All Courses

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.).

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.). This course requires familiarity with linear algebra, calculus, programming, and doing computations with images. The course does not require prior experience with photography or imaging.

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.).

The goal of this course is to acquaint students with the code required to turn ideas into games. This includes both runtime systems -- e.g., AI, sound, physics, rendering, and networking -- and the asset pipelines and creative tools that make it possible to author content that uses these systems. In the first part of the course, students will implement small games that focus on specific runtime systems, along with appropriate asset editors or exporters. In the second part, students will work in groups to build a larger, polished, open-ended game project. Students who have completed the course will have the skills required to extend -- or build from scratch -- a modern computer game. Students wishing to take this class should be familiar with the C++ language and have a basic understanding of the OpenGL API. If you meet these requirements but have not taken Computer Graphics (the formal prerequisite), please contact the instructor.

The goal of this course is to acquaint students with the code required to turn ideas into games. This includes both runtime systems -- e.g., AI, sound, physics, rendering, and networking -- and the asset pipelines and creative tools that make it possible to author content that uses these systems. In the first part of the course, students will implement small games that focus on specific runtime systems, along with appropriate asset editors or exporters. In the second part, students will work in groups to build a larger, polished, open-ended game project. Students who have completed the course will have the skills required to extend -- or build from scratch -- a modern computer game. Students wishing to take this class should be familiar with the C++ language and have a basic understanding of the OpenGL API. If you meet these requirements but have not taken Computer Graphics (the formal prerequisite), please contact the instructor.

The goal of this course is to acquaint students with the code required to turn ideas into games. This includes both runtime systems -- e.g., AI, sound, physics, rendering, and networking -- and the asset pipelines and creative tools that make it possible to author content that uses these systems. In the first part of the course, students will implement small games that focus on specific runtime systems, along with appropriate asset editors or exporters. In the second part, students will work in groups to build a larger, polished, open-ended game project.

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 equation, 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, during 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 project also 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. Cross-listing: This is both an advanced undergraduate and introductory graduate course, and it is cross-listed as 15-468 (for undergraduate students), 15-668 (for Master's students), and 15-868 (for PhD students). Please make sure to register for the section of the class that matches your current enrollment status.

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 equation, 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, during 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 project also 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 equation, 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, during 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 project also 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. Cross-listing: This is both an advanced undergraduate and introductory graduate course, and it is cross-listed as 15-468 (for undergraduate students), 15-668 (for Master's students), and 15-868 (for PhD students). Please make sure to register for the section of the class that matches your current enrollment status.

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 equation, 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, during 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 project also 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. Cross-listing: This is both an advanced undergraduate and introductory graduate course, and it is cross-listed as 15-468 (for undergraduate students), 15-668 (for Master's students), and 15-868 (for PhD students). Please make sure to register for the section of the class that matches your current enrollment status.

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; 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; 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; 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; debugging, profiling, and accelerating graphics algorithms.

Visual computing tasks such as computational imaging, image/video understanding, and real-time graphics are key responsibilities of modern computer systems ranging from sensor-rich smart phones to large datacenters. These workloads demand exceptional system efficiency and this course examines the key ideas, techniques, and challenges associated with the design of parallel, heterogeneous systems that accelerate visual computing applications. This course is intended for graduate and advanced undergraduate-level students interested in architecting efficient graphics, image processing, and computer vision platforms.

Visual computing tasks such as computational imaging, image/video understanding, and real-time graphics are key responsibilities of modern computer systems ranging from sensor-rich smart phones to large datacenters. These workloads demand exceptional system efficiency and this course examines the key ideas, techniques, and challenges associated with the design of parallel, heterogeneous systems that accelerate visual computing applications. This course is intended for graduate and advanced undergraduate-level students interested in architecting efficient graphics, image processing, and computer vision platforms.

This course explores the rapidly evolving intersection of machine learning and computer graphics, offering a modern perspective on topics traditionally covered in 15- 362. Students will learn how neural methods are transforming the way we represent, render, and animate visual content. Through a combination of lectures, seminar-style discussions, and research-based projects, the course examines how machine learning techniques can accelerate and enhance traditional graphics pipelines. Topics include Neural Texture Compression, Computer Shaders, Neural Shading, Neural Denoising, Gaussian Splatting, Neural Radiance Fields, Inverse Rendering, AI Players, Animation Cycles, Neural Frame Interpolation, & Stylized Animation.

