Title | Instructor | Location | Time | All taxonomy terms | Description | Section Description | Cross Listings | Fulfills | Registration Notes | Syllabus | Syllabus URL | Course Syllabus URL | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

AMCS 510-401 | Complex Analysis | Ningchuan Zhang | TR 01:45 PM-03:15 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. | MATH410401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

AMCS 514-101 | Advanced Linear Algebra | T 07:00 PM-09:00 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. | MATH514101, MATH314101 | <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||

AMCS 514-102 | Advanced Linear Algebra | R 07:00 PM-09:00 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. | MATH514102, MATH314102 | <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||

AMCS 514-401 | Advanced Linear Algebra | Renee H Bell | MW 10:15 AM-11:45 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. | MATH514401, MATH314401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | ||||||||

AMCS 520-401 | Ordinary Differential Equations | Michael V Pimsner | TR 12:00 PM-01:30 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. | MATH420401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

AMCS 602-001 | Algebraic Techiques I: Algebraic Techniques For Applied Math and Computational Science I | Hyunjoong Kim | TR 08:30 AM-10:00 AM | 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

AMCS 608-401 | Analysis I | Robert M. Strain | TR 10:15 AM-11:45 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 and integration Euclideanspaces, Borel measures and convergence theorems, C0 and the Riesz-Markov theorem, Lp-spaces, Fubini's Theorem. | MATH608401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

MATH 003-101 | Intro To Calculus Lab | F 08:30 AM-10:00 AM | Lab for Math 103 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH103 (see below)</span> | ||||||||||

MATH 003-102 | Intro To Calculus Lab | F 10:15 AM-11:45 AM | Lab for Math 103 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH103 (see below)</span> | ||||||||||

MATH 003-103 | Intro To Calculus Lab | F 12:00 PM-01:30 PM | Lab for Math 103 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH103 (see below)</span> | ||||||||||

MATH 003-104 | Intro To Calculus Lab | F 01:45 PM-03:15 PM | Lab for Math 103 | |||||||||||

MATH 003-105 | Intro To Calculus Lab | F 03:30 PM-05:00 PM | Lab for Math 103 | |||||||||||

MATH 004-101 | Calculus Lab I | F 08:30 AM-10:00 AM | Lab for Math 104 | <span class="penncourse-course-notes">Corequisite: MATH104 (see below)</span> | ||||||||||

MATH 004-102 | Calculus Lab I | F 10:15 AM-11:45 AM | Lab for Math 104 | <span class="penncourse-course-notes">Corequisite: MATH104 (see below)</span> | ||||||||||

MATH 004-103 | Calculus Lab I | F 12:00 PM-01:30 PM | Lab for Math 104 | <span class="penncourse-course-notes">Corequisite: MATH104 (see below)</span> | ||||||||||

MATH 004-104 | Calculus Lab I | F 01:45 PM-03:15 PM | Lab for Math 104 | <span class="penncourse-course-notes">Corequisite: MATH104 (see below)</span> | ||||||||||

MATH 004-105 | Calculus Lab I | F 03:30 PM-05:00 PM | Lab for Math 104 | <span class="penncourse-course-notes">Corequisite: MATH104 (see below)</span> | ||||||||||

MATH 010-101 | Calculus For Wharton Lab | F 08:30 AM-10:00 AM | Lab for Math 110 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||||

MATH 010-102 | Calculus For Wharton Lab | F 10:15 AM-11:45 AM | Lab for Math 110 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||||

MATH 010-103 | Calculus For Wharton Lab | F 12:00 PM-01:30 PM | Lab for Math 110 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||||

MATH 010-104 | Calculus For Wharton Lab | F 01:45 PM-03:15 PM | Lab for Math 110 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||||

MATH 010-105 | Calculus For Wharton Lab | F 03:30 PM-05:00 PM | Lab for Math 110 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||||

