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Courses for Spring 2025

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 James B. Haglund DRLB A6 MW 10:15 AM-11:44 AM 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 TOWN 313 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 Jianqi Liu BENN 231 MW 12:00 PM-1:29 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 DRLB 2C6 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. MATH3140403, MATH5140403
AMCS 5141-404 Advanced Linear Algebra CHEM 514 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. MATH3140404, MATH5140404
AMCS 5141-405 Advanced Linear Algebra DRLB 3C4 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. MATH3140405, MATH5140405
AMCS 5141-406 Advanced Linear Algebra DRLB 4E19 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. MATH3140406, MATH5140406
AMCS 5200-401 Ordinary Differential Equations Robert M. Strain DRLB 2C2 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
AMCS 5461-401 Advanced Applied Probability Robin Pemantle DRLB 3N1H MW 1:45 PM-3:14 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 LRSM 112B 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.
AMCS 6045-001 Topics in Numerical Analysis and Scientific Computing Te-Sheng Lin WILL 202 MW 10:15 AM-11:44 AM Scientific computing involves leveraging computers to analyze and address scientific and engineering challenges. It often requires the development and analysis of new computational algorithms aimed at solving mathematical models, so that scientists can simulate physical processes and enhance their understanding of natural phenomena. In this course, we will introduce a series of fundamental or latest algorithms to understand the tools needed at the research level for various numerical methods for PDEs. Tentative topics include finite difference methods, spectral and pseudo-spectral methods, and neural network methods for solving ODEs/PDEs, and immersed boundary/interface methods for simulating fluid-structure interaction problems.
AMCS 6091-401 Analysis Robert M. Strain DRLB 3C4 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 Ryan C Hynd DRLB 2C4 MW 1:45 PM-3:14 PM 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 0240-101 Calculus III Lab DRLB A6 F 8:30 AM-9:59 AM Lab for Math 2400
MATH 0240-102 Calculus III Lab DRLB A8 F 10:15 AM-11:44 AM Lab for Math 2400
MATH 0240-103 Calculus III Lab DRLB A2 F 12:00 PM-1:29 PM Lab for Math 2400
MATH 0240-104 Calculus III Lab DRLB A2 F 1:45 PM-3:14 PM Lab for Math 2400
MATH 1070-001 Mathematics of change, Part I Patrick Shields DRLB A5 TR 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. Nat Sci & Math Sector (new curriculum only)
MATH 1070-002 Mathematics of change, Part I Jiaqi Liu DRLB 3N1H MW 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. Nat Sci & Math Sector (new curriculum only)
MATH 1070-201 Mathematics of change, Part I DRLB 2C8 MW 8:30 AM-9:59 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. Nat Sci & Math Sector (new curriculum only)
MATH 1070-202 Mathematics of change, Part I MCNB 410 MW 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. Nat Sci & Math Sector (new curriculum only)
MATH 1070-211 Mathematics of change, Part I DRLB 3W2 TR 8:30 AM-9:59 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. Nat Sci & Math Sector (new curriculum only)
MATH 1070-212 Mathematics of change, Part I DRLB 4C6 TR 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. Nat Sci & Math Sector (new curriculum only)
MATH 1080-002 Mathematics of change, Part II Henry Piers Towsner DRLB 3N1H TR 3:30 PM-4:59 PM Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1080-211 Mathematics of change, Part II DRLB 3C8 MW 8:30 AM-9:59 AM Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1080-212 Mathematics of change, Part II JAFF B17 MW 10:15 AM-11:44 AM Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1300-001 Introduction to Calculus Aaron W Anderson DRLB A6 TR 3:30 PM-4:59 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202510&c=MATH1300001
MATH 1300-201 Introduction to Calculus DRLB 3C2 F 8:30 AM-9:59 AM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-202 Introduction to Calculus DRLB 3C2 F 10:15 AM-11:44 AM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-601 Introduction to Calculus Sukalpa Basu DRLB 3N1H MW 7:00 PM-8:29 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-001 Calculus, Part I Pierre Aime Feulefack MCNB 150 MW 1:45 PM-3:14 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-002 Calculus, Part I Brett S Frankel FAGN 118 MW 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-003 Calculus, Part I Brett S Frankel FAGN 118 MW 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-201 Calculus, Part I CHEM 514 F 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-202 Calculus, Part I 36MK 108 F 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-203 Calculus, Part I TOWN 303 F 12:00 PM-1:29 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-204 Calculus, Part I CANCELED Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-205 Calculus, Part I 36MK 107 F 10:15 AM-11:14 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-206 Calculus, Part I TOWN 313 F 12:00 PM-1:29 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-601 Calculus, Part I CANCELED Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-001 Calculus, Part II Andrew Cooper COLL 200 TR 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-002 Calculus, Part II Mira A Peterka DRLB A8 TR 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-003 Calculus, Part II Patrick Shields DRLB A1 TR 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-201 