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Courses for Spring 2023

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 Ching-Li Chai
Junyu Ma
MOOR 212 MW 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 Julia Hartmann BENN 419 MF 10:15 AM-11:44 AM 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 5141-402 Advanced Linear Algebra Julia Hartmann
Souparna Purohit
Yidi Wang
PCPE 200 T 7:00 PM-8:59 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. MATH3140402, MATH5140402
AMCS 5141-403 Advanced Linear Algebra Julia Hartmann
Souparna Purohit
Yidi Wang
TOWN 313 R 7:00 PM-8:59 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. MATH3140403, MATH5140403
AMCS 5141-404 Advanced Linear Algebra CANCELED 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. MATH3140404, MATH5140404
AMCS 5141-405 Advanced Linear Algebra CANCELED 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. MATH3140405, MATH5140405
AMCS 5200-401 Ordinary Differential Equations John D Green DRLB 2C6 TR 12:00 PM-1:29 PM After a rapid review of the basic techniques for solving equations, the course will discuss one or more of the following topics: stability of linear and nonlinear systems, boundary value problems and orthogonal functions, numerical techniques, Laplace transform methods. MATH4200401 https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202310&c=AMCS5200401
AMCS 5461-401 Advanced Applied Probability Jiaqi Liu
Da Wu
FAGN 214 MW 12:00 PM-1:29 PM The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). MATH5460401
AMCS 6035-001 Numerical and Applied Analysis II Yoichiro Mori DRLB 3W2 TR 1:45 PM-3:14 PM We will cover asymptotic methods, primarily for differential equations. In many problems of applied mathematics, there is a small parameter in the problem. Asymptotic analysis represents a collection of methods that takes advantage of the smallness of this parameter. After a brief discussion of non-dimensionalization, we will discuss regular perturbation methods, matched asymptotics, method of multiple scales, WKB approximation, and homogenization. Other topics will be discussed, time permitting. The prerequisite for this class is some familiarity with differential equations, but required background will be reviewed in class. https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202310&c=AMCS6035001
AMCS 6091-401 Analysis Kaitian Jin
Robert M Strain
DRLB 4C6 TR 10:15 AM-11:44 AM Real analysis: general measure theory, outer measures and Cartheodory construction, Hausdorff measures, Radon-Nikodym theorem, Fubini's theorem, Hilbert space and L2-theory of the Fourier transform. Functional analysis: normed linear spaces, convexity, the Hahn-Banach theorem, duality for Banach spaces, weak convergence, bounded linear operators, Baire category theorem, uniform boundedness principle, open mapping theorem, closed graph theorem, compact operators, Fredholm theory, interpolation theorems, Lp-theory for the Fourier transform. MATH6090401
AMCS 6491-401 Stochastic Processes Xin Sun
Da Wu
SHDH 1201 MW 8:30 AM-9:59 AM Continuation of MATH 6480/STAT 9300, the 2nd part of Probability Theory for PhD students in the math or statistics department. The main topics include Brownian motion, martingales, Ito's formula, and their applications to random walk and PDE. MATH6490401, STAT9310401
MATH 5460-401 Advanced Applied Probability Jiaqi Liu
Da Wu
FAGN 214 MW 12:00 PM-1:29 PM The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). AMCS5461401
MATH 6490-401 Stochastic Processes Xin Sun
Da Wu
SHDH 1201 MW 8:30 AM-9:59 AM Continuation of MATH 6480/STAT 9300, the 2nd part of Probability Theory for PhD students in the math or statistics department. The main topics include Brownian motion, martingales, Ito's formula, and their applications to random walk and PDE. AMCS6491401, STAT9310401