MATH 014-101 | Calculus II Lab | F 08:30 AM-10:00 AM | Lab for Math 114 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH114 (see below)</span> | ||||||||||

MATH 014-102 | Calculus II Lab | F 10:15 AM-11:45 AM | Lab for Math 114 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH114 (see below)</span> | ||||||||||

MATH 014-103 | Calculus II Lab | F 12:00 PM-01:30 PM | Lab for Math 114 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH114 (see below)</span> | ||||||||||

MATH 014-104 | Calculus II Lab | F 01:45 PM-03:15 PM | Lab for Math 114 | |||||||||||

MATH 014-105 | Calculus II Lab | F 03:30 PM-05:00 PM | Lab for Math 114 | |||||||||||

MATH 024-101 | Calculus III Lab | F 08:30 AM-10:00 AM | Lab for Math 240 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH240 (see below)</span> | ||||||||||

MATH 024-102 | Calculus III Lab | F 10:15 AM-11:45 AM | Lab for Math 240 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH240 (see below)</span> | ||||||||||

MATH 024-103 | Calculus III Lab | F 12:00 PM-01:30 PM | Lab for Math 240 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH240 (see below)</span> | ||||||||||

MATH 024-104 | Calculus III Lab | F 01:45 PM-03:15 PM | Lab for Math 240 | |||||||||||

MATH 024-105 | Calculus III Lab | F 03:30 PM-05:00 PM | Lab for Math 240 | |||||||||||

MATH 103-001 | Introduction To Calculus | M 12:00 PM-01:30 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 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH003 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||

MATH 103-002 | Introduction To Calculus | W 12:00 PM-01:30 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 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH003 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||

MATH 103-003 | Introduction To Calculus | T 10:15 AM-11:45 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 | <span class="penncourse-course-notes">Corequisite: MATH003 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||

MATH 103-004 | Introduction To Calculus | R 10:15 AM-11:45 AM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Corequisite: MATH003 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 103-201 | Introduction To Calculus | W 12:00 PM-01:30 PM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 103-202 | Introduction To Calculus | W 12:00 PM-01:30 PM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 103-203 | Introduction To Calculus | M 12:00 PM-01:30 PM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 103-204 | Introduction To Calculus | M 12:00 PM-01:30 PM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 103-211 | Introduction To Calculus | R 10:15 AM-11:45 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 103-212 | Introduction To Calculus | R 10:15 AM-11:45 AM | General Requirement in Formal Reasoning & Analysis | |||||||||||

MATH 103-213 | Introduction To Calculus | T 10:15 AM-11:45 AM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 103-214 | Introduction To Calculus | T 10:15 AM-11:45 AM | General Requirement in Formal Reasoning & Analysis | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 104-001 | Calculus I | M 10:15 AM-11:45 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 104-002 | Calculus I | W 10:15 AM-11:45 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 104-005 | Calculus I | T 12:00 PM-01:30 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 104-006 | Calculus I | R 12:00 PM-01:30 PM | ||||||||||||

MATH 104-007 | Calculus I | T 01:45 PM-03:15 PM | ||||||||||||

MATH 104-008 | Calculus I | R 01:45 PM-03:15 PM | ||||||||||||

MATH 104-009 | Calculus I | T 03:30 PM-05:00 PM | <span class="penncourse-course-notes">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||||

MATH 104-010 | Calculus I | R 03:30 PM-05:00 PM | <span class="penncourse-course-notes">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||||

MATH 104-011 | Calculus I | M 08:30 AM-10:00 AM | <span class="penncourse-course-notes">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||||