Calculus, Part II DRLB 3C8 F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-202 Calculus, Part II DRLB 3W2 F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-203 Calculus, Part II DRLB 3C8 F 1:45 PM-3:14 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-204 Calculus, Part II DRLB 3C2 F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-205 Calculus, Part II DRLB 3C6 F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-206 Calculus, Part II DRLB 4C2 F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-207 Calculus, Part II DRLB 3C6 F 1:45 PM-3:14 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-208 Calculus, Part II DRLB 3C4 F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-209 Calculus, Part II CANCELED Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-210 Calculus, Part II DRLB 3C4 F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-211 Calculus, Part II DRLB 3C4 F 1:45 PM-3:14 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-212 Calculus, Part II DRLB 3C6 F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1700-001 Ideas in Mathematics Nir Gadish DRLB A2 MW 3:30 PM-4:59 PM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-201 Ideas in Mathematics CANCELED Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-202 Ideas in Mathematics CANCELED Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-203 Ideas in Mathematics CANCELED Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-601 Ideas in Mathematics Nakia Rimmer DRLB A2 TR 7:00 PM-8:29 PM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202510&c=MATH1700601
MATH 2030-101 Proving things: Algebra DRLB 2N36 M 7:00 PM-8:29 PM This course focuses on the creative side of mathematics, with an emphasis on discovery, reasoning, proofs and effective communication, while at the same time studying arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening. General Requirement in Formal Reasoning & Analysis
MATH 2030-102 Proving things: Algebra DRLB 4C8 W 7:00 PM-8:29 PM This course focuses on the creative side of mathematics, with an emphasis on discovery, reasoning, proofs and effective communication, while at the same time studying arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening. General Requirement in Formal Reasoning & Analysis
MATH 2030-301 Proving things: Algebra Mona B Merling DRLB 4C2 TR 12:00 PM-1:29 PM This course focuses on the creative side of mathematics, with an emphasis on discovery, reasoning, proofs and effective communication, while at the same time studying arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening. General Requirement in Formal Reasoning & Analysis
MATH 2100-001 Mathematics in the Age of Information Ted C K Chinburg DRLB 3W2 TR 12:00 PM-1:29 PM This course counts as a regular elective for both the Mathematics Major and Minor. This is a course about mathematical reasoning and the media. Embedded in many stories one finds in the media are mathematical questions as well as implicit mathematical models for how the world behaves. We will discuss ways to recognize such questions and models, and how to think about them from a mathematical perspective. A key part of the course will be about what constitutes a mathematical proof, and what passes for proof in various media contexts. The course will cover a variety of topics in logic, probability and statistics as well as how these subjects can be used and abused. Nat Sci & Math Sector (new curriculum only)
MATH 2400-001 Calculus, Part III Shreya Arya DRLB A4 MW 1:45 PM-3:14 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-002 Calculus, Part III Nakia Rimmer DRLB A1 MW 8:30 AM-9:59 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-003 Calculus, Part III Nakia Rimmer LLAB 10 MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-201 Calculus, Part III DRLB 4C2 MW 3:30 PM-4:59 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-202 Calculus, Part III DRLB 3C2 MW 3:30 PM-4:59 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-203 Calculus, Part III DRLB 3C8 MW 3:30 PM-4:59 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-211 Calculus, Part III DRLB 4C6 MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-212 Calculus, Part III DRLB 2C8 MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-213 Calculus, Part III DRLB 4C4 MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-214 Calculus, Part III DRLB 2C4 MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-215 Calculus, Part III CANCELED Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-216 Calculus, Part III CANCELED Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-221 Calculus, Part III DRLB 2C8 MW 12:00 PM-1:29 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-222 Calculus, Part III DRLB 4C4 MW 12:00 PM-1:29 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-223 Calculus, Part III DRLB 4C2 MW 12:00 PM-1:29 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2410-002 Calculus, Part IV Michael A. Carchidi DRLB A2 TR 10:15 AM-11:44 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-211 Calculus, Part IV DRLB 3N6 M 8:30 AM-9:29 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-212 Calculus, Part IV DRLB 4E19 M 10:15 AM-11:14 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-213 Calculus, Part IV DRLB 4E9 F 8:30 AM-9:29 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-214 Calculus, Part IV DRLB 4E9 F 10:15 AM-11:14 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2600-001 Honors Calculus, Part II Herman Gluck DRLB A2 TR 1:45 PM-3:14 PM This is an honors version of Math 2400 which explores the same topics but with greater mathematical rigor.
