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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 514-401 Advanced Linear Algebra Florian Pop 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. MATH314401, MATH514401 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span>
AMCS 514-402 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. MATH514402, MATH314402 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
AMCS 514-403 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. MATH514403, MATH314403 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
AMCS 514-404 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. MATH514404, MATH314404 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
AMCS 514-405 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. MATH514405, MATH314405 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
AMCS 520-401 Ordinary Differ Equation 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 525-401 Partial Differential Equations Jonathan Block TR 01:45 PM-03:15 PM Method of separation of variables will be applied to solve the wave, heat, and Laplace equations. In addition, one or more of the following topics will be covered: qualitative properties of solutions of various equations (characteristics, maximum principles, uniqueness theorems), Laplace and Fourier transform methods, and approximation techniques. MATH425401 <span class="penncourse-course-notes">Undergraduates Need Permission</span>
AMCS 603-001 Algebraic Techiques II Yoichiro Mori TR 01:45 PM-03:15 PM We begin with an introduction to group theory. The emphasis is on groups as symetries and transformations of space. After an introduction to abstract groups, we turn our attention to compact Lie groups, in particular SO(3), and their representations. We explore the connections between orthogonal polynomials, classical transcendental functions and group representations. This unit is completed with a discussion of finite groups and their applications in coding theory.
AMCS 609-401 Analysis II Robert M. Strain TR 10:15 AM-11:45 AM Real analysis: general measure theory, outer measures and Cartheodory construction, Hausdorff measures, Radon-Nikodym theorem, Fubini's theorem, Hilbert space and L2-theory of the Fourier transform. Functional analysis: normed linear spaces, convexity, the Hahn-Banach theorem, duality for Banach spaces, weak convergence, bounded linear operators, Baire category theorem, uniform boundedness principle, open mapping theorem, closed graph theorem, compact operators, Fredholm theory, interpolation theorems, Lp-theory for the Fourier transform. MATH609401 <span class="penncourse-course-notes">Course Online: Synchronous Format</span>
MATH 003-101 Intro To Calculus Lab F 08:30 AM-10:00 AM Lab for Math 103 <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">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">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">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">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 014-101 Calculus II Lab F 08:30 AM-10:00 AM Lab for Math 114 <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">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">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">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">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">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">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">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">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">Corequisite: MATH240 (see below)</span>
MATH 103-001 Introduction To Calculus Fnu Rakvi 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 Recitation and Laboratory (see below)</span>
MATH 103-002 Introduction To Calculus Fnu Rakvi 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">Registration also required for Recitation and Laboratory (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">Course Online: Asynchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture and Laboratory (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 and Laboratory (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 and Laboratory (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 and Laboratory (see below)</span>
MATH 103-601 Intro To Calculus MW 07:00 PM-08:30 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
MATH 104-001 Calculus I Irfan Alam T 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 Recitation and Online Course (see below)</span>
MATH 104-002 Calculus I Irfan Alam R 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 Recitation and Online Course (see below)</span>
MATH 104-003 Calculus I Nadia M Ott 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">Registration also required for Recitation and Online Course (see below)</span>
MATH 104-004 Calculus I Nadia M Ott 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">Registration also required for Recitation and Online Course (see below)</span>
MATH 104-005 Calculus I Nakia Rimmer 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">Registration also required for Recitation and Online Course (see below)</span>
MATH 104-006 Calculus I Nakia Rimmer 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">Registration also required for Recitation and Online Course (see below)</span>
MATH 104-201 Calculus I R 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 and Online Course (see below)</span>
MATH 104-202 Calculus I R 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">Course Online: Asynchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture and Online Course (see below)</span>
MATH 104-203 Calculus I T 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">Registration also required for Lecture and Online Course (see below)</span>
MATH 104-204 Calculus I T 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">Registration also required for Lecture and Online Course (see below)</span>
MATH 104-211 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 and Online Course (see below)</span>
MATH 104-212 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 and Online Course (see below)</span>
MATH 104-213 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">Registration also required for Lecture and Online Course (see below)</span>
MATH 104-214 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">Registration also required for Lecture and Online Course (see below)</span>
MATH 104-221 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 and Online Course (see below)</span>
MATH 104-222 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 and Online Course (see below)</span>
MATH 104-223 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">Registration also required for Lecture and Online Course (see below)</span>
