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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 <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 003-105 Intro To Calculus Lab F 03:30 PM-05:00 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 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 <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 014-105 Calculus II Lab F 03:30 PM-05:00 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 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 <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 024-105 Calculus III Lab F 03:30 PM-05:00 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 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 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 103-201 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">Registration also required for Lecture (see below)</span>
MATH 103-202 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">Registration also required for Lecture (see below)</span>
MATH 103-203 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">Registration also required for Lecture (see below)</span>
MATH 103-204 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">Registration also required for Lecture (see below)</span>
MATH 103-211 Introduction To Calculus R 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">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 103-212 Introduction To Calculus R 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">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 103-213 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">Registration also required for Lecture (see below)</span>
MATH 103-214 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">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 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 104-007 Calculus I T 01:45 PM-03:15 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 104-008 Calculus I R 01:45 PM-03:15 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 104-009 Calculus I T 03:30 PM-05:00 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">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 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">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 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">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 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">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span>
MATH 104-013 Calculus I M 01:45 PM-03:15 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">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span>
MATH 104-014 Calculus I W 01:45 PM-03:15 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">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span>
MATH 104-015 Calculus I M 03:30 PM-05:00 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">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span>
MATH 104-016 Calculus I W 03:30 PM-05:00 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">Corequisite: MATH004 (see below)</span><br /><span class="penncourse-course-notes">Registration also required for Recitation (see below)</span>
MATH 104-201 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">Registration also required for Lecture (see below)</span>
MATH 104-202 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">Registration also required for Lecture (see below)</span>
MATH 104-203 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">Registration also required for Lecture (see below)</span>
MATH 104-204 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">Registration also required for Lecture (see below)</span>
MATH 104-221 Calculus I R 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">Registration also required for Lecture (see below)</span>
MATH 104-222 Calculus I R 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">Registration also required for Lecture (see below)</span>
MATH 104-223 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">Registration also required for Lecture (see below)</span>
MATH 104-224 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">Registration also required for Lecture (see below)</span>
MATH 104-231 Calculus I R 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-232 Calculus I R 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-233 Calculus I T 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-234 Calculus I T 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-241 Calculus I R 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-242 Calculus I R 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-243 Calculus I T 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-244 Calculus I T 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-251 Calculus I W 08:30 AM-10:00 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">Registration also required for Lecture (see below)</span>
MATH 104-252 Calculus I W 08:30 AM-10:00 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">Registration also required for Lecture (see below)</span>
MATH 104-253 Calculus I M 08:30 AM-10:00 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">Registration also required for Lecture (see below)</span>
MATH 104-254 Calculus I M 08:30 AM-10:00 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">Registration also required for Lecture (see below)</span>
MATH 104-261 Calculus I W 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-262 Calculus I W 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-263 Calculus I M 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-264 Calculus I M 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 104-271 Calculus I W 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-272 Calculus I W 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-273 Calculus I M 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-274 Calculus I M 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 104-601 Calculus I Sukalpa Basu MW 07:00 PM-08:30 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.