MATH 104-012 | Calculus I | W 08:30 AM-10:00 AM | ||||||||||||

MATH 104-013 | Calculus I | M 01:45 PM-03:15 PM | ||||||||||||

MATH 104-014 | Calculus I | W 01:45 PM-03:15 PM | ||||||||||||

MATH 104-015 | Calculus I | M 03:30 PM-05:00 PM | ||||||||||||

MATH 104-016 | Calculus I | W 03:30 PM-05:00 PM | ||||||||||||

MATH 104-201 | Calculus I | W 10:15 AM-11:45 AM | ||||||||||||

MATH 104-202 | Calculus I | W 10:15 AM-11:45 AM | ||||||||||||

MATH 104-203 | Calculus I | M 10:15 AM-11:45 AM | ||||||||||||

MATH 104-204 | Calculus I | M 10:15 AM-11:45 AM | ||||||||||||

MATH 104-221 | Calculus I | R 12:00 PM-01:30 PM | ||||||||||||

MATH 104-222 | Calculus I | R 12:00 PM-01:30 PM | ||||||||||||

MATH 104-223 | Calculus I | T 12:00 PM-01:30 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 104-224 | Calculus I | T 12:00 PM-01:30 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 104-231 | Calculus I | R 01:45 PM-03:15 PM | ||||||||||||

MATH 104-232 | Calculus I | R 01:45 PM-03:15 PM | ||||||||||||

MATH 104-233 | Calculus I | T 01:45 PM-03:15 PM | ||||||||||||

MATH 104-234 | Calculus I | T 01:45 PM-03:15 PM | ||||||||||||

MATH 104-241 | Calculus I | R 03:30 PM-05:00 PM | ||||||||||||

MATH 104-242 | Calculus I | R 03:30 PM-05:00 PM | ||||||||||||

MATH 104-243 | Calculus I | T 03:30 PM-05:00 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 104-244 | Calculus I | T 03:30 PM-05:00 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 104-251 | Calculus I | W 08:30 AM-10:00 AM | ||||||||||||

MATH 104-252 | Calculus I | W 08:30 AM-10:00 AM | ||||||||||||

MATH 104-253 | Calculus I | M 08:30 AM-10:00 AM | ||||||||||||

MATH 104-254 | Calculus I | M 08:30 AM-10:00 AM | ||||||||||||

MATH 104-261 | Calculus I | W 01:45 PM-03:15 PM | ||||||||||||

MATH 104-262 | Calculus I | W 01:45 PM-03:15 PM | ||||||||||||

MATH 104-263 | Calculus I | M 01:45 PM-03:15 PM | ||||||||||||

MATH 104-264 | Calculus I | M 01:45 PM-03:15 PM | ||||||||||||

MATH 104-271 | Calculus I | W 03:30 PM-05:00 PM | ||||||||||||

MATH 104-272 | Calculus I | W 03:30 PM-05:00 PM | ||||||||||||

MATH 104-273 | Calculus I | M 03:30 PM-05:00 PM | ||||||||||||

MATH 104-274 | Calculus I | M 03:30 PM-05:00 PM | ||||||||||||

MATH 104-601 | Calculus I | Sukalpa Basu | MW 07:00 PM-08:30 PM | |||||||||||

MATH 110-001 | Calculus For Wharton Stu | T 12:00 PM-01:30 PM | Differential calculus, integral calculus, series, differential equations and elements of multivariable calculus, with an emphasis on applications. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH010 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 110-002 | Calculus For Wharton Stu | R 12:00 PM-01:30 PM | Differential calculus, integral calculus, series, differential equations and elements of multivariable calculus, with an emphasis on applications. | <span class="penncourse-course-notes">Corequisite: MATH010 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 110-201 | Calculus For Wharton Students | R 12:00 PM-01:30 PM | Differential calculus, integral calculus, series, differential equations and elements of multivariable calculus, with an emphasis on applications. | |||||||||||

MATH 110-202 | Calculus For Wharton Students | R 12:00 PM-01:30 PM | ||||||||||||

MATH 110-203 | Calculus For Wharton Students | T 12:00 PM-01:30 PM | ||||||||||||

MATH 110-204 | Calculus For Wharton Students | T 12:00 PM-01:30 PM | ||||||||||||