MATH 104-224 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">Registration also required for Lecture and Online Course (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 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">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">Registration also required for Recitation (see below)</span>
MATH 114-003 Calculus II Andrew Cooper 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 Recitation (see below)</span>
MATH 114-004 Calculus II Andrew Cooper 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">Registration also required for Recitation (see below)</span>
MATH 114-005 Calculus II Robert W. Ghrist 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">Registration also required for Recitation (see below)</span>
MATH 114-006 Calculus II Robert W. Ghrist 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">Registration also required for Recitation (see below)</span>
MATH 114-007 Calculus II Danny Krashen 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">Registration also required for Recitation (see below)</span>
MATH 114-008 Calculus II Danny Krashen 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">Registration also required for Recitation (see below)</span>
MATH 114-009 Calculus II Nakia Rimmer M 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">Registration also required for Recitation (see below)</span>
MATH 114-010 Calculus II Nakia Rimmer W 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">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 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 114-212 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 114-213 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 114-214 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">Course Online: Asynchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture and Online Course (see below)</span>
MATH 114-221 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 114-222 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 114-223 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 114-224 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 114-231 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">Registration also required for Lecture (see below)</span>
MATH 114-232 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">Registration also required for Lecture (see below)</span>
MATH 114-233 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">Registration also required for Lecture (see below)</span>
MATH 114-234 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">Registration also required for Lecture (see below)</span>
MATH 114-241 Calculus II W 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">Registration also required for Lecture (see below)</span>
MATH 114-242 Calculus II W 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">Registration also required for Lecture (see below)</span>
MATH 114-243 Calculus II M 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">Registration also required for Lecture (see below)</span>
MATH 114-244 Calculus II M 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">Registration also required for Lecture (see below)</span>
MATH 170-001 Ideas in Mathematics Brett S Frankel MW 03:30 PM-05:00 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 Patrick Shields 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">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 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 170-202 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 170-203 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 170-204 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 170-205 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">Registration also required for Lecture (see below)</span>
MATH 170-206 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">Registration also required for Lecture (see below)</span>
MATH 170-211 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">Registration also required for Lecture (see below)</span>
MATH 170-212 Ideas in Mathematics CANCELED 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">Registration also required for Lecture (see below)</span>
MATH 170-213 Ideas in Mathematics F 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">Registration also required for Lecture (see below)</span>
MATH 170-214 Ideas in Mathematics F 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">Registration also required for Lecture (see below)</span>
MATH 170-215 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">Registration also required for Lecture (see below)</span>
MATH 170-216 Ideas in Mathematics CANCELED 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">Registration also required for Lecture (see below)</span>
MATH 170-217 Ideas in Mathematics F 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">Registration also required for Lecture (see below)</span>
MATH 170-218 Ideas in Mathematics F 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">Registration also required for Lecture (see below)</span>
MATH 170-601 Ideas in Mathematics TR 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 203-101 Proving Things: Algebra M 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 arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening. <span class="penncourse-course-notes">Registration also required for Seminar (see below)</span>
MATH 203-102 Proving Things: Algebra W 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 arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening. <span class="penncourse-course-notes">Registration also required for Seminar (see below)</span>
MATH 203-301 Proving Things: Algebra Renee H Bell 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 arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening. <span class="penncourse-course-notes">Freshman Seminar</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span>
MATH 210-001 Math in Age of Info: Math in the Media Truong-Son Van TR 01:45 PM-03:15 PM This course counts as a regular elective for both the Mathematics Major and Minor. This is a course about mathematical reasoning and the media. Embedded in many stories one finds in the media are mathematical questions as well as implicit mathematical models for how the world behaves. We will discuss ways to recognize such questions and models, and how to think about them from a mathematical perspective. A key part of the course will be about what constitutes a mathematical proof, and what passes for proof in various media contexts. The course will cover a variety of topics in logic, probability and statistics as well as how these subjects can be used and abused. Nat Sci & Math Sector (new curriculum only) <span class="penncourse-course-notes">Course is available to Freshmen and Upperclassmen.</span><br /><span class="penncourse-course-notes">Natural Science & Math Sector</span>
