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 | MW 10:15 AM-11:44 AM | Complex numbers, DeMoivre's theorem, complex valued functions of a complex variable, the derivative, analytic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, residues, computation of definite integrals by residues, and elementary conformal mapping. | MATH4100401 | ||||||||||

AMCS 5141-001 | Advanced Linear Algebra | Angela Gibney | MW 12:00 PM-1:29 PM | Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. | MATH3140001, MATH5140001 | |||||||||

AMCS 5141-102 | 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. | MATH3140102, MATH5140102 | ||||||||||

AMCS 5141-103 | 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. | MATH3140103, MATH5140103 | ||||||||||

AMCS 5461-001 | Advanced Applied Probability | Robin Pemantle | MW 1:45 PM-3:14 PM | The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). | MATH5460001 | |||||||||

AMCS 6025-001 | Numerical and Applied Analysis I |
Joshua A Mcginnis James Perry Wolfe |
We turn to linear algebra and the structural properties of linear systems of equations relevant to their numerical solution. In this context we introduce eigenvalues and the spectral theory of matrices. Methods appropriate to the numerical solution of very large systems are discussed. We discuss modern techniques using randomized algorithms for fast matrix-vector multiplication, and fast direct solvers. Topics covered include the classical Fast Multipole Method, the interpolative decomposition, structured matrix algebra, randomized methods for low-rank approximation, and fast direct solvers for sparse matrices. These techniques are of central importance in applications of linear algebra to the numerical solution of PDE, and in Machine Learning. The theoretical content of this course is illustrated and supplemented throughout the year with substantial computational examples and assignments. | |||||||||||

AMCS 6081-401 | Analysis | Philip Gressman | TR 10:15 AM-11:44 AM | Complex analysis: analyticity, Cauchy theory, meromorphic functions, isolated singularities, analytic continuation, Runge's theorem, d-bar equation, Mittlag-Leffler theorem, harmonic and sub-harmonic functions, Riemann mapping theorem, Fourier transform from the analytic perspective. Introduction to real analysis: Weierstrass approximation, Lebesgue measure in Euclidean spaces, Borel measures and convergence theorems, C0 and the Riesz-Markov theorem, Lp-spaces, Fubini Theorem. | MATH6080401 | |||||||||

AMCS 6481-401 | Probability Theory | Jiaoyang Huang | MW 1:45 PM-3:14 PM | Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. | MATH6480401, STAT9300401 | |||||||||

MATH 0240-101 | Calculus III Lab | Dennis M Deturck | F 8:30 AM-9:59 AM | Lab for Math 2400 | ||||||||||

MATH 0240-102 | Calculus III Lab | Dennis M Deturck | F 10:15 AM-11:44 AM | Lab for Math 2400 | ||||||||||

MATH 0240-103 | Calculus III Lab | Dennis M Deturck | F 12:00 PM-1:29 PM | Lab for Math 2400 | ||||||||||

MATH 0240-104 | Calculus III Lab | Dennis M Deturck | F 1:45 PM-3:14 PM | Lab for Math 2400 | ||||||||||

MATH 1070-001 | Mathematics of change, Part I | MW 1:45 PM-3:14 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 | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202430&c=MATH1070001 | |||||||||

MATH 1070-002 | Mathematics of change, Part I | Andrew Cooper | 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 1070-003 | Mathematics of change, Part I | Andrew Cooper | TR 12:00 PM-1:29 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 | TR 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1070-202 | Mathematics of change, Part I | TR 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1070-211 | Mathematics of change, Part I | MW 8:30 AM-10:00 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

