# 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 | MATH3140404, MATH5140404 | |||||||||||

AMCS 5141-405 | Advanced Linear Algebra | CANCELED | 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 |