MATH 240-001 Calculus IIi Angela Gibney 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 Recitation (see below)</span>
MATH 240-002 Calculus IIi Angela Gibney 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 Recitation (see below)</span>
MATH 240-003 Calculus IIi Maximilien Peroux 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 Recitation (see below)</span>
MATH 240-004 Calculus IIi Maximilien Peroux 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 Recitation (see below)</span>
MATH 240-005 Calculus IIi Ching-Li Chai M 05:15 PM-06:45 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 Recitation (see below)</span>
MATH 240-006 Calculus IIi Ching-Li Chai W 05:15 PM-06:45 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 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 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">Registration also required for Lecture (see below)</span>
MATH 240-212 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">Registration also required for Lecture (see below)</span>
MATH 240-213 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">Registration also required for Lecture (see below)</span>
MATH 240-214 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">Registration also required for Lecture (see below)</span>
MATH 240-221 Calculus IIi W 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">Registration also required for Lecture (see below)</span>
MATH 240-222 Calculus IIi W 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">Registration also required for Lecture (see below)</span>
MATH 240-223 Calculus IIi M 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">Registration also required for Lecture (see below)</span>
MATH 240-224 Calculus IIi M 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">Registration also required for Lecture (see below)</span>
MATH 241-001 Calculus IV Michael A. Carchidi MWF 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 Recitation (see below)</span>
MATH 241-002 Calculus IV Marino Romero 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 CANCELED 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 CANCELED 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 M 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 CANCELED 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 CANCELED 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 260-001 Honors Calculus (Continuation) Herman Gluck TR 01:45 PM-03:15 PM This is an honors version of Math 240 which explores the same topics but with greater mathematical rigor. <span class="penncourse-course-notes">Registration also required for Recitation (see below)</span>
MATH 260-201 Honors Calculus (Continuation) M 07:00 PM-09:00 PM This is an honors version of Math 240 which explores the same topics but with greater mathematical rigor. <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 260-202 Honors Calculus (Continuation) W 07:00 PM-09:00 PM This is an honors version of Math 240 which explores the same topics but with greater mathematical rigor. <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 280-301 Entropy Math Evolution: Entropy and the Mathematics of Evolution Ted C K Chinburg CANCELED The goal of this is to explore a new theory of evolution developed by L. Demetrius at MIT based on the second law of thermodynamics. The essential idea is that life exists because if increases overall entropy quicker than other process es. The course will include an introduction to thermodynamics as well as to the information theory difinition of entropy. Eventually I want to apply this to other systems. For instance, I think the theory explains why political candidates who create chaos, tweet and require more bits of information to describe each day are favored by the second law. Demetrius makes a distinction between robust high entropy environments and precarious low entropy environments which is a very interesting in many different systems. <span class="penncourse-course-notes">Benjamin Franklin Seminars</span>
MATH 290-001 Undergrad Math Research Ryan C Hynd TR 12:00 PM-01:30 PM This is a project-oriented mathematics research course that teaches students tosolve real-world problems by constructing and analyzing mathematical models. Typically the problems considered will come from mathematics, chemistry, biology, and materials science but sometimes they will also come from economics, finance, and social sciences. The research problems in the course vary from year to year.
MATH 312-001 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.
MATH 312-002 Linear Algebra Andrew Cooper TR 10:15 AM-11:45 AM 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.
MATH 313-401 Comput Linear Algebra TR 10:15 AM-11:45 AM Many important problems in a wide range of disciplines within computer science and throughout science are solved using techniques from linear algebra. This course will introduce students to some of the most widely used algorithms and illustrate how they are actually used. Prerequisite: Students who have alreadyreceived credit for either math 370, 371, 502 or 503 cannot receive further credit for Math 313. Students can receive ccredit for at most one of Math 312 and Math 313. Some specific topics: the solution of systems of linear equations by Gaussian elimination, dimension of a linear space, inner product, cross product, change of basis, affine and rigid motions, eigenvalues and eigenvectors, diagonalization of both symmetric and non-symmetric matrices, quadratic polynomials, and least squares optimazation. MATH513401
MATH 314-401 Advanced Linear Algebra Florian Pop 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 314-402 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. AMCS514402, MATH514402 <span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 314-403 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. AMCS514403, MATH514403 <span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 314-404 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. AMCS514404, MATH514404 <span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 314-405 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. AMCS514405, MATH514405 <span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 341-401 Discrete Mathematics II Andre Scedrov TR 10:15 AM-11:45 AM Topics will be drawn from some subjects useful in the analysis of information and computation: logic, set theory, theory of computation, number theory, probability, and basic cryptography. LGIC220401
MATH 350-001 Number Theory Ching-Li Chai MWF 10:15 AM-11:15 AM Congruences, Diophantine equations, continued fractions, nonlinear congruences, and quadratic residues.
