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.

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.

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.

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

Resource use—the amount of time, memory, and energy a program requires for its execution—is one of the central subjects of computer science. Nevertheless, resource use traditionally does not play a central role in programming-language concepts, such as operational semantics, type systems, and program logics. This course revisits these concepts to model and analyze resource use of programs in a compositional and mathematically-precise way. The emphasis is on practical, type-based techniques that automatically inform programmers about the resource use of their code. We first study such techniques for functional programs and then develop generalizations to imperative, probabilistic, and concurrent programs.

The course covers the Istari proof assistant: its type theory and its practical use in proving theorems and reasoning about programs.

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.

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. 

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.

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.

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.

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.

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 seminar-based course delves into the heart of physics-based animations of solids and fluids, a key component in fields ranging from visual effects and VR to digital fashion. Central to this is solving partial differential equations (PDEs) using numerical methods, with applications extending to computational mechanics, robotic training, and 3D content creation. Combining lectures with student presentations, we will explore the simulation of various physical entities, such as rigid bodies, deformable bodies (open-source online book available, including Python and CUDA examples), shells, rods, liquids, and smoke, all the way from the discretization of the governing PDEs to the efficient implementation and evaluation of the numerical solvers. Students will acquire a thorough understanding of both classic and state-of-the-art methods of solids and fluids simulation in computer graphics. They will also gain insights into the existing challenges in enhancing and applying these methods within the broader field.

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.

Many problems in machine learning, visual computing, robotics, and mechanics lack exact analytical solutions. Numerical computing provides powerful techniques to approximate these solutions using computational methods, combining applied math and programming to solve real-world problems such as simulation, optimization, and data analysis. The course begins with a review on calculus and linear algebra, followed by an introduction to how numbers are represented on computers and error analysis. It then moves on to core topics, including matrix factorization, solving linear and nonlinear systems, optimization, and numerical solution of differential equations. Students will gain hands-on experience developing numerical algorithms and learn to balance accuracy, stability, and efficiency in problem-specific contexts, such as image processing, physics-based animation, motion planning and control, structural analysis, etc.

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.

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.

Machine learning (ML) techniques, especially recent advances in large language models and generative AI, have surpassed human predictive performance in a variety of real-world tasks. This success is enabled by the recent development of ML systems (e.g., PyTorch) that provide high-level programming interfaces for people to easily prototype different ML models on modern hardware platforms. In this course, we will explore the design of modern ML systems by learning how an ML model written in high-level languages is decomposed into low-level kernels and executed across heterogeneous hardware accelerators (e.g., TPUs and GPUs) in a distributed fashion. Topics covered in this course include: programming models for expressing ML models, deep learning accelerators, ML compilation, programming techniques on modern GPUs (e.g., H100 and B200), distributed training techniques, auto-parallelization, computation graph optimizations, automated kernel generation, memory optimizations, etc. The main goal of this course is to provide a comprehensive view on how existing ML systems work. Throughout this course, we will also learn the design principles behind these systems and discuss the challenges and opportunities for building future ML systems for next-generation ML applications and hardware platforms.

This course provides a broad perspective on AI, with a focus on foundational principles powering modern AI. This course will cover (i) machine learning and neural networks, (ii) large language models and generative AI, (iii) search and reinforcement learning, (iv) game theory and multi-agent systems, and (v) issues of bias and unfairness in AI. The material will be presented from a mathematical perspective, with assignments emphasizing implementation alongside foundational principles.

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.

As AI systems become more capable and widely deployed, ensuring their reliability, robustness, and alignment with human intent is critical. This advanced seminar explores the principles behind building trustworthy AI, with a focus on both theoretical foundations and empirical guarantees. We will examine key challenges such as robustness to distribution shifts, adversarial attacks, data poisoning, privacy risks, and jailbreaks, as well as broader concerns in AI alignment and governance. Through a mix of foundational papers and recent advances, the class will investigate recurring themes across security, robustness, and alignment, drawing connections to classical machine learning principles and modern scaling trends. Discussions will emphasize not only what works but also why it works (or fails)—aiming to equip students with the conceptual tools to critically assess current methods and develop principled approaches for trustworthy AI. This course is designed for students interested in both theoretical insights and practical implications, bridging research in machine learning, security, and AI alignment to address some of the most pressing challenges in modern AI development. " Through a mix of foundational papers and recent advances, the class will investigate recurring themes across security, robustness, and alignment, drawing connections to classical machine learning principles and modern scaling trends. Discussions will emphasize not only what works but also why it works (or fails)—aiming to equip students with the conceptual tools to critically assess current methods and develop principled approaches for trustworthy AI. This course is designed for students interested in both theoretical insights and practical implications, bridging research in machine learning, security, and AI alignment to address some of the most pressing challenges in modern AI development.

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 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 will provide some implementation motivated perspectives on algebraic and numerical algorithms, and will somewhat follow the Complexity and Linear Algebra semester program at the Simons Institute in Fall 2025 (https://simons.berkeley.edu/programs/complexity-linear-algebra). It will normally meet on Wednesdays and Fridays, with some Monday meetings to fit the schedule of the program.

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.

In this seminar class, we will discuss state-of-the-art methods in generative AI for music and general audio (everyday sounds, speech, bioacoustics, etc.), with applications to both generation and understanding. We will examine and compare the two primary families of methods that are used in modern audio generation research: large language models applied to discrete audio tokens, and diffusion models applied to continuous audio representations. With an eye towards offering intuitive controls for music generation, we will also examine classic methods and tasks in music information retrieval such as spectral analysis, synchronization, beat detection, and transcription. Moreover, we will explore emerging topics in generative AI for music and audio such as new architectures, training data attribution, interaction, compression, multimodality, and evaluation. Finally, we will discuss the ethical and societal implications of music generation specifically, and its potential effects on music both economically and culturally. Much of the course activity will center around (1) in-class lectures and demonstrations on small scale datasets, (2) student-led discussions of research papers, and (3) an open-ended research project.

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.