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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 5100-401 Complex Analysis MW 10:15 AM-11:44 AM Complex numbers, DeMoivre's theorem, complex valued functions of a complex variable, the derivative, analytic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, residues, computation of definite integrals by residues, and elementary conformal mapping. MATH4100401
AMCS 5141-001 Advanced Linear Algebra Angela Gibney MW 12:00 PM-1:29 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. MATH3140001, MATH5140001
AMCS 5141-102 Advanced Linear Algebra T 7:00 PM-8:59 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra.
AMCS 5461-001 Advanced Applied Probability Robin Pemantle MW 1:45 PM-3:14 PM The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). MATH5460001
AMCS 6025-001 Numerical and Applied Analysis I Joshua A Mcginnis
James Perry Wolfe
We turn to linear algebra and the structural properties of linear systems of equations relevant to their numerical solution. In this context we introduce eigenvalues and the spectral theory of matrices. Methods appropriate to the numerical solution of very large systems are discussed. We discuss modern techniques using randomized algorithms for fast matrix-vector multiplication, and fast direct solvers. Topics covered include the classical Fast Multipole Method, the interpolative decomposition, structured matrix algebra, randomized methods for low-rank approximation, and fast direct solvers for sparse matrices. These techniques are of central importance in applications of linear algebra to the numerical solution of PDE, and in Machine Learning. The theoretical content of this course is illustrated and supplemented throughout the year with substantial computational examples and assignments.
AMCS 6081-401 Analysis Philip Gressman TR 10:15 AM-11:44 AM Complex analysis: analyticity, Cauchy theory, meromorphic functions, isolated singularities, analytic continuation, Runge's theorem, d-bar equation, Mittlag-Leffler theorem, harmonic and sub-harmonic functions, Riemann mapping theorem, Fourier transform from the analytic perspective. Introduction to real analysis: Weierstrass approximation, Lebesgue measure in Euclidean spaces, Borel measures and convergence theorems, C0 and the Riesz-Markov theorem, Lp-spaces, Fubini Theorem. MATH6080401
AMCS 6481-401 Probability Theory Jiaoyang Huang MW 1:45 PM-3:14 PM Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. MATH6480401, STAT9300401
MATH 0240-101 Calculus III Lab Dennis M Deturck F 8:30 AM-9:59 AM Lab for Math 2400
MATH 0240-102 Calculus III Lab Dennis M Deturck F 10:15 AM-11:44 AM Lab for Math 2400
MATH 0240-103 Calculus III Lab Dennis M Deturck F 12:00 PM-1:29 PM Lab for Math 2400
MATH 0240-104 Calculus III Lab Dennis M Deturck F 1:45 PM-3:14 PM Lab for Math 2400
MATH 1070-001 Mathematics of change, Part I MW 1:45 PM-3:14 PM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202430&c=MATH1070001
MATH 1070-002 Mathematics of change, Part I Andrew Cooper TR 8:30 AM-9:59 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-003 Mathematics of change, Part I Andrew Cooper TR 12:00 PM-1:29 PM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-201 Mathematics of change, Part I TR 8:30 AM-9:59 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-202 Mathematics of change, Part I TR 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-211 Mathematics of change, Part I MW 8:30 AM-10:00 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-212 Mathematics of change, Part I MW 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-221 Mathematics of change, Part I MW 8:30 AM-9:59 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1070-222 Mathematics of change, Part I MW 10:15 AM-11:44 AM Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1080-001 Mathematics of change, Part II Robin Pemantle MW 10:15 AM-11:44 AM Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1080-201 Mathematics of change, Part II TR 8:30 AM-9:59 AM Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1080-202 Mathematics of change, Part II TR 10:15 AM-11:44 AM Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences. General Requirement in Formal Reasoning & Analysis
MATH 1300-001 Introduction to Calculus TR 8:30 AM-9:59 AM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-002 Introduction to Calculus Philip Gressman TR 1:45 PM-3:14 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-003 Introduction to Calculus John D Green TR 12:00 PM-1:29 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-201 Introduction to Calculus F 8:30 AM-9:59 AM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-202 Introduction to Calculus F 12:00 PM-1:29 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-203 Introduction to Calculus F 1:45 PM-3:14 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-204 Introduction to Calculus F 3:30 PM-4:59 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-211 Introduction to Calculus F 8:30 AM-9:59 AM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-212 Introduction to Calculus F 12:00 PM-1:29 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-213 Introduction to Calculus F 1:45 PM-3:14 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-214 