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

MATH 1070-221 | Mathematics of change, Part I | MW 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1070-222 | Mathematics of change, Part I | MW 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1080-001 | Mathematics of change, Part II | Robin Pemantle | 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 1080-201 | Mathematics of change, Part II | TR 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 1080-202 | Mathematics of change, Part II | TR 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 | TR 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 1300-002 | Introduction to Calculus | Philip Gressman | TR 1:45 PM-3:14 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 1300-003 | Introduction to Calculus | John D Green | TR 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 | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-202 | Introduction to Calculus | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-203 | Introduction to Calculus | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-204 | Introduction to Calculus | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-211 | Introduction to Calculus | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-212 | Introduction to Calculus | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-213 | Introduction to Calculus | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-214 | Introduction to Calculus | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-215 | Introduction to Calculus | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-216 | Introduction to Calculus | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-217 | Introduction to Calculus | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-218 | Introduction to Calculus | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1300-601 | Introduction to Calculus | Sukalpa Basu | MW 7:00 PM-8:29 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-001 | Calculus, Part I | MW 8:30 AM-9:59 AM | Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-003 | Calculus, Part I | 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 1400-004 | Calculus, Part I | Patrick Shields | 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 1400-005 | Calculus, Part I | Marco Zaninelli | MW 3:30 PM-4:59 PM | 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 1400-215 | Calculus, Part I | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-216 | Calculus, Part I | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-217 | Calculus, Part I | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-601 | Calculus, Part I | Nakia Rimmer | MW 7:00 PM-8:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1410-001 | Calculus, Part II | Robert W. Ghrist | 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 | Nakia Rimmer | 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 | Nakia Rimmer | 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 1410-004 | Calculus, Part II | TR 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-005 | Calculus, Part II | Jingwen Chen | TR 3:30 PM-4:59 PM | 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 1410-214 | Calculus, Part II | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-215 | Calculus, Part II | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-216 | Calculus, Part II | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-217 | Calculus, Part II | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-218 | Calculus, Part II | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-219 | Calculus, Part II | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-220 | Calculus, Part II | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1410-601 | Calculus, Part II | TR 7:00 PM-8:29 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1610-001 | Honors Calculus | Herman Gluck | TR 12:00 PM-1:29 PM | Students who are interested in math or science might also want to consider a more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1610 and 2400, but more in depth and involve discussion of the underlying theory as well as computations. | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1610-201 | Honors Calculus | M 7:00 PM-8:59 PM | Students who are interested in math or science might also want to consider a more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1610 and 2400, but more in depth and involve discussion of the underlying theory as well as computations. | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1610-202 | Honors Calculus | W 7:00 PM-8:59 PM | Students who are interested in math or science might also want to consider a more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1610 and 2400, but more in depth and involve discussion of the underlying theory as well as computations. | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1700-001 | Ideas in Mathematics | Mona B Merling | MW 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. | General Requirement in Formal Reasoning & Analysis | |||||||||

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. | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1700-202 | Ideas in Mathematics | T 10:15 AM-11:44 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. | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1700-203 | Ideas in Mathematics | R 8:30 AM-9:29 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1700-601 | Ideas in Mathematics | Matthew P Wiener | MW 7:00 PM-8:29 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 2400-001 | Calculus, Part III | Dennis M Deturck | 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 | TR 10:15 AM-11:44 AM | Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems. | ||||||||||

MATH 2400-201 | Calculus, Part III | 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 | ||||||||||||

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 | TR 12:00 PM-1:29 PM | ||||||||||||

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

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

MATH 2410-001 | Calculus, Part IV | Michael A. Carchidi | TR 1:45 PM-3:14 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 2410-201 | 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 2410-202 | 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 2410-203 | Calculus, Part IV | W 8:30 AM-9:29 AM | ||||||||||||

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

MATH 3120-001 | Linear Algebra | Davi Maximo-Alexandrino-Nogueir | TR 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 | Marco Zaninelli | MW 1:45 PM-3:14 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 3140-001 | Advanced Linear Algebra | Angela Gibney | MW 12:00 PM-1:29 PM | Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products: Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. | AMCS5141001, MATH5140001 | |||||||||

MATH 3140-102 | 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. | AMCS5141102, MATH5140102 | ||||||||||

MATH 3140-103 | 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. | AMCS5141103, MATH5140103 | ||||||||||