MATH 114-001 | Calculus II | M 12:00 PM-01:30 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH014 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 114-002 | Calculus II | W 12:00 PM-01:30 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH014 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 114-003 | Calculus II | T 08:30 AM-10:00 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH014 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 114-004 | Calculus II | R 08:30 AM-10:00 AM | ||||||||||||

MATH 114-005 | Calculus II | T 01:45 PM-03:15 PM | ||||||||||||

MATH 114-006 | Calculus II | R 01:45 PM-03:15 PM | ||||||||||||

MATH 114-007 | Calculus II | M 03:30 PM-05:00 PM | ||||||||||||

MATH 114-008 | Calculus II | W 03:30 PM-05:00 PM | ||||||||||||

MATH 114-009 | Calculus II | T 12:00 PM-01:30 PM | ||||||||||||

MATH 114-010 | Calculus II | R 12:00 PM-01:30 PM | ||||||||||||

MATH 114-011 | Calculus II | M 10:15 AM-11:45 AM | ||||||||||||

MATH 114-012 | Calculus II | W 10:15 AM-11:45 AM | ||||||||||||

MATH 114-201 | Calculus II | W 12:00 PM-01:30 PM | ||||||||||||

MATH 114-202 | Calculus II | W 12:00 PM-01:30 PM | ||||||||||||

MATH 114-203 | Calculus II | M 12:00 PM-01:30 PM | ||||||||||||

MATH 114-204 | Calculus II | M 12:00 PM-01:30 PM | ||||||||||||

MATH 114-211 | Calculus II | R 08:30 AM-10:00 AM | ||||||||||||

MATH 114-212 | Calculus II | R 08:30 AM-10:00 AM | ||||||||||||

MATH 114-213 | Calculus II | T 08:30 AM-10:00 AM | ||||||||||||

MATH 114-214 | Calculus II | T 08:30 AM-10:00 AM | ||||||||||||

MATH 114-221 | Calculus II | R 01:45 PM-03:15 PM | ||||||||||||

MATH 114-222 | Calculus II | R 01:45 PM-03:15 PM | ||||||||||||

MATH 114-223 | Calculus II | T 01:45 PM-03:15 PM | ||||||||||||

MATH 114-224 | Calculus II | T 01:45 PM-03:15 PM | ||||||||||||

MATH 114-231 | Calculus II | W 03:30 PM-05:00 PM | ||||||||||||

MATH 114-232 | Calculus II | W 03:30 PM-05:00 PM | ||||||||||||

MATH 114-233 | Calculus II | M 03:30 PM-05:00 PM | ||||||||||||

MATH 114-234 | Calculus II | M 03:30 PM-05:00 PM | ||||||||||||

MATH 114-241 | Calculus II | R 12:00 PM-01:30 PM | ||||||||||||

MATH 114-242 | Calculus II | R 12:00 PM-01:30 PM | ||||||||||||

MATH 114-243 | Calculus II | T 12:00 PM-01:30 PM | ||||||||||||

MATH 114-244 | Calculus II | T 12:00 PM-01:30 PM | ||||||||||||

MATH 114-251 | Calculus II | W 10:15 AM-11:45 AM | ||||||||||||

MATH 114-252 | Calculus II | W 10:15 AM-11:45 AM | ||||||||||||

MATH 114-253 | Calculus II | M 10:15 AM-11:45 AM | ||||||||||||

MATH 114-254 | Calculus II | M 10:15 AM-11:45 AM | ||||||||||||

MATH 114-601 | Calculus II | TR 07:00 PM-08:30 PM | ||||||||||||

MATH 116-001 | Honors Calculus | TR 12:00 PM-01:30 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 116 and Math 260 (the analogues of Math 114 and Math 240, respectively). These courses will cover essentially the same material as 114 and 240, but more in depth and involve discussion of the underlying theory as well as computations. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 116-201 | Honors Calculus | M 07:00 PM-09:00 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 116 and Math 260 (the analogues of Math 114 and Math 240, respectively). These courses will cover essentially the same material as 114 and 240, but more in depth and involve discussion of the underlying theory as well as computations. | |||||||||||