MATH 360-001 Advanced Calculus TR 01:45 PM-03:15 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 M 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 W 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">Registration also required for Lecture (see below)</span>
MATH 361-001 Advanced Calculus Truong-Son Van TR 10:15 AM-11:45 AM Continuation of MATH 360. <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 361-101 Advanced Calculus M 07:00 PM-09:00 PM Continuation of MATH 360. <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 361-102 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 Svetlana Makarova TR 03:30 PM-05:00 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 Laboratory (see below)</span>
MATH 370-101 Algebra M 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 W 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 TR 12:00 PM-01:30 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 Laboratory (see below)</span>
MATH 371-101 Algebra M 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 W 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 420-401 Ordinary Differ Equation 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 425-401 Partial Differential Equations Jonathan Block TR 01:45 PM-03:15 PM Method of separation of variables will be applied to solve the wave, heat, and Laplace equations. In addition, one or more of the following topics will be covered: qualitative properties of solutions of various equations (characteristics, maximum principles, uniqueness theorems), Laplace and Fourier transform methods, and approximation techniques. AMCS525401
MATH 465-401 Differential Geometry Alexandre A Kirillov TR 10:15 AM-11:45 AM Differential geometry of curves in the plane and in 3-space;n gauge theories Surfaces in 3-space; The geometry of the Gauss map;ons. The language of Intrinsic geometry of surfaces; Geodesics; Moving frames; of vector bundles, The Gauss-Bonnet Theorem; Assorted additional topics. MATH501401 <span class="penncourse-course-notes">Course Online: Synchronous Format</span>
MATH 501-401 Differential Geometry Alexandre A Kirillov TR 10:15 AM-11:45 AM The course moves from a study of extrinsic geometry (curves and surfaces in n-space) to the intrinsic geometry of manifolds. After a review of vector calculus and a section on tensor algebra, we study manifolds and their intrinsic geometry, including metrics, connections, geodesics, and the Riemann curvature tensor. Topics include Eulerian curvature and Euler's theorems, the Gauss map and first/second fundamental forms, the Theorema Egregium, minimal surfaces in n-space; other topics as time permits. MATH465401
MATH 503-001 Abstract Algebra Brett S Frankel MW 10:15 AM-11:45 AM Continuation of Math 502. Prerequisite: Students who have already received credit fo reither 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 503-101 Abstract Algebra T 07:00 PM-09:00 PM Continuation of Math 502. Prerequisite: Students who have already received credit fo reither 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 503-102 Abstract Algebra R 07:00 PM-09:00 PM Continuation of Math 502. Prerequisite: Students who have already received credit fo reither 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">Registration also required for Lecture (see below)</span>
MATH 509-001 Advanced Analysis Philip Gressman TR 10:15 AM-11:45 AM Continuation of Math 508. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods. <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span>
MATH 509-101 Advanced Analysis M 07:00 PM-09:00 PM Continuation of Math 508. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods. <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 509-102 Advanced Analysis W 07:00 PM-09:00 PM Continuation of Math 508. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods. <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 513-401 Comput Linear Algebra TR 10:15 AM-11:45 AM A number of important and interesting problems in a wide range of disciplines within computer science are solved by recourse to techniques from linear algebra. The goal of this course will be to introduce students to some of the most important and widely used algorithms in matrix computation and to illustrate how they are actually used in various settings. Motivating applications will include: the solution of systems of linear equations, applications matrix computations to modeling geometric transformations in graphics, applications of the Discrete Fourier Transform and related techniques in digital signal processing, the solution of linear least squares optimization problems and the analysis of systems of linear differential equations. The course will cover the theoretical underpinnings of these problems and the numerical algorithms that are used to perform important matrixcomputations such as Gaussian Elimination, LU Decomposition and Singular Value Decomposition. MATH313401 <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 514-401 Advanced Linear Algebra Florian Pop 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">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Laboratory (see below)</span>
MATH 514-402 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. AMCS514402, MATH314402 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 514-403 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. AMCS514403, MATH314403 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 514-404 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. AMCS514404, MATH314404 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 514-405 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. AMCS514405, MATH314405 <span class="penncourse-course-notes">Undergraduates Need Permission</span><br /><span class="penncourse-course-notes">Course Online: Synchronous Format</span><br /><span class="penncourse-course-notes">Registration also required for Lecture (see below)</span>
MATH 520-001 Selections From Algebra: Representation Theory of Finite Groups Mona B Merling MW 12:00 PM-01:30 PM Informal introduction to such subjects as homological algebra, number theory, and algebraic geometry. <span class="penncourse-course-notes">Undergraduates Need Permission</span> https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2022A&course=MATH520001
MATH 540-001 Select Class & Func Anal: Topics in Modern Harmonic Analysis Yumeng Ou MW 12:00 PM-01:30 PM Informal introduction to such subjects as compact operators and Fredholm theory, Banach algebras, harmonic analysis, differential equations, nonlinear functional analysis, and Riemann surfaces.
