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Courses for Fall 2022

Title Instructor Location Time All taxonomy terms Description Section Description Cross Listings Fulfills Registration Notes Syllabus Syllabus URL Course Syllabus URL
AMCS 5100-401 Complex Analysis Jonathan Block TR 1:45 PM-3:14 PM 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. MATH4100401
AMCS 5141-401 Advanced Linear Algebra Irfan Alam TR 1:45 PM-3:14 PM 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. MATH3140401, MATH5140401
AMCS 6025-001 Numerical and Applied Analysis I Daniel Gomez TR 8:30 AM-9:59 AM 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.
AMCS 6081-401 Analysis Robert M Strain TR 10:15 AM-11:44 AM 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. MATH6080401
AMCS 6481-401 Probability Theory MW 1:45 PM-3:14 PM Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. MATH6480401, STAT9300401
MATH 6480-401 Probability Theory MW 1:45 PM-3:14 PM Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. AMCS6481401, STAT9300401