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AMCS 5100-401 |
Complex Analysis |
James B Haglund |
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TR 12:00 PM-1:29 PM |
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Complex numbers, DeMoivre's theorem, complex valued functions of a complex variable, the derivative, analytic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, residues, computation of definite integrals by residues, and elementary conformal mapping. |
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MATH4100401 |
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AMCS 5141-401 |
Advanced Linear Algebra |
Angela Gibney |
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TR 1:45 PM-3:14 PM |
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Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. |
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MATH3140401, MATH5140401 |
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AMCS 5141-402 |
Advanced Linear Algebra |
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M 7:00 PM-8:59 PM |
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Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. |
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MATH3140402, MATH5140402 |
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AMCS 5141-403 |
Advanced Linear Algebra |
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W 7:00 PM-8:59 PM |
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Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. |
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MATH3140403, MATH5140403 |
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AMCS 6025-001 |
Numerical and Applied Analysis I |
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TR 1:45 PM-3:14 PM |
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We turn to linear algebra and the structural properties of linear systems of equations relevant to their numerical solution. In this context we introduce eigenvalues and the spectral theory of matrices. Methods appropriate to the numerical solution of very large systems are discussed. We discuss modern techniques using randomized algorithms for fast matrix-vector multiplication, and fast direct solvers. Topics covered include the classical Fast Multipole Method, the interpolative decomposition, structured matrix algebra, randomized methods for low-rank approximation, and fast direct solvers for sparse matrices. These techniques are of central importance in applications of linear algebra to the numerical solution of PDE, and in Machine Learning. The theoretical content of this course is illustrated and supplemented throughout the year with substantial computational examples and assignments. |
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AMCS 6081-401 |
Analysis |
Ryan C Hynd |
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TR 10:15 AM-11:44 AM |
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Complex analysis: analyticity, Cauchy theory, meromorphic functions, isolated singularities, analytic continuation, Runge's theorem, d-bar equation, Mittlag-Leffler theorem, harmonic and sub-harmonic functions, Riemann mapping theorem, Fourier transform from the analytic perspective. Introduction to real analysis: Weierstrass approximation, Lebesgue measure in Euclidean spaces, Borel measures and convergence theorems, C0 and the Riesz-Markov theorem, Lp-spaces, Fubini Theorem. |
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MATH6080401 |
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AMCS 6481-401 |
Probability Theory |
Jiaoyang Huang |
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MW 1:45 PM-3:14 PM |
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Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. |
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MATH6480401, STAT9300401 |
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MATH 6480-401 |
Probability Theory |
Jiaoyang Huang |
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MW 1:45 PM-3:14 PM |
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Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. |
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AMCS6481401, STAT9300401 |
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AMCS