MATH 3200-001 | Computer Methods in Mathematical Science I | TR 12:00 PM-1:29 PM | Students will use symbolic manipulation software and write programs to solve problems in numerical quadrature, equation-solving, linear algebra and differential equations. Theoretical and computational aspects of the methods will be discussed along with error analysis and a critical comparison of methods. | |||||||||||

MATH 3400-401 | Discrete Mathematics I | Andre Scedrov | TR 10:15 AM-11:44 AM | Topics will be drawn from some subjects in combinatorial analysis with applications to many other branches of math and science: graphs and networks, generating functions, permutations, posets, asymptotics. | LGIC2100401 | |||||||||

MATH 3600-001 | Advanced Calculus | James B. Haglund | MW 12:00 PM-1:29 PM | Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course. | ||||||||||

MATH 3600-002 | Advanced Calculus | Andrew Cooper | TR 1:45 PM-3:14 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 | T 7:00 PM-8:59 PM | Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course. | |||||||||||

MATH 3600-102 | Advanced Calculus | R 7:00 PM-8:59 PM | ||||||||||||

MATH 3600-103 | Advanced Calculus | M 7:00 PM-8:59 PM | ||||||||||||

MATH 3600-104 | Advanced Calculus | W 7:00 PM-8:59 PM | ||||||||||||

MATH 3610-001 | Advanced Calculus | Mira A Peterka | TR 12:00 PM-1:29 PM | Continuation of MATH 3600. | ||||||||||

MATH 3610-101 | Advanced Calculus | M 7:00 PM-8:59 PM | Continuation of MATH 3600. | |||||||||||

MATH 3610-102 | Advanced Calculus | W 7:00 PM-8:59 PM | Continuation of MATH 3600. | |||||||||||

MATH 3700-001 | Algebra | Julia Hartmann | MF 10:15 AM-11:44 AM | Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course. | ||||||||||

MATH 3700-101 | Algebra | T 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 | R 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 10:15 AM-11:44 AM | 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 | MW 10:15 AM-11:44 AM | Complex numbers, DeMoivre's theorem, complex valued functions of a complex variable, the derivative, analytic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, residues, computation of definite integrals by residues, and elementary conformal mapping. | AMCS5100401 | ||||||||||

MATH 5000-401 | Topology | Ryan C Hynd | TR 12:00 PM-1:29 PM | Point set topology: metric spaces and topological spaces, compactness, connectedness, continuity, extension theorems, separation axioms, quotient spaces, topologies on function spaces, Tychonoff theorem. Fundamental groups and covering spaces, and related topics. | ||||||||||

MATH 5020-001 | Abstract Algebra | Ted C K Chinburg | TR 1:45 PM-3:14 PM | An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 3700. | ||||||||||

MATH 5020-101 | Abstract Algebra | M 7:00 PM-8:59 PM | An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 3700. | |||||||||||

MATH 5020-102 | Abstract Algebra | W 7:00 PM-8:59 PM | An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 3700. | |||||||||||

MATH 5080-001 | Advanced Analysis | Yumeng Ou | TR 12:00 PM-1:29 PM | Construction of real numbers, the topology of the real line and the foundations of single variable calculus. Notions of convergence for sequences of functions. Basic approximation theorems for continuous functions and rigorous treatment of elementary transcendental functions. The course is intended to teach students how to read and construct rigorous formal proofs. A more theoretical course than Math 3600. | ||||||||||

MATH 5080-101 | Advanced Analysis | M 7:00 PM-8:59 PM | Construction of real numbers, the topology of the real line and the foundations of single variable calculus. Notions of convergence for sequences of functions. Basic approximation theorems for continuous functions and rigorous treatment of elementary transcendental functions. The course is intended to teach students how to read and construct rigorous formal proofs. A more theoretical course than Math 3600. | |||||||||||

MATH 5080-102 | Advanced Analysis | W 7:00 PM-8:59 PM | Construction of real numbers, the topology of the real line and the foundations of single variable calculus. Notions of convergence for sequences of functions. Basic approximation theorems for continuous functions and rigorous treatment of elementary transcendental functions. The course is intended to teach students how to read and construct rigorous formal proofs. A more theoretical course than Math 3600. | |||||||||||