MATH 2600-201 Honors Calculus, Part II DRLB 2C6 M 7:00 PM-8:59 PM This is an honors version of Math 2400 which explores the same topics but with greater mathematical rigor.
MATH 2600-202 Honors Calculus, Part II DRLB 2C6 W 7:00 PM-8:59 PM This is an honors version of Math 2400 which explores the same topics but with greater mathematical rigor.
MATH 3120-001 Linear Algebra Matthew P Wiener DRLB A4 TR 8:30 AM-9:59 AM Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 3120 cannot be taken to satisfy the major requirements.
MATH 3120-002 Linear Algebra Mira A Peterka FAGN 213 TR 12:00 PM-1:29 PM Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 3120 cannot be taken to satisfy the major requirements.
MATH 3130-401 Computational Linear Algebra Jiaqi Liu FAGN 118 MW 12:00 PM-1:29 PM Many important problems in a wide range of disciplines within computer science and throughout science are solved using techniques from linear algebra. This course will introduce students to some of the most widely used algorithms and illustrate how they are actually used. Some specific topics: the solution of systems of linear equations by Gaussian elimination, dimension of a linear space, inner product, cross product, change of basis, affine and rigid motions, eigenvalues and eigenvectors, diagonalization of both symmetric and non-symmetric matrices, quadratic polynomials, and least squares optimazation. Applications will include the use of matrix computations to computer graphics, use of the discrete Fourier transform and related techniques in digital signal processing, the analysis of systems of linear differential equations, and singular value deompositions with application to a principal component analysis. The ideas and tools provided by this course will be useful to students who intend to tackle higher level courses in digital signal processing, computer vision, robotics, and computer graphics. MATH5130401
MATH 3140-401 Advanced Linear Algebra Julia Hartmann TOWN 313 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. AMCS5141401, MATH5140401
MATH 3140-402 Advanced Linear Algebra Jianqi Liu BENN 231 MW 12:00 PM-1:29 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. AMCS5141402, MATH5140402
MATH 3140-403 Advanced Linear Algebra DRLB 2C6 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. AMCS5141403, MATH5140403
MATH 3140-404 Advanced Linear Algebra CHEM 514 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. AMCS5141404, MATH5140404
MATH 3140-405 Advanced Linear Algebra DRLB 3C4 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. AMCS5141405, MATH5140405
MATH 3140-406 Advanced Linear Algebra DRLB 4E19 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. AMCS5141406, MATH5140406
MATH 3410-401 Discrete Mathematics II Andre Scedrov DRLB 3C2 TR 10:15 AM-11:44 AM Topics will be drawn from some subjects useful in the analysis of information and computation: logic, set theory, theory of computation, number theory, probability, and basic cryptography. LGIC2200401 https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202510&c=MATH3410401
MATH 3500-001 Number Theory Brett S Frankel CHEM 119 MWF 1:45 PM-2:44 PM Congruences, Diophantine equations, continued fractions, nonlinear congruences,and quadratic residues. https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202510&c=MATH3500001
MATH 3600-001 Advanced Calculus Pierre Aime Feulefack DRLB 3W2 MW 12:00 PM-1:29 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-101 Advanced Calculus DRLB 4E19 T 7:00 PM-8:59 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-102 Advanced Calculus DRLB 4E9 R 7:00 PM-8:59 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3610-001 Advanced Calculus Andrew Cooper CHEM 102 TR 1:45 PM-3:14 PM Continuation of MATH 3600.
MATH 3610-002 Advanced Calculus John D Green CHEM B13 MW 12:00 PM-1:29 PM Continuation of MATH 3600. https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202510&c=MATH3610002
MATH 3610-101 Advanced Calculus DRLB 4E19 M 7:00 PM-7:59 PM Continuation of MATH 3600.
MATH 3610-102 Advanced Calculus DRLB 2C2 W 7:00 PM-7:59 PM Continuation of MATH 3600.
