Penn Arts & Sciences Logo
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 Mona B Merling TR 12:00 PM-1:29 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 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 Fnu Rakvi 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. MATH3140402, MATH5140402
AMCS 5141-403 Advanced Linear Algebra 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 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 M 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 W 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 Andrew Cooper 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 Jiaqi Liu
Da Wu
MW 10:15 AM-11:44 AM 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 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 6091-401 Analysis Ryan C Hynd 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
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 F 8:30 AM-9:59 AM Lab for Math 2400
MATH 0240-102 Calculus III Lab F 10:15 AM-11:44 AM Lab for Math 2400
MATH 0240-103 Calculus III Lab F 12:00 PM-1:29 PM Lab for Math 2400
MATH 0240-104 Calculus III Lab F 1:45 PM-3:14 PM Lab for Math 2400
MATH 1070-001 Mathematics of change, Part I Robin Pemantle 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. General Requirement in Formal Reasoning & Analysis
MATH 1070-002 Mathematics of change, Part I Patrick Shields MW 7:00 PM-8:29 PM 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. General Requirement in Formal Reasoning & Analysis
MATH 1070-201 Mathematics of change, Part I 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. General Requirement in Formal Reasoning & Analysis
MATH 1070-202 Mathematics of change, Part I 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. General Requirement in Formal Reasoning & Analysis
MATH 1070-211 Mathematics of change, Part I 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. General Requirement in Formal Reasoning & Analysis
MATH 1070-212 Mathematics of change, Part I 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. General Requirement in Formal Reasoning & Analysis
MATH 1080-002 Mathematics of change, Part II Nakia Rimmer TR 1:45 PM-3:14 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 1080-003 Mathematics of change, Part II Henry Piers Towsner 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 https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202410&c=MATH1080003
MATH 1080-211 Mathematics of change, Part II 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 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 1080-221 Mathematics of change, Part II 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 1080-224 Mathematics of change, Part II 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 Irfan Alam MW 12:00 PM-1:29 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 1300-201 Introduction to Calculus 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 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 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 Brett S Frankel 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 1400-002 Calculus, Part I Beca Lufi MW 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 1400-003 Calculus, Part I Jingwen Chen 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 1400-201 Calculus, Part I 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 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 F 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 1400-204 Calculus, Part I F 3:30 PM-4:59 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 1400-205 Calculus, Part I 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 1400-206 Calculus, Part I 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 1400-207 Calculus, Part I F 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 1400-208 Calculus, Part I F 3:30 PM-4:59 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 1400-209 Calculus, Part I 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 1400-210 Calculus, Part I 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 1400-211 Calculus, Part I F 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 1400-212 Calculus, Part I F 3:30 PM-4:59 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 1400-213 Calculus, Part I 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 1400-214 Calculus, Part I 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 1400-601 Calculus, Part I MW 7:00 PM-8:29 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 1410-001 Calculus, Part II Andrew Cooper TR 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 1410-002 Calculus, Part II Sarah L Strikwerda 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 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 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 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 F 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 1410-204 Calculus, Part II 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 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 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 F 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 1410-208 Calculus, Part II 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 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 1410-210 Calculus, Part II 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 F 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 1410-212 Calculus, Part II 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 1410-213 Calculus, Part II 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 1700-001 Ideas in Mathematics MF 1:45 PM-3:14 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-002 Ideas in Mathematics Yumeng Ou TR 1:45 PM-3:14 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-201 Ideas in Mathematics T 8:30 AM-9:29 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-202 Ideas in Mathematics T 10:15 AM-11:14 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-203 Ideas in Mathematics R 8:30 AM-9:29 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-204 Ideas in Mathematics R 10:15 AM-11:14 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-211 Ideas in Mathematics W 8:30 AM-9:29 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-212 Ideas in Mathematics W 10:15 AM-11:14 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-213 Ideas in Mathematics F 8:30 AM-9:29 AM 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. Nat Sci & Math Sector (new curriculum only)
MATH 1700-601 Ideas in Mathematics 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. Nat Sci & Math Sector (new curriculum only)
MATH 2030-101 Proving things: Algebra T 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 R 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 Angela Gibney MWF 12:00 PM-12:59 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 TR 3:30 PM-4:59 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 Davi Maximo-Alexandrino-Nogueir 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 2400-002 Calculus, Part III Mira A Peterka 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 2400-003 Calculus, Part III Nakia Rimmer TR 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 2400-201 Calculus, Part III 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 2400-202 Calculus, Part III 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 2400-203 Calculus, Part III 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 2400-204 Calculus, Part III 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 2400-211 Calculus, Part III 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 2400-212 Calculus, Part III 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 2400-213 Calculus, Part III 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 2400-221 Calculus, Part III TR 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 2400-222 Calculus, Part III TR 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 2400-223 Calculus, Part III TR 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 2400-224 Calculus, Part III TR 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 2400-225 Calculus, Part III TR 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 2400-226 Calculus, Part III TR 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 2410-001 Calculus, Part IV MW 12:00 PM-1:29 PM 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 2410-002 Calculus, Part IV Michael A. Carchidi 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 2410-201 Calculus, Part IV T 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 2410-202 Calculus, Part IV T 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 2410-203 Calculus, Part IV R 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 2410-204 Calculus, Part IV R 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 2410-211 Calculus, Part IV 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 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 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 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 TR 12:00 PM-1:29 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 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 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 Irfan Alam MW 10:15 AM-11:44 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 Yumeng Ou 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 John D Green TR 10:15 AM-11:44 AM 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 https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202410&c=MATH3130401
MATH 3140-401 Advanced Linear Algebra Julia Hartmann 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 Fnu Rakvi 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. AMCS5141402, MATH5140402
MATH 3140-403 Advanced Linear Algebra 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 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 M 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 W 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 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
MATH 3500-001 Number Theory Ted C K Chinburg TR 12:00 PM-1:29 PM Congruences, Diophantine equations, continued fractions, nonlinear congruences,and quadratic residues.