MATH 5140-001 | Advanced Linear Algebra | Angela Gibney | MW 12:00 PM-1:29 PM | AMCS5141001, MATH3140001 | ||||||||||

MATH 5140-102 | Advanced Linear Algebra | T 7:00 PM-8:59 PM | AMCS5141102, MATH3140102 | |||||||||||

MATH 5140-103 | Advanced Linear Algebra | R 7:00 PM-8:59 PM | AMCS5141103, MATH3140103 | |||||||||||

MATH 5200-001 | Selections from Algebra | Julia Hartmann | MF 1:45 PM-3:14 PM | Informal introduction to such subjects as homological algebra, number theory, and algebraic geometry. | ||||||||||

MATH 5300-001 | Mathematics of Finance | Ryan C Hynd | TR 10:15 AM-11:44 AM | This course presents the basic mathematical tools to model financial markets and to make calculations about financial products, especially financial derivatives. Mathematical topics covered: stochastic processes, partial differential equations and their relationship. No background in finance is assumed. | ||||||||||

MATH 5460-001 | Advanced Applied Probability | Robin Pemantle | MW 1:45 PM-3:14 PM | The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). | AMCS5461001 | |||||||||

MATH 5700-401 | Logic and Computability 1 | Henry Piers Towsner | TR 3:30 PM-4:59 PM | The course focuses on topics drawn from the central areas of mathematical logic: model theory, proof theory, set theory, and computability theory. | LGIC3100401, PHIL4721401, PHIL6721401 | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202430&c=MATH5700401 | ||||||||

MATH 5800-001 | Combinatorial Analysis | James B. Haglund | MW 10:15 AM-11:44 AM | Standard tools of enumerative combinatorics including partitions and compositions of integers, set partitions, generating functions, permutations with restricted positions, inclusion-exclusion, partially ordered sets. Permission of the instructor required to enroll. | ||||||||||

MATH 5861-401 | Mathematical Modeling in Biology | MW 1:45 PM-3:14 PM | This course will cover various mathematical models and tools that are used to study modern biological problems. Mathematical models may be drawn from cell biology, physiology, population genetics, or ecology. Tools in dynamical systems or stochastic processes will be introduced as necessary. No prior knowledge of biology is needed to take this course, but some familiarity with differential equations and probability will be assumed. | BIOL5860401 | ||||||||||

MATH 5940-401 | Mathematical Methods of Physics | Martin Claassen | TR 10:15 AM-11:44 AM | A discussion of those concepts and techniques of classical analysis employed inphysical theories. Topics include complex analysis. Fourier series and transforms, ordinary and partial equations, Hilbert spaces, among others. | PHYS5500401 | |||||||||

MATH 6000-001 | Topology and Geometric Analysis | Herman Gluck | TR 1:45 PM-3:14 PM | Differentiable functions, inverse and implicit function theorems. Theory of manifolds: differentiable manifolds, charts, tangent bundles, transversality, Sard's theorem, vector and tensor fields and differential forms: Frobenius' theorem, integration on manifolds, Stokes' theorem in n dimensions, de Rham cohomology. Introduction to Lie groups and Lie group actions. | ||||||||||

MATH 6020-001 | Algebra | Danny Krashen | MW 10:15 AM-11:44 AM | Group theory: permutation groups, symmetry groups, linear algebraic groups, Jordan-Holder and Sylow theorems, finite abelian groups, solvable and nilpotent groups, p-groups, group extensions. Ring theory: Prime and maximal ideals, localization, Hilbert basis theorem, integral extensions, Dedekind domains, primary decomposition, rings associated to affine varieties, semisimple rings, Wedderburn's theorem, elementary representation theory. Linear algebra: Diagonalization and canonical form of matrices, elementary representation theory, bilinear forms, quotient spaces, dual spaces, tensor products, exact sequences, exterior and symmetric algebras. Module theory: Tensor products, flat and projective modules, introduction to homological algebra, Nakayama's Lemma. Field theory: separable and normal extensions, cyclic extensions, fundamental theorem of Galois theory, solvability of equations. | ||||||||||

