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Subject offerings of new and developing areas of knowledge in computer science intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. Course Information: May be repeated in the same or separate terms if topics vary.

The applications and numerical methods for problems involving tensors have grown widely in recent years. Tensor contractions and decompositions are prevalent in scientific computing (especially in computational chemistry and physics) as well as data mining and machine learning. This course will go into depth on core fundamentals in numerical linear algebra and numerical optimization relevant to tensors. We will introduce diagrammatic notation to study tensor networks and tensor decomposition algorithms. Further, the course will provide algebraic formulations of graph and combinatorial algorithms using sparse matrices and tensors. The use of tensors for algorithmic analysis will also be studied, including bilinear algorithms for matrix multiplication and convolution. Going beyond computational complexity, the course will analyze algorithms in terms of arithmetic intensity, parallelism, and communication cost. Prerequisites: familiarity with parallel programming, numerical linear algebra