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 |
Nikita Borisov James B Haglund |
TOWN 313 | 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 |
Avik Chakravarty Angela Gibney |
ANNS 109 | 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. | MATH3140401, MATH5140401 | ||||||||

AMCS 5141-402 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
DRLB 2C8 | 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. | MATH3140402, MATH5140402 | ||||||||

AMCS 5141-403 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
DRLB 2C8 | 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. | MATH3140403, MATH5140403 | ||||||||

AMCS 6025-001 | Numerical and Applied Analysis I |
Joshua A Mcginnis James Perry Wolfe |
TOWN 309 | TR 1:45 PM-3:14 PM | 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 |
Ryan C Hynd Kaitian Jin |
DRLB 4C2 | 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 | SHDH 1201 | 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 | DRLB A2 | F 8:30 AM-9:59 AM | Lab for Math 2400 | |||||||||

MATH 0240-102 | Calculus III Lab | Dennis M Deturck | DRLB A2 | F 10:15 AM-11:44 AM | Lab for Math 2400 | |||||||||

MATH 0240-103 | Calculus III Lab | Dennis M Deturck | DRLB A6 | F 12:00 PM-1:29 PM | Lab for Math 2400 | |||||||||

MATH 0240-104 | Calculus III Lab | Dennis M Deturck | DRLB A6 | F 1:45 PM-3:14 PM | Lab for Math 2400 | |||||||||

MATH 1070-001 | Mathematics of change, Part I | Robin Pemantle | DRLB A5 | MW 10:15 AM-11:44 AM | Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. | Nat Sci & Math Sector (new curriculum only) | ||||||||

MATH 1070-002 | Mathematics of change, Part I |
Frenly Espino Jiaqi Liu |
DRLB A5 | MW 8:30 AM-9:59 AM | Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. | Nat Sci & Math Sector (new curriculum only) | ||||||||

MATH 1070-003 | Mathematics of change, Part I | Andrew Cooper | DRLB A5 | 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. | Nat Sci & Math Sector (new curriculum only) | ||||||||

MATH 1070-201 | Mathematics of change, Part I | DRLB 4C2 | TR 8:30 AM-9:59 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1070-202 | Mathematics of change, Part I | DRLB 2C4 | TR 10:15 AM-11:44 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1070-211 | Mathematics of change, Part I |
Frenly Espino Jiaqi Liu |
DRLB 2C4 | TR 8:30 AM-9:59 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||

MATH 1070-212 | Mathematics of change, Part I | DRLB 3C6 | TR 10:15 AM-11:44 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1070-221 | Mathematics of change, Part I |
Andrew Cooper Hannah Cui |
DRLB 4C2 | MW 8:30 AM-9:59 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||

MATH 1070-222 | Mathematics of change, Part I | HAYD 358 | MW 10:15 AM-11:44 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1080-001 | Mathematics of change, Part II | Robin Pemantle | VANC 112 | MW 12:00 PM-1:29 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 1080-201 | Mathematics of change, Part II | DRLB 2C8 | 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 | CHEM 119 | 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 1234-001 | Community Algebra Initiative | Mona B Merling |
DRLB 3N1H FAGN 214 |
M 12:00 PM-1:29 PM W 12:00 PM-1:29 PM |
Community Algebra Initiative | |||||||||

MATH 1300-001 | Introduction to Calculus | Fnu Rakvi | DRLB A8 | TR 3:30 PM-4:59 PM | Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. | General Requirement in Formal Reasoning & Analysis | ||||||||