MATH 116-202 | Honors Calculus | W 07:00 PM-09:00 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 116 and Math 260 (the analogues of Math 114 and Math 240, respectively). These courses will cover essentially the same material as 114 and 240, but more in depth and involve discussion of the underlying theory as well as computations. | |||||||||||

MATH 123-001 | Community Math Teach Pro | TR 12:00 PM-01:30 PM | This course allows Penn students to teach a series of hands-on activities to students in math classes at University City High School. The semester starts with an introduction to successful approaches for teaching math in urban high schools. The rest of the semester will be devoted to a series of weekly hands-on activities designed to teach fundamental aspects of geometry. The first class meeting of each week, Penn faculty teach Penn students the relevant mathematical background and techniques for a hands-on activity. During the second session of each week, Penn students will teach the hands-on activity to a small group of UCHS students. The Penn students will also have an opportunity to develop their own activity and to implement it with the UCHS students. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||||

MATH 170-001 | Ideas in Mathematics | TR 01:45 PM-03:15 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. Prerequisite: May also be counted toward the General Requirement in Natural Science & Mathematics. | Nat Sci & Math Sector (new curriculum only) | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Natural Science & Math Sector</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||

MATH 170-002 | Ideas in Mathematics | MWF 01:45 PM-02:45 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. Prerequisite: May also be counted toward the General Requirement in Natural Science & Mathematics. | Nat Sci & Math Sector (new curriculum only) | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Natural Science & Math Sector</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | |||||||||

MATH 170-201 | Ideas in Mathematics | M 08:30 AM-09:30 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. Prerequisite: May also be counted toward the General Requirement in Natural Science & Mathematics. | Nat Sci & Math Sector (new curriculum only) | ||||||||||

MATH 170-202 | Ideas in Mathematics | M 10:15 AM-11:15 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-203 | Ideas in Mathematics | W 08:30 AM-09:30 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-204 | Ideas in Mathematics | W 10:15 AM-11:15 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-211 | Ideas in Mathematics | T 08:30 AM-09:30 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-212 | Ideas in Mathematics | T 10:15 AM-11:15 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-213 | Ideas in Mathematics | R 08:30 AM-09:30 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-214 | Ideas in Mathematics | R 10:15 AM-11:15 AM | Nat Sci & Math Sector (new curriculum only) | |||||||||||

MATH 170-601 | Ideas in Mathematics | MW 07:00 PM-08:30 PM | Nat Sci & Math Sector (new curriculum only) | <span class="penncourse-course-notes">Natural Science & Math Sector</span> | ||||||||||

MATH 202-101 | Proving Things: Analysis | T 07:00 PM-09:00 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Seminar (see below)</span> | ||||||||||

MATH 202-102 | Proving Things: Analysis | R 07:00 PM-09:00 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Seminar (see below)</span> | ||||||||||

MATH 202-301 | Proving Things: Analysis | Florian Pop | MWF 12:00 PM-01:00 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Freshman Seminar</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | |||||||||

MATH 240-001 | Calculus III | T 10:15 AM-11:45 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH024 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 240-002 | Calculus III | R 10:15 AM-11:45 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH024 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 240-003 | Calculus III | T 08:30 AM-10:00 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Corequisite: MATH024 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 240-004 | Calculus III | R 08:30 AM-10:00 AM | ||||||||||||

