version of the course will be required to create a final project which develops a new algorithm, device, or technique in the realm of textiles fabrication.

Textile artifacts are -- quite literally -- all around us; from clothing to carpets to car seats. These items are often produced by sophisticated, computer-controlled fabrication machinery. In this course we will discuss everywhere code touches textiles fabrication, including design tools, simulators, and machine control languages. Students will work on a series of multi-week, open-ended projects, where they use code to create patterns for modern sewing/embroidery, weaving, and knitting machines; and then fabricate these patterns in the textiles lab. Students in the 800-level version of the course will be required to create a final project which develops a new algorithm, device, or technique in the realm of textiles fabrication.

This course is an introduction to physics-based rendering at the advanced undergraduate and introductory graduate level. During the course, we will cover fundamentals of light transport, including topics such as the rendering and radiative transfer equations, light transport operators, path integral formulations, and approximations such as diffusion and single scattering. Additionally, we will discuss state-of-the-art models for illumination, surface and volumetric scattering, and sensors. Finally, we will use these theoretical foundations to develop Monte Carlo algorithms and sampling techniques for efficiently simulating physically-accurate images. Towards the end of the course, we will look at advanced topics such as rendering wave optics, neural rendering, and differentiable rendering. The course has a strong programming component, in the form of assignments through which students will develop their own working implementation of a physics-based renderer, including support for a variety of rendering algorithms, materials, illumination sources, and sensors. The course also emphasizes theoretical aspects of physics-based rendering, through weekly take-home quizzes. Lastly, the course includes a final project, during which students will select and implement some advanced rendering technique, and use their implementation to produce an image that is both technically and artistically compelling. The course will conclude with a rendering competition, where students submit their rendered images to win prizes.

This course is an introduction to physics-based rendering at the advanced undergraduate and introductory graduate level. During the course, we will cover fundamentals of light transport, including topics such as the rendering and radiative transfer equations, light transport operators, path integral formulations, and approximations such as diffusion and single scattering. Additionally, we will discuss state-of-the-art models for illumination, surface and volumetric scattering, and sensors. Finally, we will use these theoretical foundations to develop Monte Carlo algorithms and sampling techniques for efficiently simulating physically-accurate images. Towards the end of the course, we will look at advanced topics such as rendering wave optics, neural rendering, and differentiable rendering. The course has a strong programming component, in the form of assignments through which students will develop their own working implementation of a physics-based renderer, including support for a variety of rendering algorithms, materials, illumination sources, and sensors. The course also emphasizes theoretical aspects of physics-based rendering, through weekly take-home quizzes. Lastly, the course includes a final project, during which students will select and implement some advanced rendering technique, and use their implementation to produce an image that is both technically and artistically compelling. The course will conclude with a rendering competition, where students submit their rendered images to win prizes.

The course will focus on multi-step imperfect-information games because most real-world strategic settings are such games. Such games beget additional issues beyond perfect-information games like chess and Go, such as signaling, deception, and understanding deception by others. There has been tremendous progress in the AI community on solving such games since around 2003. This course covers the fundamentals and the state of the art of solving such games.

This seminar class will cover some advanced topics in RL including foundations, algorithms, applications (in foundation model fine-tuning, robotics, scientific applications, etc). This course is expected to involve paper reading each week, including a discussion of these papers in the class, followed by a class project.

A broad introduction to Computer Science Pedagogy. Although the course focus is on CS pedagogy and developing curricular content, students will learn some fundamentals of modern mobile application programming.

In this course, we will cover various advanced topics at the intersection of cryptography and algorithms, especially how algorithmic techniques are used in the construction of modern cryptographic schemes.