MATH 1300-002 | Introduction to Calculus | Nakia Rimmer | DRLB A8 | TR 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 1300-201 | Introduction to Calculus | DRLB 3C4 | F 8:30 AM-9:59 AM | Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1300-202 | Introduction to Calculus | DRLB 3C2 | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-203 | Introduction to Calculus | MEYH B13 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-204 | Introduction to Calculus | DRLB 3W2 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-211 | Introduction to Calculus | TOWN 309 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-212 | Introduction to Calculus | DRLB 3C4 | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-213 | Introduction to Calculus | DRLB 3C2 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-214 | Introduction to Calculus | DRLB 3C4 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1300-601 | Introduction to Calculus | CANCELED | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1400-001 | Calculus, Part I | Brett S Frankel | DRLB A1 | 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 1400-002 | Calculus, Part I | Brett S Frankel | DRLB A8 | 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 1400-003 | Calculus, Part I | Patrick Shields | DRLB A2 | 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 | Irfan Alam | MEYH B3 | MW 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1400-005 | Calculus, Part I | John D Green | DRLB A8 | MW 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1400-201 | Calculus, Part I | DRLB 4C2 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-202 | Calculus, Part I | DRLB 4C6 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-203 | Calculus, Part I | DRLB 4C2 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-204 | Calculus, Part I | DRLB 4C2 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-205 | Calculus, Part I | DRLB 4C6 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-206 | Calculus, Part I | DRLB 2C4 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-207 | Calculus, Part I | DRLB 4C6 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-208 | Calculus, Part I | DRLB 4C6 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-209 | Calculus, Part I | DRLB 4C4 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-210 | Calculus, Part I | DRLB 4C4 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-211 | Calculus, Part I | DRLB 4C4 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-212 | Calculus, Part I | DRLB 4C4 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-213 | Calculus, Part I |
Irfan Alam Brett S Frankel John D Green The Gia T Hoang Patrick Shields |
DRLB 2C4 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1400-214 | Calculus, Part I |
Irfan Alam Brett S Frankel John D Green The Gia T Hoang Patrick Shields |
DRLB 2C6 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1400-215 | Calculus, Part I | DRLB 2C4 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-216 | Calculus, Part I | DRLB 2C4 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-217 | Calculus, Part I | DRLB 2C6 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-218 | Calculus, Part I | HAYD 358 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-219 | Calculus, Part I | DRLB 2C8 | F 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-220 | Calculus, Part I | DRLB 2C6 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-221 | Calculus, Part I | DRLB 3C2 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-222 | Calculus, Part I | DRLB 3C4 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1400-601 | Calculus, Part I | Nakia Rimmer | DRLB 2C6 | MW 7:00 PM-8:59 PM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Perm Needed From Department</span> | ||||||||

MATH 1410-001 | Calculus, Part II | Robert W Ghrist | LEVH 101 | 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 | Andrew Cooper | DRLB A4 | 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 | ARCH 208 | 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 | Jingwen Chen | DRLB A8 | TR 1:45 PM-3:14 PM | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1410-005 | Calculus, Part II | Jianqi Liu | DRLB A4 | TR 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | |||||||||

MATH 1410-201 | Calculus, Part II | DRLB A1 | F 8:30 AM-9:59 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1410-202 | Calculus, Part II | DRLB A1 | F 10:15 AM-11:44 AM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1410-203 | Calculus, Part II | DRLB A1 | F 12:00 PM-1:29 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1410-204 | Calculus, Part II | DRLB A1 | F 3:30 PM-4:59 PM | General Requirement in Formal Reasoning & Analysis | ||||||||||

MATH 1410-601 | Calculus, Part II | CANCELED | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 1610-001 | Honors Calculus |
Eben M Blaisdell Herman Gluck |
DRLB A4 | 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 | TOWN 315 | 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 | TOWN 309 | 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 | Danny Krashen | DRLB A1 | TR 3:30 PM-4:59 PM | Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. | Nat Sci & Math Sector (new curriculum only) | ||||||||

MATH 1700-201 | Ideas in Mathematics | DRLB 4C4 | M 8:30 AM-9:59 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 | DRLB 4C4 | M 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 | DRLB 4C4 | W 8:30 AM-9:29 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1700-204 | Ideas in Mathematics | DRLB 4C4 | W 10:15 AM-11:14 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1700-205 | Ideas in Mathematics | DRLB 3C6 | M 8:30 AM-9:29 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1700-206 | Ideas in Mathematics | DRLB 3C6 | W 8:30 AM-9:29 AM | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 1700-601 | Ideas in Mathematics | Matthew P Wiener | DRLB 3C6 | MW 7:00 PM-8:29 PM | Nat Sci & Math Sector (new curriculum only) | |||||||||