MATH 240-005 | Calculus III | T 01:45 PM-03:15 PM | ||||||||||||

MATH 240-006 | Calculus III | R 01:45 PM-03:15 PM | ||||||||||||

MATH 240-201 | Calculus III | R 10:15 AM-11:45 AM | ||||||||||||

MATH 240-202 | Calculus III | R 10:15 AM-11:45 AM | ||||||||||||

MATH 240-203 | Calculus III | T 10:15 AM-11:45 AM | ||||||||||||

MATH 240-204 | Calculus III | T 10:15 AM-11:45 AM | ||||||||||||

MATH 240-211 | Calculus III | R 08:30 AM-10:00 AM | ||||||||||||

MATH 240-212 | Calculus III | R 08:30 AM-10:00 AM | ||||||||||||

MATH 240-213 | Calculus III | T 08:30 AM-10:00 AM | ||||||||||||

MATH 240-214 | Calculus III | T 08:30 AM-10:00 AM | ||||||||||||

MATH 240-221 | Calculus III | R 01:45 PM-03:15 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 240-222 | Calculus III | R 01:45 PM-03:15 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 240-223 | Calculus III | T 01:45 PM-03:15 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 240-224 | Calculus III | T 01:45 PM-03:15 PM | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||||

MATH 241-001 | Calculus IV | MWF 01:45 PM-02:45 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 241-002 | Calculus IV | TR 10:15 AM-11:45 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span> | ||||||||||

MATH 241-201 | Calculus IV | T 08:30 AM-09:30 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 241-202 | Calculus IV | T 10:15 AM-11:15 AM | ||||||||||||

MATH 241-203 | Calculus IV | R 08:30 AM-09:30 AM | ||||||||||||

MATH 241-204 | Calculus IV | R 10:15 AM-11:15 AM | ||||||||||||

MATH 241-211 | Calculus IV | W 08:30 AM-09:30 AM | ||||||||||||

MATH 241-212 | Calculus IV | W 10:15 AM-11:15 AM | ||||||||||||

MATH 241-213 | Calculus IV | F 08:30 AM-09:30 AM | ||||||||||||

MATH 241-214 | Calculus IV | F 10:15 AM-11:15 AM | ||||||||||||

MATH 312-001 | Linear Algebra | Andrew Cooper | TR 01:45 PM-03:15 PM | Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 312 cannot be taken to satisfy the major requirements. Prerequisite: Students who have already received credit for either Math 370, 371,502, or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and 313/513. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | |||||||||

MATH 312-002 | Linear Algebra | Mira A Peterka | MWF 12:00 PM-01:00 PM | Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 312 cannot be taken to satisfy the major requirements. Prerequisite: Students who have already received credit for either Math 370, 371,502, or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and 313/513. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | |||||||||

MATH 314-101 | Advanced Linear Algebra | T 07:00 PM-09:00 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. Prerequisite: Math 314/514 covers Linear Algebra at the advanced level with a theoretical approach. Students can receive credit for at most one of Math 312 or Math 314. | AMCS514101, MATH514101 | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||

MATH 314-102 | Advanced Linear Algebra | R 07:00 PM-09:00 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. Prerequisite: Math 314/514 covers Linear Algebra at the advanced level with a theoretical approach. Students can receive credit for at most one of Math 312 or Math 314. | AMCS514102, MATH514102 | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | |||||||||

MATH 314-401 | Advanced Linear Algebra | Renee H Bell | MW 10:15 AM-11:45 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. Prerequisite: Math 314/514 covers Linear Algebra at the advanced level with a theoretical approach. Students can receive credit for at most one of Math 312 or Math 314. | AMCS514401, MATH514401 | <span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | ||||||||

MATH 320-001 | Computer Methods I | Robert M. Strain | TR 12:00 PM-01:30 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 340-401 | Discrete Mathematics I | Andre Scedrov | TR 10:15 AM-11:45 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. | LGIC210401 | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span> | ||||||||

MATH 360-001 | Advanced Calculus | MWF 12:00 PM-01:00 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. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | ||||||||||