Autonomous agents use perception, cognition, actuation, and learning to reliably achieve desired goals, where the agents can be smart homes, mobile robots, intelligent factories, self-driving cars, etc. The goal of this course is to introduce students to techniques needed for developing complete, integrated AI-based autonomous agents. Topics include architectures for intelligent agents; autonomous behaviors, perception, and execution; reasoning under uncertainty; optimization; execution monitoring; machine learning; scheduling; and explanation. A focus of the course will be on the integration and testing of autonomous systems to achieve reliable and robust behavior in the face of sensor noise and uncertainty. The course is project-oriented where small teams of students will design, implement, and evaluate agents that can grow plants autonomously, without human intervention.

Autonomous agents use perception, cognition, actuation, and learning to reliably achieve desired goals, where the agents can be smart homes, mobile robots, intelligent factories, self-driving cars, etc. The goal of this course is to introduce students to techniques needed for developing complete, integrated AI-based autonomous agents. Topics include architectures for intelligent agents; autonomous behaviors, perception, and execution; reasoning under uncertainty; optimization; execution monitoring; machine learning; scheduling; and explanation. A focus of the course will be on the integration and testing of autonomous systems to achieve reliable and robust behavior in the face of sensor noise and uncertainty. The course is project-oriented where small teams of students will design, implement, and evaluate agents that can grow plants autonomously, without human intervention.

Autonomous agents use perception, cognition, actuation, and learning to reliably achieve desired goals, where the agents can be smart homes, mobile robots, intelligent factories, self-driving cars, etc. The goal of this course is to introduce students to techniques needed for developing complete, integrated AI-based autonomous agents. Topics include architectures for intelligent agents; autonomous behaviors, perception, and execution; reasoning under uncertainty; optimization; execution monitoring; machine learning; scheduling; and explanation. A focus of the course will be on the integration and testing of autonomous systems to achieve reliable and robust behavior in the face of sensor noise and uncertainty. The course is project-oriented where small teams of students will design, implement, and evaluate agents that can grow plants autonomously, without human intervention.

This course explores the implementation of intelligent behavior in mobile robots, focusing on the VEX AIM robot by Innovation First, and the GPT series of large language models from OpenAI. It consistes of a series of Monday/Wednesday lectures, a parallel series of Friday hands-on labs and problem sets, and a capstone project taking up the last several weeks.

This course will explore the future of robot toys by analyzing and programming Anki Cozmo, a new robot with built-in artificial intelligence algorithms. Como is distinguished from earlier consumer robots by its reliance on vision as the primary sensing mode and its sophisticated use of A.I. Its capabilities include face and object recognition, map building, path planning, and object pushing and stacking. Although marketed as a pre-programmed children's toy, Cozmo's open source Python SDK allows anyone to develop new software for it, which means it can also be used for robotics education and research. The course will cover robot software architecture, human-robot interaction, perception, and planning algorithms for navigation and manipulation. Prior robotics experience is not required, just strong programming skills.

This course will explore the future of robot toys by analyzing and programming Anki Cozmo, a new robot with built-in artificial intelligence algorithms. Como is distinguished from earlier consumer robots by its reliance on vision as the primary sensing mode and its sophisticated use of A.I. Its capabilities include face and object recognition, map building, path planning, and object pushing and stacking. Although marketed as a pre-programmed children's toy, Cozmo's open source Python SDK allows anyone to develop new software for it, which means it can also be used for robotics education and research. The course will cover robot software architecture, human-robot interaction, perception, and planning algorithms for navigation and manipulation. Prior robotics experience is not required, just strong programming skills.

This course will explore the future of robot toys by analyzing and programming Anki Cozmo, a new robot with built-in artificial intelligence algorithms. Como is distinguished from earlier consumer robots by its reliance on vision as the primary sensing mode and its sophisticated use of A.I. Its capabilities include face and object recognition, map building, path planning, and object pushing and stacking. Although marketed as a pre-programmed children's toy, Cozmo's open source Python SDK allows anyone to develop new software for it, which means it can also be used for robotics education and research. The course will cover robot software architecture, human-robot interaction, perception, and planning algorithms for navigation and manipulation. Prior robotics experience is not required, just strong programming skills.

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. Topics covered include polynomials, bit complexity, and numerical approximation/perturbation schemes. Evaluations is by written problem sets, and either compilation and presentation of research, or performances in the UCup/AtCoder series of weekly programming contests. Presentation will assume some proficiency with algebra, number theory, and problem solving. An ideal background is mastery of either: Putnam A1~A3/B1~B3 (minus geometry); or IMO Shortlist C1~C4/N1~N2/A1~A2; or AtCoder ~1000-rated problems (minus data structures).