MATH 2020-101 | Proving Things: Analysis | DRLB 3N6 | M 7:00 PM-8:59 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 real and complex numbers, sequences, series, continuity, differentiability and integrability. 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. | Nat Sci & Math Sector (new curriculum only) | |||||||||

MATH 2020-102 | Proving Things: Analysis | DRLB 3C4 | W 7:00 PM-8:59 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 real and complex numbers, sequences, series, continuity, differentiability and integrability. 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. | Nat Sci & Math Sector (new curriculum only) | |||||||||

MATH 2020-301 | Proving Things: Analysis | Henry Piers Towsner | DRLB 3C8 | TR 12:00 PM-1:29 PM | This course focuses on the creative side of mathematics, with an emphasis on discovery, reasoning, proofs and effective communication, while at the same time studying real and complex numbers, sequences, series, continuity, differentiability and integrability. 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. | Nat Sci & Math Sector (new curriculum only) | ||||||||

MATH 2400-001 | Calculus, Part III | Dennis M Deturck | DRLB A1 | TR 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 | DRLB A2 | MW 1:45 PM-3:14 PM | Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems. | |||||||||

MATH 2400-201 | Calculus, Part III | DRLB 3C2 | 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 2400-202 | Calculus, Part III | DRLB 3W2 | TR 10:15 AM-11:44 AM | |||||||||||

MATH 2400-203 | Calculus, Part III | MUSE 330 | TR 10:15 AM-11:44 AM | |||||||||||

MATH 2400-204 | Calculus, Part III | WILL 319 | TR 10:15 AM-11:44 AM | |||||||||||

MATH 2400-205 | Calculus, Part III | MEYH B13 | TR 10:15 AM-11:44 AM | |||||||||||

MATH 2400-206 | Calculus, Part III | COHN 337 | TR 10:15 AM-11:44 AM | |||||||||||

MATH 2400-207 | Calculus, Part III | CANCELED | ||||||||||||

MATH 2400-211 | Calculus, Part III | DRLB 4C2 | MW 12:00 PM-1:29 PM | |||||||||||

MATH 2400-212 | Calculus, Part III | DRLB 2C8 | MW 12:00 PM-1:29 PM | |||||||||||

MATH 2400-213 | Calculus, Part III | DRLB 2C6 | MW 12:00 PM-1:29 PM | |||||||||||

MATH 2410-001 | Calculus, Part IV | Michael A Carchidi | DRLB A4 | 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 | DRLB 4C6 | 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 | DRLB 3N6 | 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 | DRLB 4C6 | W 8:30 AM-9:29 AM | |||||||||||

MATH 2410-204 | Calculus, Part IV | DRLB 4C8 | W 10:15 AM-11:14 AM | |||||||||||

MATH 3120-001 | Linear Algebra |
Thomas Y Chung Davi Maximo-Alexandrino-Nogueir |
FAGN 216 | 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 |
Yaojie Hu Mira A Peterka |
FAGN 116 | MW 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 3120-003 | Linear Algebra | CANCELED | 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 3140-401 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
ANNS 109 | 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. | AMCS5141401, MATH5140401 | ||||||||

MATH 3140-402 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
DRLB 2C8 | 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. | AMCS5141402, MATH5140402 | ||||||||

MATH 3140-403 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
DRLB 2C8 | 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. | AMCS5141403, MATH5140403 | ||||||||

MATH 3200-001 | Computer Methods in Mathematical Science I |
Nikita Borisov Robert M Strain |
DRLB 4C8 | TR 10:15 AM-11:44 AM | 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 | DRLB 3C4 | 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 | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202330&c=MATH3400401 | |||||||

MATH 3600-001 | Advanced Calculus |
Changhao Ge John D Green |
ANNS 111 | 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. | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202330&c=MATH3600001 | ||||||||

MATH 3600-002 | Advanced Calculus |
Chayansudha Biswas Sarah L Strikwerda |
DRLB 3N1H | 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. | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202330&c=MATH3600002 | ||||||||