Introduction to Calculus F 3:30 PM-4:59 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-215 Introduction to Calculus F 8:30 AM-9:59 AM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-216 Introduction to Calculus F 12:00 PM-1:29 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-217 Introduction to Calculus F 1:45 PM-3:14 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-218 Introduction to Calculus F 3:30 PM-4:59 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1300-601 Introduction to Calculus Sukalpa Basu MW 7:00 PM-8:29 PM Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-001 Calculus, Part I MW 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-003 Calculus, Part I MW 12:00 PM-1:29 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-004 Calculus, Part I Patrick Shields MW 1:45 PM-3:14 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-005 Calculus, Part I Marco Zaninelli MW 3:30 PM-4:59 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-201 Calculus, Part I F 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-202 Calculus, Part I F 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-203 Calculus, Part I F 1:45 PM-3:14 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-204 Calculus, Part I F 3:30 PM-4:59 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-205 Calculus, Part I F 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-206 Calculus, Part I F 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-207 Calculus, Part I F 1:45 PM-3:14 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-208 Calculus, Part I F 3:30 PM-4:59 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-209 Calculus, Part I F 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-210 Calculus, Part I F 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-211 Calculus, Part I F 1:45 PM-3:14 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-212 Calculus, Part I F 3:30 PM-4:59 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-213 Calculus, Part I F 8:30 AM-9:59 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-214 Calculus, Part I F 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-215 Calculus, Part I F 1:45 PM-3:14 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-216 Calculus, Part I F 3:30 PM-4:59 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-217 Calculus, Part I F 10:15 AM-11:44 AM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1400-601 Calculus, Part I Nakia Rimmer MW 7:00 PM-8:59 PM Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-001 Calculus, Part II Robert W. Ghrist TR 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-002 Calculus, Part II Nakia Rimmer TR 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-003 Calculus, Part II Nakia Rimmer TR 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-004 Calculus, Part II TR 1:45 PM-3:14 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-005 Calculus, Part II Jingwen Chen TR 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-201 Calculus, Part II F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-202 Calculus, Part II F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-203 Calculus, Part II F 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-204 Calculus, Part II F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-205 Calculus, Part II F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-206 Calculus, Part II F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-207 Calculus, Part II F 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-208 Calculus, Part II F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-209 Calculus, Part II F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-210 Calculus, Part II F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-211 Calculus, Part II F 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-212 Calculus, Part II F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-213 Calculus, Part II F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-214 Calculus, Part II F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-215 Calculus, Part II F 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-216 Calculus, Part II F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-217 Calculus, Part II F 8:30 AM-9:59 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-218 Calculus, Part II F 10:15 AM-11:44 AM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-219 Calculus, Part II F 12:00 PM-1:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-220 Calculus, Part II F 3:30 PM-4:59 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1410-601 Calculus, Part II TR 7:00 PM-8:29 PM Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. General Requirement in Formal Reasoning & Analysis
MATH 1610-001 Honors Calculus Herman Gluck TR 12:00 PM-1:29 PM Students who are interested in math or science might also want to consider a more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1610 and 2400, but more in depth and involve discussion of the underlying theory as well as computations. General Requirement in Formal Reasoning & Analysis
MATH 1610-201 Honors Calculus M 7:00 PM-8:59 PM Students who are interested in math or science might also want to consider a more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1610 and 2400, but more in depth and involve discussion of the underlying theory as well as computations. General Requirement in Formal Reasoning & Analysis