MATH 6080-401 | Analysis | Philip Gressman | TR 10:15 AM-11:44 AM | Complex analysis: analyticity, Cauchy theory, meromorphic functions, isolated singularities, analytic continuation, Runge's theorem, d-bar equation, Mittlag-Leffler theorem, harmonic and sub-harmonic functions, Riemann mapping theorem, Fourier transform from the analytic perspective. Introduction to real analysis: Weierstrass approximation, Lebesgue measure in Euclidean spaces, Borel measures and convergence theorems, C0 and the Riesz-Markov theorem, Lp-spaces, Fubini Theorem. | AMCS6081401 | |||||||||

MATH 6180-001 | Algebraic Topology, Part I | Jonathan Block | TR 10:15 AM-11:44 AM | Homotopy groups, Hurewicz theorem, Whitehead theorem, spectral sequences. Classification of vector bundles and fiber bundles. Characteristic classes and obstruction theory. | ||||||||||

MATH 6240-001 | Algebraic Geometry | Florian Pop | MW 12:00 PM-1:29 PM | Algebraic geometry over algebraically closed fields, using ideas from commutative algebra. Topics include: Affine and projective algebraic varieties, morphisms and rational maps, singularities and blowing up, rings of functions, algebraic curves, Riemann Roch theorem, elliptic curves, Jacobian varieties, sheaves, schemes, divisors, line bundles, cohomology of varieties, classification of surfaces. | ||||||||||

MATH 6260-001 | Commutative Algebra | MW 8:30 AM-9:59 AM | Topics in commutative algebra taken from the literature. Material will vary from year to year depending upon the instructor's interests. | |||||||||||

MATH 6340-001 | Arithmetic Geometry | Florian Pop | MW 1:45 PM-3:14 PM | Arithmetic Geometry | ||||||||||

MATH 6480-401 | Probability Theory | Jiaoyang Huang | MW 1:45 PM-3:14 PM | Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. | AMCS6481401, STAT9300401 | |||||||||

MATH 6600-001 | Differential Geometry | Davi Maximo-Alexandrino-Nogueir | TR 12:00 PM-1:29 PM | Riemannian metrics and connections, geodesics, completeness, Hopf-Rinow theorem, sectional curvature, Ricci curvature, scalar curvature, Jacobi fields, second fundamental form and Gauss equations, manifolds of constant curvature, first and second variation formulas, Bonnet-Myers theorem, comparison theorems, Morse index theorem, Hadamard theorem, Preissmann theorem, and further topics such as sphere theorems, critical points of distance functions, the soul theorem, Gromov-Hausdorff convergence. | ||||||||||

MATH 6710-301 | Topics in Logic | Andre Scedrov | TR 1:45 PM-3:14 PM | Discusses advanced topics in logic. | ||||||||||

MATH 6770-401 | Topics in Logic | Scott Weinstein | TR 10:15 AM-11:44 AM | 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 6940-001 | Mathematical Foundations of Theoretical Physics | Ron Donagi | MF 1:45 PM-3:14 PM | Selected topics in mathematical physics, such as mathematical methods of classical mechanics, electrodynamics, relativity, quantum mechanics and quantum field theory. | ||||||||||

MATH 7020-001 | Topics in Algebra | Ching-Li Chai | MW 1:45 PM-3:14 PM | Topics from the literature. The specific subjects will vary from year to year. | ||||||||||

MATH 8100-010 | Reading Seminar | Ron Donagi | Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member | |||||||||||

MATH 8100-017 | Reading Seminar | Jonathan Block | Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member | |||||||||||

MATH 8100-021 | Reading Seminar | Florian Pop | Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member | |||||||||||

MATH 8100-024 | Reading Seminar | Tony G Pantev | ||||||||||||

MATH 8100-039 | Reading Seminar | Henry Piers Towsner |