MATH 3610-103 Advanced Calculus DRLB 3C8 T 7:00 PM-7:59 PM Continuation of MATH 3600.
MATH 3610-104 Advanced Calculus DRLB 2C2 R 7:00 PM-7:59 PM Continuation of MATH 3600.
MATH 3700-001 Algebra Jianqi Liu DRLB 2C2 MW 10:15 AM-11:44 AM Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course.
MATH 3700-101 Algebra DRLB 4E9 T 7:00 PM-7:59 PM Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course.
MATH 3700-102 Algebra DRLB 3N6 R 7:00 PM-7:59 PM Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course.
MATH 3710-001 Algebra Andres Fernandez Herrero DRLB 4C2 TR 10:15 AM-11:44 AM Continuation of MATH 3700.
MATH 3710-101 Algebra DRLB 4E9 M 7:00 PM-8:59 PM Continuation of MATH 3700.
MATH 3710-102 Algebra DRLB 4E19 W 7:00 PM-8:59 PM Continuation of MATH 3700.
MATH 4100-401 Complex Analysis James B. Haglund DRLB A6 MW 10:15 AM-11:44 AM 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. AMCS5100401
MATH 4200-401 Ordinary Differential Equations Robert M. Strain DRLB 2C2 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. AMCS5200401
MATH 4250-001 Partial Differential Equations Jingwen Chen DRLB 3C2 MW 12:00 PM-1:29 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.
MATH 4320-001 Game Theory. Jonathan Block DRLB 2C6 MW 1:45 PM-3:14 PM A mathematical approach to game theory, with an emphasis on examples of actual games. Topics will include mathematical models of games, combinatorial games, two person (zero sum and general sum) games, non-cooperating games and equilibria.
MATH 4650-401 Differential Geometry Dennis M Deturck DRLB 3C8 TR 8:30 AM-9:59 AM Differential geometry of curves in the plane and in 3-space;n gauge theories Surfaces in 3-space; The geometry of the Gauss map;ons. The language of Intrinsic geometry of surfaces; Geodesics; Moving frames; of vector bundles, The Gauss-Bonnet Theorem; Assorted additional topics. MATH5010401
MATH 5010-401 Differential Geometry Dennis M Deturck DRLB 3C8 TR 8:30 AM-9:59 AM The course moves from a study of extrinsic geometry (curves and surfaces in n-space) to the intrinsic geometry of manifolds. After a review of vector calculus and a section on tensor algebra, we study manifolds and their intrinsic geometry, including metrics, connections, geodesics, and the Riemann curvature tensor. Topics include Eulerian curvature and Euler's theorems, the Gauss map and first/second fundamental forms, the Theorema Egregium, minimal surfaces in n-space; other topics as time permits. MATH4650401
MATH 5030-001 Abstract Algebra Ted C K Chinburg DRLB 3C4 TR 1:45 PM-3:14 PM Continuation of Math 5020.
MATH 5030-101 Abstract Algebra DRLB 4N30 M 7:00 PM-7:59 PM Continuation of Math 5020.
MATH 5030-102 Abstract Algebra DRLB 4N30 W 7:00 PM-7:59 PM Continuation of Math 5020.
MATH 5090-001 Advanced Analysis Yumeng Ou DRLB 3C6 TR 12:00 PM-1:29 PM Continuation of Math 5080. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods.
MATH 5090-101 Advanced Analysis DRLB 3N6 M 7:00 PM-8:59 PM Continuation of Math 5080. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods.
MATH 5090-102 Advanced Analysis DRLB 4E9 W 7:00 PM-8:59 PM Continuation of Math 5080. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods.