MATH 1610-202 Honors Calculus W 7:00 PM-8:59 PM Students who are interested in math or science might also want to consider a more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1610 and 2400, but more in depth and involve discussion of the underlying theory as well as computations. General Requirement in Formal Reasoning & Analysis
MATH 1700-001 Ideas in Mathematics Mona B Merling MW 1:45 PM-3:14 PM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-201 Ideas in Mathematics T 8:30 AM-9:29 AM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-202 Ideas in Mathematics T 10:15 AM-11:44 AM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-203 Ideas in Mathematics R 8:30 AM-9:29 AM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 1700-601 Ideas in Mathematics Matthew P Wiener MW 7:00 PM-8:29 PM Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. General Requirement in Formal Reasoning & Analysis
MATH 2400-001 Calculus, Part III Dennis M Deturck MW 8:30 AM-9:59 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-002 Calculus, Part III Mira A Peterka TR 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-201 Calculus, Part III MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-202 Calculus, Part III MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-203 Calculus, Part III MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-204 Calculus, Part III MW 10:15 AM-11:44 AM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-211 Calculus, Part III TR 12:00 PM-1:29 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-212 Calculus, Part III TR 12:00 PM-1:29 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2400-213 Calculus, Part III TR 12:00 PM-1:29 PM Linear algebra: vectors, matrices, systems of linear equations, vector spaces, subspaces, spans, bases, and dimension, eigenvalues, and eigenvectors, maxtrix exponentials. Ordinary differential equations: higher-order homogeneous and inhomogeneous ODEs and linear systems of ODEs, phase plane analysis, non-linear systems.
MATH 2410-001 Calculus, Part IV Michael A. Carchidi TR 1:45 PM-3:14 PM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-201 Calculus, Part IV M 8:30 AM-9:29 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-202 Calculus, Part IV M 10:15 AM-11:14 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-203 Calculus, Part IV W 8:30 AM-9:29 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 2410-204 Calculus, Part IV W 10:15 AM-11:14 AM Partial differential equations and their solutions, including solutions of the wave, heat and Laplace equations, and Sturm-Liouville problems. Introduction to Fourier series and Fourier transforms. Computation of solutions, modeling using PDE's, geometric intuition, and qualitative understanding of the evolution of systems according to the type of partial differential operator.
MATH 3120-001 Linear Algebra Davi Maximo-Alexandrino-Nogueir TR 10:15 AM-11:44 AM Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 3120 cannot be taken to satisfy the major requirements.
MATH 3120-002 Linear Algebra Marco Zaninelli MW 1:45 PM-3:14 PM Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 3120 cannot be taken to satisfy the major requirements.
MATH 3140-001 Advanced Linear Algebra Angela Gibney MW 12:00 PM-1:29 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products: Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. AMCS5141001, MATH5140001
MATH 3140-102 Advanced Linear Algebra T 7:00 PM-8:59 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products: Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra.
MATH 3140-103 Advanced Linear Algebra R 7:00 PM-8:59 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products: Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra.
MATH 3200-001 Computer Methods in Mathematical Science I TR 12:00 PM-1:29 PM Students will use symbolic manipulation software and write programs to solve problems in numerical quadrature, equation-solving, linear algebra and differential equations. Theoretical and computational aspects of the methods will be discussed along with error analysis and a critical comparison of methods.
MATH 3400-401 Discrete Mathematics I Andre Scedrov TR 10:15 AM-11:44 AM Topics will be drawn from some subjects in combinatorial analysis with applications to many other branches of math and science: graphs and networks, generating functions, permutations, posets, asymptotics. LGIC2100401
MATH 3600-001 Advanced Calculus James B. Haglund MW 12:00 PM-1:29 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-002 Advanced Calculus Andrew Cooper TR 1:45 PM-3:14 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-101 Advanced Calculus T 7:00 PM-8:59 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-102 Advanced Calculus R 7:00 PM-8:59 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-103 Advanced Calculus M 7:00 PM-8:59 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3600-104 Advanced Calculus W 7:00 PM-8:59 PM Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
MATH 3610-001 Advanced Calculus Mira A Peterka TR 12:00 PM-1:29 PM Continuation of MATH 3600.
