Spring 2026 Courses

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

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.

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. The course is appropriate for graduate students in software systems and for advanced undergraduates with straight up dirty systems programming skills.

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.

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

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.

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

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

Probabilistic programs are traditional computer programs that are augmented with the ability to make and constrain random choices. These techniques form the basis of Monte Carlo simulation, randomized algorithms, and statistical inference in probabilistic models from machine learning and artificial intelligence. What are the principles for developing probabilistic programming systems, and how can we use them in practice? This course provides a first introduction to probabilistic programming from theoretical and applied perspectives. The first part of the course covers foundational concepts in probabilistic language design and semantics. The second part covers algorithms and programmatic interfaces for inference, learning, and reasoning with probabilistic programs. Applications will be given in topics that range from program analysis to data science.

This is an advanced course on the theory, and some practice, of parallel and concurrent algorithms. We will start by discussing models and then go through a variety of topics including algorithms for sorting, strings, graphs, and geometry. The focus will be on so-called work-efficient algorithms (i.e. algorithms that do more work than their sequential counterpart). The goal is both to get a broad view of the techniques used to design of such algorithms, as well as going into some depth on a handful of recent breakthroughs in the design of parallel algorithms. We will discuss practical implementations of most of the algorithms we cover.

Markov processes are a fundamental mathematical concept with broad applications, including emerging fields such as reinforcement learning and diffusion models. This course is structured into two parts. Part I covers the core theory of Markov processes, including discrete-time and continuous-time Markov chains, as well as Markov processes with continuous state space such as diffusion processes. Part II builds on the core theory and covers selected topics in the theoretical foundation of reinforcement learning and diffusion models in generative AI.

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 number is used for scheduling distinguished lectures offered throughout the semester.

This course number is for registering for reading and research while working on research and your dissertation.

The course number should be used for registering units for internships.