Current Courses
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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.
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Doctoral Breadth: Software Systems - (-)
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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.
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Doctoral Breadth: Software Systems - (*)
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).
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Doctoral Breadth: Algorithms and Complexity - (*)
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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.
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Doctoral Breadth: Artificial Intelligence - (*)
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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.
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Doctoral Breadth: Programming Languages - (*)
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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.
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Doctoral Breadth: Algorithms and Complexity - (*)
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.
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Doctoral Breadth: Algorithms and Complexity - (*)
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