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

AMCS 5141-405 | Advanced Linear Algebra | M 7:00 PM-8:59 PM | MATH3140405, MATH5140405 | |||||||||||

AMCS 5141-406 | Advanced Linear Algebra | W 7:00 PM-8:59 PM | 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 | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1070-211 | Mathematics of change, Part I | TR 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1070-212 | Mathematics of change, Part I | TR 10:15 AM-11:44 AM | 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 | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1080-221 | Mathematics of change, Part II | MW 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1080-224 | Mathematics of change, Part II | MW 10:15 AM-11:44 AM | 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 | 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 | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-202 | Calculus, Part I | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-203 | Calculus, Part I | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-204 | Calculus, Part I | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-205 | Calculus, Part I | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-206 | Calculus, Part I | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-207 | Calculus, Part I | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-208 | Calculus, Part I | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-209 | Calculus, Part I | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-210 | Calculus, Part I | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-211 | Calculus, Part I | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-212 | Calculus, Part I | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-213 | Calculus, Part I | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-214 | Calculus, Part I | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-601 | Calculus, Part I | MW 7:00 PM-8:29 PM | 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 | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-202 | Calculus, Part II | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-203 | Calculus, Part II | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-204 | Calculus, Part II | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-205 | Calculus, Part II | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-206 | Calculus, Part II | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-207 | Calculus, Part II | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-208 | Calculus, Part II | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-209 | Calculus, Part II | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-210 | Calculus, Part II | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-211 | Calculus, Part II | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-212 | Calculus, Part II | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-213 | Calculus, Part II | F 8:30 AM-9:59 AM | 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 | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 1700-203 | Ideas in Mathematics | R 8:30 AM-9:29 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 1700-204 | Ideas in Mathematics | R 10:15 AM-11:14 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 1700-211 | Ideas in Mathematics | W 8:30 AM-9:29 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 1700-212 | Ideas in Mathematics | W 10:15 AM-11:14 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 1700-213 | Ideas in Mathematics | F 8:30 AM-9:29 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 1700-601 | Ideas in Mathematics | TR 7:00 PM-8:29 PM | 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 | ||||||||||||

MATH 2400-202 | Calculus, Part III | MW 10:15 AM-11:44 AM | ||||||||||||

MATH 2400-203 | Calculus, Part III | MW 10:15 AM-11:44 AM | ||||||||||||

MATH 2400-204 | Calculus, Part III | MW 10:15 AM-11:44 AM | ||||||||||||

MATH 2400-211 | Calculus, Part III | MW 12:00 PM-1:29 PM | ||||||||||||

MATH 2400-212 | Calculus, Part III | MW 12:00 PM-1:29 PM | ||||||||||||

MATH 2400-213 | Calculus, Part III | MW 12:00 PM-1:29 PM | ||||||||||||

MATH 2400-221 | Calculus, Part III | TR 1:45 PM-3:14 PM | ||||||||||||

MATH 2400-222 | Calculus, Part III | TR 1:45 PM-3:14 PM | ||||||||||||

MATH 2400-223 | Calculus, Part III | TR 1:45 PM-3:14 PM | ||||||||||||

MATH 2400-224 | Calculus, Part III | TR 1:45 PM-3:14 PM | ||||||||||||

MATH 2400-225 | Calculus, Part III | TR 1:45 PM-3:14 PM | ||||||||||||

MATH 2400-226 | Calculus, Part III | TR 1:45 PM-3:14 PM | ||||||||||||

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 | ||||||||||||

MATH 2410-203 | Calculus, Part IV | R 8:30 AM-9:29 AM | ||||||||||||

MATH 2410-204 | Calculus, Part IV | R 10:15 AM-11:14 AM | ||||||||||||

MATH 2410-211 | Calculus, Part IV | M 8:30 AM-9:29 AM | ||||||||||||

MATH 2410-212 | Calculus, Part IV | M 10:15 AM-11:14 AM | ||||||||||||

MATH 2410-213 | Calculus, Part IV | F 8:30 AM-9:29 AM | ||||||||||||

MATH 2410-214 | Calculus, Part IV | F 10:15 AM-11:14 AM | ||||||||||||

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 | AMCS5141404, MATH5140404 | |||||||||||

MATH 3140-405 | Advanced Linear Algebra | M 7:00 PM-8:59 PM | AMCS5141405, MATH5140405 | |||||||||||

MATH 3140-406 | Advanced Linear Algebra | W 7:00 PM-8:59 PM | 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 | AMCS5141401, MATH3140401 | ||||||||||

MATH 5140-402 | Advanced Linear Algebra | Fnu Rakvi | TR 1:45 PM-3:14 PM | AMCS5141402, MATH3140402 | ||||||||||

MATH 5140-403 | Advanced Linear Algebra | T 7:00 PM-8:59 PM | AMCS5141403, MATH3140403 | |||||||||||

MATH 5140-404 | Advanced Linear Algebra | R 7:00 PM-8:59 PM | AMCS5141404, MATH3140404 | |||||||||||

MATH 5140-405 | Advanced Linear Algebra | M 7:00 PM-8:59 PM | AMCS5141405, MATH3140405 | |||||||||||

MATH 5140-406 | Advanced Linear Algebra | W 7:00 PM-8:59 PM | 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. |