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. <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 110-202 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. <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 110-203 Calculus For Wharton Students 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">Registration also required for Lecture (see below)</span>
MATH 110-204 Calculus For Wharton Students 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">Registration also required for Lecture (see below)</span>
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 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 114-005 Calculus II T 01:45 PM-03:15 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 114-006 Calculus II R 01:45 PM-03:15 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 114-007 Calculus II M 03:30 PM-05:00 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 114-008 Calculus II W 03:30 PM-05:00 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 114-009 Calculus II T 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 114-010 Calculus II R 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 114-011 Calculus II M 10:15 AM-11:45 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 114-012 Calculus II W 10:15 AM-11:45 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 114-201 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">Registration also required for Lecture (see below)</span>
MATH 114-202 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">Registration also required for Lecture (see below)</span>
MATH 114-203 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">Registration also required for Lecture (see below)</span>
MATH 114-204 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">Registration also required for Lecture (see below)</span>
MATH 114-211 Calculus II R 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">Registration also required for Lecture (see below)</span>
MATH 114-212 Calculus II R 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">Registration also required for Lecture (see below)</span>
MATH 114-213 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">Registration also required for Lecture (see below)</span>
MATH 114-214 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">Registration also required for Lecture (see below)</span>
MATH 114-221 Calculus II R 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 114-222 Calculus II R 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 114-223 Calculus II T 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 114-224 Calculus II T 01:45 PM-03:15 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">Registration also required for Lecture (see below)</span>
MATH 114-231 Calculus II W 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 114-232 Calculus II W 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 114-233 Calculus II M 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 114-234 Calculus II M 03:30 PM-05:00 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">Registration also required for Lecture (see below)</span>
MATH 114-241 Calculus II R 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">Registration also required for Lecture (see below)</span>
MATH 114-242 Calculus II R 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">Registration also required for Lecture (see below)</span>
MATH 114-243 Calculus II T 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">Registration also required for Lecture (see below)</span>
MATH 114-244 Calculus II T 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">Registration also required for Lecture (see below)</span>
MATH 114-251 Calculus II W 10:15 AM-11:45 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">Registration also required for Lecture (see below)</span>
MATH 114-252 Calculus II W 10:15 AM-11:45 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">Registration also required for Lecture (see below)</span>
MATH 114-253 Calculus II M 10:15 AM-11:45 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">Registration also required for Lecture (see below)</span>
MATH 114-254 Calculus II M 10:15 AM-11:45 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">Registration also required for Lecture (see below)</span>
MATH 114-601 Calculus II TR 07:00 PM-08:30 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.
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. <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 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. <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 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) <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 170-202 Ideas in Mathematics M 10:15 AM-11:15 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) <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 170-203 Ideas in Mathematics W 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) <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 170-204 Ideas in Mathematics W 10:15 AM-11:15 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) <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 170-211 Ideas in Mathematics T 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) <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 170-212 Ideas in Mathematics T 10:15 AM-11:15 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) <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 170-213 Ideas in Mathematics R 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) <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 170-214 Ideas in Mathematics R 10:15 AM-11:15 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) <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 170-601 Ideas in Mathematics MW 07:00 PM-08:30 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">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 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 240-005 Calculus III T 01:45 PM-03:15 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. <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 240-006 Calculus III R 01:45 PM-03:15 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. <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 240-201 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">Registration also required for Lecture (see below)</span>
MATH 240-202 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">Registration also required for Lecture (see below)</span>
MATH 240-203 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">Registration also required for Lecture (see below)</span>
MATH 240-204 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">Registration also required for Lecture (see below)</span>
MATH 240-211 Calculus III R 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">Registration also required for Lecture (see below)</span>
MATH 240-212 Calculus III R 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">Registration also required for Lecture (see below)</span>
MATH 240-213 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">Registration also required for Lecture (see below)</span>
MATH 240-214 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">Registration also required for Lecture (see below)</span>
MATH 240-221 Calculus III R 01:45 PM-03:15 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. <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 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">Registration also required for Lecture (see below)</span>
MATH 240-223 Calculus III T 01:45 PM-03:15 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. <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 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">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. <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 241-202 Calculus IV T 10:15 AM-11:15 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 Lecture (see below)</span>
MATH 241-203 Calculus IV R 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. <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 241-204 Calculus IV R 10:15 AM-11:15 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 Lecture (see below)</span>
MATH 241-211 Calculus IV W 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. <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 241-212 Calculus IV W 10:15 AM-11:15 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 Lecture (see below)</span>
MATH 241-213 Calculus IV F 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. <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 241-214 Calculus IV F 10:15 AM-11:15 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 Lecture (see below)</span>
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. <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 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. <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 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. <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 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. <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 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. <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 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. <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 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. <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
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. <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
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. <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
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 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
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 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
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 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span>
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