MATH 546-001 Adv Applied Probability Robin Pemantle MW 12:00 PM-01:30 PM The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). After a summary of the necessary results from measure theory, we will learn the probabilist's lexicon (random variables, independence, etc.). We will then study laws of large numbers, Central Limit Theorem, Poisson convergence and processes, conditional expectations, and martingales. Emphasis is on using these for probability modeling. Application areas include genetics, linguistics, machine learning, agent-based models, statistical physics, and hidden Markov models. <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 571-401 Intro Logic & Computabty Scott Weinstein TR 03:30 PM-05:00 PM Continuation of Math 570. Prerequisite: Permission of instructor if course prerequisites not met LGIC320401, PHIL413401 <span class="penncourse-course-notes">Course Online: Synchronous Format</span> https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2022A&course=MATH571401
MATH 581-001 Topics in Combinatorial: Algorithmic Combinatorics and Symbolic Computation James B. Haglund TR 12:00 PM-01:30 PM Variable topics connected to current research in combinatorial theory. Recent topics include algebraic combinatorics and symmetric functions, analytic combinatorics and discrete probability. <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 601-001 Geo Analysis & Topology Ningchuan Zhang TR 01:45 PM-03:15 PM Covering spaces and fundamental groups, van Kampen's theorem and classification of surfaces. Basics of homology and cohomology, singular and cellular; isomorphism with de Rham cohomology. Brouwer fixed point theorem, CW complexes, cup and cap products, Poincare duality, Kunneth and universal coefficient theorems, Alexander duality, Lefschetz fixed point theorem. <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 603-001 Algebra Renee H Bell MF 01:45 PM-03:15 PM Continuation of Math 602. <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 609-401 Analysis II Robert M. Strain TR 10:15 AM-11:45 AM Real analysis: general measure theory, outer measures and Cartheodory construction, Hausdorff measures, Radon-Nikodym theorem, Fubini's theorem, Hilbert space and L2-theory of the Fourier transform. Functional analysis: normed linear spaces, convexity, the Hahn-Banach theorem, duality for Banach spaces, weak convergence, bounded linear operators, Baire category theorem, uniform boundedness principle, open mapping theorem, closed graph theorem, compact operators, Fredholm theory, interpolation theorems, Lp-theory for the Fourier transform. AMCS609401 <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 619-001 Algebrc Topology, Part I Mona B Merling CANCELED Rational homotopy theory, cobordism, K-theory, Morse theory and the h-corbodism theorem. Surgery theory.
MATH 621-001 Algebraic Number Theory Ted C K Chinburg TR 03:30 PM-05:00 PM Continuation of Math 620. <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 623-001 Complex Algebraic Geom Ron Donagi TR 12:00 PM-01:30 PM Continuation of Math 622. <span class="penncourse-course-notes">Undergraduates Need Permission</span>
MATH 649-401 Stochastic Processes Xin Sun MW 12:00 PM-01:30 PM Markov chains, Markov processes, and their limit theory. Renewal theory. Martingales and optimal stopping. Stable laws and processes with independen increments. Brownian motion and the theory of weak convergence. Point processes. STAT931401 <span class="penncourse-course-notes">Undergraduates Need Permission</span> https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2022A&course=MATH649401
MATH 660-001 Differential Geometry Davi Maximo-Alexandrino-Nogueir CANCELED Riemannian metrics and connections, geodesics, completeness, Hopf-Rinow theorem, sectional curvature, Ricci curvature, scalar curvature, Jacobi fields, second fundamental form and Gauss equations, manifolds of constant curvature, first and second variation formulas, Bonnet-Myers theorem, comparison theorems, Morse index theorem, Hadamard theorem, Preissmann theorem, and further topics such as sphere theorems, critical points of distance functions, the soul theorem, Gromov-Hausdorff convergence.
MATH 702-001 Topics in Algebra Florian Pop MF 01:45 PM-03:15 PM Topics from the literature. The specific subjects will vary from year to year.
MATH 810-002 Reading Seminar: Metric Geometry Wolfgang Ziller
MATH 810-010 Reading Seminar: Rick Miranda's Algebraic Curves and Riemann Surfaces Ron Donagi
MATH 810-016 Reading Seminar: Spectral Geometry of Hyperbolic Manifolds Ted C K Chinburg
MATH 810-021 Reading Seminar: Rigid Geometry Florian Pop
MATH 810-024 Reading Seminar: Stacks Tony G Pantev
MATH 810-028 Reading Seminar Scott Weinstein https://pennintouchdaemon.apps.upenn.edu/pennInTouchProdDaemon/jsp/fast.do?webService=syllabus&term=2022A&course=MATH810028
MATH 810-063 Reading Seminar: Geometric Measure Theory Davi Maximo-Alexandrino-Nogueir
MATH 810-089 Reading Seminar: Chromatic Homotopy Theory Ningchuan Zhang