MATH 3600-001 Advanced Calculus Andrew Cooper TR 3:30 PM-4:59 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 3600-101 Advanced Calculus M 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 W 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 Mira A Peterka MW 12:00 PM-1:29 PM Continuation of MATH 3600.
MATH 3610-002 Advanced Calculus Robert M. Strain TR 1:45 PM-3:14 PM Continuation of MATH 3600.
MATH 3610-101 Advanced Calculus T 7:00 PM-8:59 PM Continuation of MATH 3600.
MATH 3610-102 Advanced Calculus R 7:00 PM-8:59 PM Continuation of MATH 3600.
MATH 3610-103 Advanced Calculus M 7:00 PM-8:59 PM Continuation of MATH 3600.
MATH 3610-104 Advanced Calculus W 7:00 PM-8:59 PM Continuation of MATH 3600.
MATH 3700-001 Algebra Fnu Rakvi TR 3:30 PM-4:59 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 3700-101 Algebra M 7:00 PM-8:59 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 W 7:00 PM-8:59 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 Jianqi Liu MW 12:00 PM-1:29 PM Continuation of MATH 3700.
MATH 3710-101 Algebra T 7:00 PM-8:59 PM Continuation of MATH 3700.
MATH 3710-102 Algebra R 7:00 PM-8:59 PM Continuation of MATH 3700.
MATH 4100-401 Complex Analysis Mona B Merling TR 12:00 PM-1:29 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. AMCS5100401
MATH 4200-401 Ordinary Differential Equations Andrew Cooper 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 Ching-Li Chai 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 4650-401 Differential Geometry Krishan M Canzius
Dennis M Deturck
TR 12:00 PM-1:29 PM 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 Krishan M Canzius
Dennis M Deturck
TR 12:00 PM-1:29 PM 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 Jianqi Liu MW 10:15 AM-11:44 AM Continuation of Math 5020.
MATH 5030-101 Abstract Algebra T 7:00 PM-8:59 PM Continuation of Math 5020.
MATH 5030-102 Abstract Algebra R 7:00 PM-8:59 PM Continuation of Math 5020.
MATH 5090-001 Advanced Analysis Philip Gressman TR 10:15 AM-11:44 AM 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 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 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 John D Green TR 10:15 AM-11:44 AM 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 https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202410&c=MATH5130401
MATH 5140-401 Advanced Linear Algebra Julia Hartmann 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 Fnu Rakvi 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. AMCS5141402, MATH3140402
MATH 5140-403 Advanced Linear Algebra 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 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 M 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 W 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 5460-401 Advanced Applied Probability Jiaqi Liu
Da Wu
MW 10:15 AM-11:44 AM 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 Andre Scedrov TR 1:45 PM-3:14 PM A continuation of PHIL 6721. LGIC3200401, PHIL4722401, PHIL6722401
MATH 5810-001 Topics in Combinatorial Theory James B. Haglund TR 10:15 AM-11:44 AM 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 Mona B Merling TR 1:45 PM-3:14 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 Florian Pop MW 10:15 AM-11:44 AM Continuation of Math 6020.
MATH 6090-401 Analysis Ryan C Hynd 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 Jonathan Block TR 10:15 AM-11:44 AM Rational homotopy theory, cobordism, K-theory, Morse theory and the h-corbodism theorem. Surgery theory.
MATH 6210-001 Algebraic Number Theory Ted C K Chinburg TR 1:45 PM-3:14 PM Continuation of Math 6200.
MATH 6230-001 Complex Algebraic Geometry Tony G Pantev MW 8:30 AM-9:59 AM Continuation of Math 6220.
MATH 6490-401 Stochastic Processes Xin Sun
Da Wu
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 6770-401 Topics in Mathematical Logic: Game Theory, Artificial Intelligence, and Existential Risk Aydin Mohseni MW 1:45 PM-3:14 PM This graduate course focuses on topics drawn from the central areas of mathematical logic: model theory, proof theory, set theory, and computability theory. LGIC4960401, PHIL4720401, PHIL6720401
MATH 7210-001 Advanced Number Theory Ching-Li Chai MW 1:45 PM-3:14 PM Continuation of Math 7200.
MATH 7250-001 Topics in Algebraic Geometry Danny Krashen MW 3:30 PM-4:59 PM Topics from the literature. The specific subject will vary from year to year.