MATH 360-101 | Advanced Calculus | T 07:00 PM-09:00 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 360-102 | Advanced Calculus | R 07:00 PM-09:00 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 361-001 | Advanced Calculus | Michael V Pimsner | TR 03:30 PM-05:00 PM | Continuation of MATH 360. | <span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | |||||||||

MATH 361-101 | Advanced Calculus | M 07:00 PM-09:00 PM | Continuation of MATH 360. | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 361-102 | Advanced Calculus | W 07:00 PM-09:00 PM | Continuation of MATH 360. | <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 370-001 | Algebra | MWF 10:15 AM-11:15 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. Prerequisite: MATH 502-503 is a masters level version of this course. Students who have already received credit for either Math 370, 371, 502, or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive creidt for at most one of Math 312 and math 313/513. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | ||||||||||

MATH 370-101 | Algebra | T 07:00 PM-09:00 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. Prerequisite: MATH 502-503 is a masters level version of this course. Students who have already received credit for either Math 370, 371, 502, or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive creidt for at most one of Math 312 and math 313/513. | |||||||||||

MATH 370-102 | Algebra | R 07:00 PM-09:00 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. Prerequisite: MATH 502-503 is a masters level version of this course. Students who have already received credit for either Math 370, 371, 502, or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive creidt for at most one of Math 312 and math 313/513. | |||||||||||

MATH 371-001 | Algebra | Maximilien Peroux | MWF 10:15 AM-11:15 AM | Prerequisite: Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. | <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | |||||||||

MATH 371-101 | Algebra | T 07:00 PM-09:00 PM | Prerequisite: Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. | |||||||||||

MATH 371-102 | Algebra | R 07:00 PM-09:00 PM | Prerequisite: Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. | |||||||||||

MATH 410-401 | Complex Analysis | Ningchuan Zhang | TR 01:45 PM-03:15 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. | AMCS510401 | |||||||||

MATH 420-401 | Ordinary Differential Equations | Michael V Pimsner | TR 12:00 PM-01:30 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. | AMCS520401 | |||||||||

MATH 432-001 | Game Theory | Ryan C Hynd | TR 08:30 AM-10:00 AM | 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 460-401 | Topology | Mona B Merling | TR 01:45 PM-03:15 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. | MATH500401 | |||||||||

MATH 500-401 | Topology | Mona B Merling | TR 01:45 PM-03:15 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. | MATH460401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

MATH 502-001 | Abstract Algebra | Brett S Frankel | MW 10:15 AM-11:45 AM | An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 370. Prerequisite: If course requirement not met, permission of instructor required. Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. | <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | |||||||||

MATH 502-101 | Abstract Algebra | T 07:00 PM-09:00 PM | An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 370. Prerequisite: If course requirement not met, permission of instructor required. Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. | <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span> | ||||||||||

MATH 502-102 | Abstract Algebra | R 07:00 PM-09:00 PM | An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 370. Prerequisite: If course requirement not met, permission of instructor required. Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. | |||||||||||

MATH 508-001 | Advanced Analysis | Philip Gressman | TR 10:15 AM-11:45 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 360. | <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span> | |||||||||

MATH 508-101 | Advanced Analysis | M 07:00 PM-09:00 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 360. | |||||||||||

MATH 508-102 | Advanced Analysis | W 07:00 PM-09:00 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 360. | |||||||||||

MATH 514-101 | Advanced Linear Algebra | T 07:00 PM-09:00 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. | AMCS514101, MATH314101 | ||||||||||

MATH 514-102 | Advanced Linear Algebra | R 07:00 PM-09:00 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. | AMCS514102, MATH314102 | ||||||||||

MATH 514-401 | Advanced Linear Algebra | Renee H Bell | MW 10:15 AM-11:45 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. | AMCS514401, MATH314401 | |||||||||

MATH 540-001 | Select Class & Func Anal | Yumeng Ou | MW 01:45 PM-03:15 PM | Informal introduction to such subjects as compact operators and Fredholm theory, Banach algebras, harmonic analysis, differential equations, nonlinear functional analysis, and Riemann surfaces. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2021C&course=MATH540001 | ||||||||

