# Courses for Spring 2022

Title | Instructor | Location | Time | All taxonomy terms | Description | Section Description | Cross Listings | Fulfills | Registration Notes | Syllabus | Syllabus URL | Course Syllabus URL | ||
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AMCS 514-401 | Advanced Linear Algebra | Florian Pop | MW 10:15 AM-11:45 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. | MATH314401, MATH514401 |
Undergraduates Need Permission Registration also required for Laboratory (see below) |
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AMCS 514-402 | Advanced Linear Algebra | T 07:00 PM-09:00 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. | MATH314402, MATH514402 |
Undergraduates Need Permission Registration also required for Lecture (see below) |
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AMCS 514-403 | Advanced Linear Algebra | R 07:00 PM-09:00 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. | MATH314403, MATH514403 |
Undergraduates Need Permission Registration also required for Lecture (see below) |
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AMCS 514-404 | Advanced Linear Algebra | T 07:00 PM-09:00 PM | MATH314404, MATH514404 |
Undergraduates Need Permission Registration also required for Lecture (see below) |
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AMCS 514-405 | Advanced Linear Algebra | R 07:00 PM-09:00 PM | MATH314405, MATH514405 |
Undergraduates Need Permission Registration also required for Lecture (see below) |
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AMCS 520-401 | Ordinary Differ Equation | Svetlana Makarova | TR 12:00 PM-01:30 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. | MATH420401 | Undergraduates Need Permission | ||||||||

AMCS 525-401 | Partial Differential Equations | Jonathan Block | TR 01:45 PM-03:15 PM | Method of separation of variables will be applied to solve the wave, heat, and Laplace equations. In addition, one or more of the following topics will be covered: qualitative properties of solutions of various equations (characteristics, maximum principles, uniqueness theorems), Laplace and Fourier transform methods, and approximation techniques. | MATH425401 | Undergraduates Need Permission | ||||||||

AMCS 603-001 | Algebraic Techiques II | Yoichiro Mori | TR 01:45 PM-03:15 PM | We begin with an introduction to group theory. The emphasis is on groups as symetries and transformations of space. After an introduction to abstract groups, we turn our attention to compact Lie groups, in particular SO(3), and their representations. We explore the connections between orthogonal polynomials, classical transcendental functions and group representations. This unit is completed with a discussion of finite groups and their applications in coding theory. | ||||||||||

AMCS 609-401 | Analysis II | Robert M. Strain | TR 10:15 AM-11:45 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. | MATH609401 | |||||||||

MATH 546-001 | Adv Applied Probability | Robin Pemantle |
M 12:00 PM-01:30 PM W 12:00 PM-01:30 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). After a summary of the necessary results from measure theory, we will learn the probabilist's lexicon (random variables, independence, etc.). We will then study laws of large numbers, Central Limit Theorem, Poisson convergence and processes, conditional expectations, and martingales. Emphasis is on using these for probability modeling. Application areas include genetics, linguistics, machine learning, agent-based models, statistical physics, and hidden Markov models. | Undergraduates Need Permission | |||||||||

MATH 649-401 | Stochastic Processes | Xin Sun | MW 12:00 PM-01:30 PM | Markov chains, Markov processes, and their limit theory. Renewal theory. Martingales and optimal stopping. Stable laws and processes with independen increments. Brownian motion and the theory of weak convergence. Point processes. | STAT931401 | Undergraduates Need Permission | https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2022A&course=MATH649401 |