MATH 3600-101 | Advanced Calculus |
Changhao Ge John D Green |
DRLB 2C8 | 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 |
Changhao Ge John D Green |
DRLB 2C8 | R 7:00 PM-8:59 PM | ||||||||||

MATH 3600-103 | Advanced Calculus |
Chayansudha Biswas Sarah L Strikwerda |
DRLB 4C4 | M 7:00 PM-8:59 PM | ||||||||||

MATH 3600-104 | Advanced Calculus |
Chayansudha Biswas Sarah L Strikwerda |
DRLB 4C4 | W 7:00 PM-8:59 PM | ||||||||||

MATH 3610-001 | Advanced Calculus | Jingwen Chen | DRLB 2C2 | TR 12:00 PM-1:29 PM | Continuation of MATH 3600. | |||||||||

MATH 3610-101 | Advanced Calculus | DRLB 2C2 | M 7:00 PM-8:59 PM | Continuation of MATH 3600. | ||||||||||

MATH 3610-102 | Advanced Calculus | DRLB 2C2 | W 7:00 PM-8:59 PM | Continuation of MATH 3600. | ||||||||||

MATH 3700-001 | Algebra |
Daebeom Choi Brett S Frankel |
DRLB 4C2 | MW 1:45 PM-3:14 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 |
Daebeom Choi Brett S Frankel |
DRLB 3C2 | 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 |
Daebeom Choi Brett S Frankel |
DRLB 3C8 | 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 |
Florian Pop Jacob Van Hook |
DRLB 4C6 | MW 12:00 PM-1:29 PM | Continuation of MATH 3700. | |||||||||

MATH 3710-101 | Algebra |
Florian Pop Jacob Van Hook |
DRLB 3C6 | T 7:00 PM-8:59 PM | Continuation of MATH 3700. | |||||||||

MATH 3710-102 | Algebra |
Florian Pop Jacob Van Hook |
DRLB 3C6 | R 7:00 PM-8:59 PM | Continuation of MATH 3700. | |||||||||

MATH 4100-401 | Complex Analysis |
Nikita Borisov James B Haglund |
TOWN 313 | 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 4320-001 | Game Theory. |
Ryan C Hynd Matthew P Wiener |
DRLB 3W2 | TR 12:00 PM-1:29 PM | A mathematical approach to game theory, with an emphasis on examples of actual games. Topics will include mathematical models of games, combinatorial games, two person (zero sum and general sum) games, non-cooperating games and equilibria. | |||||||||

MATH 5000-401 | Topology |
Dennis M Deturck Jacob Van Hook |
DRLB 2C6 | 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 | Julia Hartmann | BENN 141 | MW 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 | DRLB 4C8 | T 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 | DRLB 3C2 | R 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 |
Jae Ho Choi Philip Gressman |
DRLB 3C8 | TR 10:15 AM-11:44 AM | 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. | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202330&c=MATH5080001 | ||||||||

MATH 5080-101 | Advanced Analysis |
Jae Ho Choi Philip Gressman |
DRLB 3C2 | 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 |
Jae Ho Choi Philip Gressman |
DRLB 2N36 | 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 5140-401 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
ANNS 109 | TR 1:45 PM-3:14 PM | AMCS5141401, MATH3140401 | |||||||||

MATH 5140-402 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
DRLB 2C8 | M 7:00 PM-8:59 PM | AMCS5141402, MATH3140402 | |||||||||

MATH 5140-403 | Advanced Linear Algebra |
Avik Chakravarty Angela Gibney |
DRLB 2C8 | W 7:00 PM-8:59 PM | AMCS5141403, MATH3140403 | |||||||||

MATH 5700-401 | Logic and Computability 1 | Henry Piers Towsner | WILL 25 | 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 | ||||||||

MATH 5800-001 | Combinatorial Analysis | James B Haglund | DRLB 2C2 | TR 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 | Albane Thery | GLAB 101 | 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 | https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202330&c=MATH5861401 | |||||||