MATH 570-401 | Introduction To Logic & Computability | Henry Piers Towsner | TR 03:30 PM-05:00 PM | Propositional logic: semantics, formal deductions, resolution method. First order logic: validity, models, formal deductions; Godel's completeness theorem, Lowenheim-Skolem theorem: cut-elimination, Herbrand's theorem, resolution method.Computability: finite automata, Turing machines, Godel's incompleteness theorems. Algorithmically unsolvable problems in mathematics. | LGIC310401, PHIL410401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

MATH 580-001 | Combinatorial Analysis | James B. Haglund | TR 12:00 PM-01:30 PM | 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 594-401 | Mathematical Methods of Physics | Randall Kamien | TR 10:15 AM-11:45 AM | Introduction to mathematics used in physics and engineering, with the goal of developing facility in classical techniques. Vector spaces, linear algebra, computation of eigenvalues and eigenvectors, boundary value problems, spectral theory of second order equations, asymptotic expansions, partial differential equations, differential operators and Green's functions, orthogonal functions, generating functions, contour integration, Fourier and Laplace transforms and an introduction to representation theory of SU(2) and SO(3). The course will draw on examples in continuum mechanics, electrostatics and transport problems. | PHYS500401 | https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2021C&course=MATH594401 | ||||||||

MATH 600-001 | Geo Analysis & Topology | Herman Gluck | TR 01:45 PM-03:15 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 602-001 | Algebra | David Harbater | MF 10:15 AM-11:45 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 608-401 | Analysis I | Robert M. Strain | TR 10:15 AM-11:45 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. | AMCS608401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

MATH 618-001 | Algebrc Topology, Part I | Jonathan Block | TR 01:45 PM-03:15 PM | Homotopy groups, Hurewicz theorem, Whitehead theorem, spectral sequences. Classification of vector bundles and fiber bundles. Characteristic classes and obstruction theory. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 620-001 | Algebraic Number Theory | Ted C K Chinburg | TR 03:30 PM-05:00 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 622-001 | Complex Algebraic Geom | Ron Donagi | TR 12:00 PM-01:30 PM | 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 644-001 | Partial Differ Equations | Ryan C Hynd | TR 10:15 AM-11:45 AM | 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 be developed as needed. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 648-401 | Probability Theory | Robin Pemantle | MW 12:00 PM-01:30 PM | Measure theory and foundations of Probability theory. Zero-one Laws. Probability inequalities. Weak and strong laws of large numbers. Central limit theorems and the use of characteristic functions. Rates of convergence. Introduction to Martingales and random walk. | STAT930401 | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | ||||||||

MATH 654-001 | Lie Groups | Wolfgang Ziller | TR 12:00 PM-01:30 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 660-001 | Differential Geometry | Davi Maximo-Alexandrino-Nogueir | TR 10:15 AM-11:45 AM | 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 720-001 | Advanced Number Theory | Ching-Li Chai | MF 10:15 AM-11:45 AM | 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. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 724-001 | Topics in Algebraic Geom | Svetlana Makarova | TR 10:15 AM-11:45 AM | Topics from the literature. The specific subjects will vary from year to year. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | |||||||||

MATH 748-001 | Topics in Class Analysis | Xin Sun | MF 03:30 PM-05:00 PM | Harmonic analysis in Euclidean space, Riemann surfaces, Discontinuous groups and harmonic analysis in hyperbolic space, Pseudodifferential operators and index theorems, Variational methods in non-linear PDE, Hyperbolic equations and conservation laws, Probability and stochastic processes, Geometric measure theory, Applications of analysis to problems in differential geometry. The specific subjects will vary from year to year. | <span class="penncourse-course-notes">Undergraduates Need Permission</span> | https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2021C&course=MATH748001 |