MATH 5130-401 Computational Linear Algebra Jiaqi Liu FAGN 118 MW 12:00 PM-1:29 PM A number of important and interesting problems in a wide range of disciplines within computer science are solved by recourse to techniques from linear algebra. The goal of this course will be to introduce students to some of the most important and widely used algorithms in matrix computation and to illustrate how they are actually used in various settings. Motivating applications will include: the solution of systems of linear equations, applications matrix computations to modeling geometric transformations in graphics, applications of the Discrete Fourier Transform and related techniques in digital signal processing, the solution of linear least squares optimization problems and the analysis of systems of linear differential equations. The course will cover the theoretical underpinnings of these problems and the numerical algorithms that are used to perform important matrixcomputations such as Gaussian Elimination, LU Decomposition and Singular Value Decomposition. MATH3130401
MATH 5140-401 Advanced Linear Algebra Julia Hartmann TOWN 313 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. AMCS5141401, MATH3140401
MATH 5140-402 Advanced Linear Algebra Jianqi Liu BENN 231 MW 12:00 PM-1:29 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. AMCS5141402, MATH3140402
MATH 5140-403 Advanced Linear Algebra DRLB 2C6 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. AMCS5141403, MATH3140403
MATH 5140-404 Advanced Linear Algebra CHEM 514 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. AMCS5141404, MATH3140404
MATH 5140-405 Advanced Linear Algebra DRLB 3C4 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. AMCS5141405, MATH3140405
MATH 5140-406 Advanced Linear Algebra DRLB 4E19 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. AMCS5141406, MATH3140406
MATH 5400-001 Selections from Classical and Functional Analysis Yumeng Ou CHEM 119 TR 1:45 PM-3:14 PM Informal introduction to such subjects as compact operators and Fredholm theory, Banach algebras, harmonic analysis, differential equations, nonlinear functional analysis, and Riemann surfaces.
MATH 5460-401 Advanced Applied Probability Robin Pemantle DRLB 3N1H MW 1:45 PM-3:14 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 5710-401 Logic and Computability 2 Marco Zaninelli WILL 216 TR 3:30 PM-4:59 PM A continuation of PHIL 6721. LGIC3200401, PHIL4722401, PHIL6722401
MATH 5810-001 Topics in Combinatorial Theory Robin Pemantle DRLB 4C8 MW 3:30 PM-4:59 PM Variable topics connected to current research in combinatorial theory. Recent topics include algebraic combinatorics and symmetric functions, analytic combinatorics and discrete probability.
MATH 6010-001 Topology and Geometric Analysis Wolfgang Ziller DRLB 3C4 TR 12:00 PM-1:29 PM Covering spaces and fundamental groups, van Kampen's theorem and classification of surfaces. Basics of homology and cohomology, singular and cellular; isomorphism with de Rham cohomology. Brouwer fixed point theorem, CW complexes, cup and cap products, Poincare duality, Kunneth and universal coefficient theorems, Alexander duality, Lefschetz fixed point theorem.
MATH 6030-001 Algebra Danny Krashen CHEM 109 MW 10:15 AM-11:44 AM Continuation of Math 6020.
MATH 6090-401 Analysis Robert M. Strain DRLB 3C4 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. AMCS6091401
MATH 6190-001 Algebraic Topology, Part I Mona B Merling CANCELED Rational homotopy theory, cobordism, K-theory, Morse theory and the h-corbodism theorem. Surgery theory.
MATH 6190-002 Algebraic Topology, Part I Mona B Merling DRLB 4E9 TR 5:15 PM-6:44 PM Rational homotopy theory, cobordism, K-theory, Morse theory and the h-corbodism theorem. Surgery theory.
MATH 6250-001 Algebraic Geometry Florian Pop DRLB 2N36 MW 12:00 PM-1:29 PM Continuation of Math 6240.
MATH 6450-001 Partial Differential Equations John D Green DRLB 4C2 MW 1:45 PM-3:14 PM Subject matter varies from year to year. Some topics are: the classical theory of the wave and Laplace equations, general hyperbolic and elliptic equations, theory of equations with constant coefficients, pseudo-differential operators, and nonlinear problems. Sobolev spaces and the theory of distributions will be developed as needed. https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202510&c=MATH6450001
MATH 6490-401 Stochastic Processes Ryan C Hynd DRLB 2C4 MW 1:45 PM-3:14 PM 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
MATH 6610-001 Differential Geometry Jingwen Chen DRLB 2C8 MW 1:45 PM-3:14 PM Continuation of Math 6600.
MATH 6950-001 Mathematical Foundations of Theoretical Physics Ron Donagi DRLB 4E19 MW 1:45 PM-3:14 PM Selected topics in mathematical physics, such as mathematical methods of classical mechanics, electrodynamics, relativity, quantum mechanics and quantum field theory.
MATH 7250-001 Topics in Algebraic Geometry Angela Gibney DRLB 3C8 MW 12:00 PM-1:29 PM Topics from the literature. The specific subject will vary from year to year.
MATH 7610-001 Topics in Differential Geometry Davi Maximo-Alexandrino-Nogueir DRLB 4C8 TR 12:00 PM-1:29 PM Topics from the literature. The specific subjects will vary from year to year.