MATH 5940-401 | Mathematical Methods of Physics | Randall Kamien | DRLB 2C8 | 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 |
Ziqi Fang Herman Gluck |
DRLB 4C8 | 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 |
Zhenyue Guan Florian Pop |
DRLB 3C2 | 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 |
Ryan C Hynd Kaitian Jin |
DRLB 4C2 | 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 | DRLB 4N30 | 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 6200-001 | Algebraic Number Theory | Ted C K Chinburg | DRLB 2C4 | TR 1:45 PM-3:14 PM | Dedekind domains, local fields, basic ramification theory, product formula, Dirichlet unit theory, finiteness of class numbers, Hensel's Lemma, quadratic and cyclotomic fields, quadratic reciprocity, abelian extensions, zeta and L-functions, functional equations, introduction to local and global class field theory. Other topics may include: Diophantine equations, continued fractions, approximation of irrational numbers by rationals, Poisson summation, Hasse principle for binary quadratic forms, modular functions and forms, theta functions. | |||||||||

MATH 6220-001 | Complex Algebraic Geometry | Tony G Pantev | DRLB 3C8 | MW 8:30 AM-9:59 AM | Algebraic geometry over the complex numbers, using ideas from topology, complex variable theory, and differential geometry. Topics include: Complex algebraic varieties, cohomology theories, line bundles, vanishing theorems, Riemann surfaces, Abel's theorem, linear systems, complex tori and abelian varieties, Jacobian varieties, currents, algebraic surfaces, adjunction formula, rational surfaces, residues. | |||||||||

MATH 6440-001 | Partial Differential Equations | Robert M Strain | DRLB 4C2 | TR 12:00 PM-1:29 PM | Subject matter varies from year to year. Some topics are: the classical theory of the wave and Laplace equations, general hyperbolic and elliptic equations, theory of equations with constant coefficients, pseudo-differential operators, and non-linear problems. Sobolev spaces and the theory of distributions will bedeveloped as needed. | |||||||||

MATH 6480-401 | Probability Theory | Jiaoyang Huang | SHDH 1201 | 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 6540-001 | Lie Groups | Wolfgang Ziller | DRLB 4E9 | TR 1:45 PM-3:14 PM | Connection of Lie groups with Lie algebras, Lie subgroups, exponential map. Algebraic Lie groups, compact and complex Lie groups, solvable and nilpotent groups. Other topics may include relations with symplectic geometry, the orbit method, moment map, symplectic reduction, geometric quantization, Poisson-Lie and quantum groups. | |||||||||

MATH 6600-001 | Differential Geometry | Davi Maximo-Alexandrino-Nogueir | DRLB 3C4 | 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 6770-401 | Topics in Logic | Scott Weinstein | HAYD 360 | 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 | Tony G Pantev | CANCELED | 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 | Julia Hartmann | DRLB 4C6 | MW 10:15 AM-11:44 AM | Topics from the literature. The specific subjects will vary from year to year. | |||||||||

MATH 7200-001 | Advanced Number Theory | Ching-Li Chai | DRLB 2C2 | MW 1:45 PM-3:14 PM | Ramification theory, adeles and ideles, Tate's thesis, group cohomology and Galois cohomology, class field theory in terms of ideles and cohomology, Lubin-Tate formal groups, Artin and Swan conductors, central simple algebras over local and global fields, general Hasse principles. Other topics may include the following: zero-dimensional Arakelov theory, Tate duality, introduction to arithmetic of elliptic curves, local and global epsilon factors in functional equations, p-adic L-functions and Iwasawa theory, modular forms and functions and modular curves. | |||||||||

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 8100-012 | Reading Seminar | Julia Hartmann | 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 8100-015 | Reading Seminar | Angela Gibney | 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 | ||||||||||||

MATH 8100-021 | Reading Seminar | Florian Pop | ||||||||||||

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

MATH 8100-039 | Reading Seminar | Henry Piers Towsner | DRLB 4N30 | R 8:30 AM-9:59 AM | ||||||||||

MATH 8100-065 | Reading Seminar | Ryan C Hynd |