This course aims to give implementation motivated perspectives on some algorithmic ideas that fall outside of the scopes of most courses. It is intended for graduate students, as well as undergraduate students who have high grades in 15-210, 15-251, 15-259 (and preferably 15-451). Evaluation will consist of about 30 auto-graded coding tasks, plus either participation in the East Central NA ICPC Regional Contest, or presentations of problem-solving reports from the Chinese IOI Team Selection Camp. 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, palindromic automata, automated recurrence finding, and maximum adjacency search.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Topics covered include: machine-level code and its generation by optimizing compilers, performance evaluation and optimization, computer arithmetic, memory organization and management, networking technology and protocols, and supporting concurrent computation. **This online course is only available to incoming master's students who need a refresher course on computer systems. Not open to undergraduates.**

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability, and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Topics covered include: machine-level code and its generation by optimizing compilers, performance evaluation and optimization, computer arithmetic, memory organization and management, networking technology and protocols, and supporting concurrent computation. **This remote course is only available to incoming master's students who need a refresher course on computer systems. Not open to undergraduates.**

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Topics covered include: machine-level code and its generation by optimizing compilers, performance evaluation and optimization, computer arithmetic, memory organization and management, networking technology and protocols, and supporting concurrent computation.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Topics covered include: machine-level code and its generation by optimizing compilers, performance evaluation and optimization, computer arithmetic, memory organization and management, networking technology and protocols, and supporting concurrent computation.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Topics covered include: machine-level code and its generation by optimizing compilers, performance evaluation and optimization, computer arithmetic, memory organization and management, networking technology and protocols, and supporting concurrent computation.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required.

This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Topics covered include: machine-level code and its generation by optimizing compilers, performance evaluation and optimization, computer arithmetic, memory organization and management, networking technology and protocols, and supporting concurrent computation. **This course is not available to undergraduates.**

This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context. Probability theory is indispensable in computer science. It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty. It is integral to computer science theory, where probabilistic analysis and ideas based on randomization form the basis of many important algorithms. It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity.

Probability theory is indispensable in computer science. It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty. It is integral to computer science theory, where probabilistic analysis and ideas based on randomization form the basis of many important algorithms. It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context.

Probability theory is indispensable in computer science. It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty. It is integral to computer science theory, where probabilistic analysis and ideas based on randomization form the basis of many important algorithms. It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context.

Probability theory is indispensable in computer science today. In areas such as artificial intelligence and computer science theory, probabilistic reasoning and randomization are central. Within networks and systems, probability is used to model uncertainty and queuing latency. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation. The course has 3 parts: Part I is an introduction to probability, including discrete and continuous random variables, heavy tails, simulation, Laplace transforms, z-transforms, and applications of generating functions. Part II is an in-depth coverage of concentration inequalities, like the Chernoff bound and SLLN bounds, as well as their use in randomized algorithms. Part III covers Markov chains (both discrete-time and continuous-time) and stochastic processes and their application to queuing systems performance modeling. This is a fast-paced class which will cover more material than the other probability options and will cover it in greater depth.

Probability theory is indispensable in computer science today. In areas such as artificial intelligence and computer science theory, probabilistic reasoning and randomization are central. Within networks and systems, probability is used to model uncertainty and queuing latency. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation. The course has 3 parts: Part I is an introduction to probability, including discrete and continuous random variables, heavy tails, simulation, Laplace transforms, z-transforms, and applications of generating functions. Part II is an in-depth coverage of concentration inequalities, like the Chernoff bound and SLLN bounds, as well as their use in randomized algorithms. Part III covers Markov chains (both discrete-time and continuous-time) and stochastic processes and their application to queuing systems performance modeling. This is a fast-paced class which will cover more material than the other probability options and will cover it in greater depth.

Probability theory is indispensable in computer science. It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty. It is integral to computer science theory, where probabilistic analysis and ideas based on randomization form the basis of many important algorithms. It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context.

The Kenneth C. Griffin School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the Griffin School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The Kenneth C. Griffin School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the Griffin School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the School of Computer Science.

The Kenneth C. Griffin School of Computer Science offers Independent Study courses, which allow motivated students to work on projects under the supervision of a faculty advisor while receiving academic credit. Independent studies are usually one semester in duration and require prior approval from the faculty member and the Griffin School of Computer Science.