MATH 3610-101 Advanced Calculus M 7:00 PM-8:59 PM Continuation of MATH 3600.
MATH 3610-102 Advanced Calculus W 7:00 PM-8:59 PM Continuation of MATH 3600.
MATH 3700-001 Algebra Julia Hartmann MF 10:15 AM-11:44 AM Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course.
MATH 3700-101 Algebra T 7:00 PM-8:59 PM Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course.
MATH 3700-102 Algebra R 7:00 PM-8:59 PM Syllabus for MATH 370-371: an introduction to the basic concepts of modern algebra. Linear algebra, eigenvalues and eigenvectors of matrices, groups, rings and fields. MATH 502-503 is a masters level version of this course.
MATH 3710-001 Algebra Jianqi Liu MW 10:15 AM-11:44 AM Continuation of MATH 3700.
MATH 3710-101 Algebra T 7:00 PM-8:59 PM Continuation of MATH 3700.
MATH 3710-102 Algebra R 7:00 PM-8:59 PM Continuation of MATH 3700.
MATH 4100-401 Complex Analysis MW 10:15 AM-11:44 AM Complex numbers, DeMoivre's theorem, complex valued functions of a complex variable, the derivative, analytic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, residues, computation of definite integrals by residues, and elementary conformal mapping. AMCS5100401
MATH 5000-401 Topology Ryan C Hynd TR 12:00 PM-1:29 PM Point set topology: metric spaces and topological spaces, compactness, connectedness, continuity, extension theorems, separation axioms, quotient spaces, topologies on function spaces, Tychonoff theorem. Fundamental groups and covering spaces, and related topics.
MATH 5020-001 Abstract Algebra Ted C K Chinburg TR 1:45 PM-3:14 PM An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 3700.
MATH 5020-101 Abstract Algebra M 7:00 PM-8:59 PM An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 3700.
MATH 5020-102 Abstract Algebra W 7:00 PM-8:59 PM An introduction to groups, rings, fields and other abstract algebraic systems, elementary Galois Theory, and linear algebra -- a more theoretical course than Math 3700.
MATH 5080-001 Advanced Analysis Yumeng Ou TR 12:00 PM-1:29 PM Construction of real numbers, the topology of the real line and the foundations of single variable calculus. Notions of convergence for sequences of functions. Basic approximation theorems for continuous functions and rigorous treatment of elementary transcendental functions. The course is intended to teach students how to read and construct rigorous formal proofs. A more theoretical course than Math 3600.
MATH 5080-101 Advanced Analysis M 7:00 PM-8:59 PM Construction of real numbers, the topology of the real line and the foundations of single variable calculus. Notions of convergence for sequences of functions. Basic approximation theorems for continuous functions and rigorous treatment of elementary transcendental functions. The course is intended to teach students how to read and construct rigorous formal proofs. A more theoretical course than Math 3600.
MATH 5080-102 Advanced Analysis W 7:00 PM-8:59 PM Construction of real numbers, the topology of the real line and the foundations of single variable calculus. Notions of convergence for sequences of functions. Basic approximation theorems for continuous functions and rigorous treatment of elementary transcendental functions. The course is intended to teach students how to read and construct rigorous formal proofs. A more theoretical course than Math 3600.
MATH 5140-001 Advanced Linear Algebra Angela Gibney MW 12:00 PM-1:29 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra. AMCS5141001, MATH3140001
MATH 5140-102 Advanced Linear Algebra T 7:00 PM-8:59 PM Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products; Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra.
MATH 5200-001 Selections from Algebra Julia Hartmann MF 1:45 PM-3:14 PM Informal introduction to such subjects as homological algebra, number theory, and algebraic geometry.
MATH 5300-001 Mathematics of Finance Ryan C Hynd TR 10:15 AM-11:44 AM This course presents the basic mathematical tools to model financial markets and to make calculations about financial products, especially financial derivatives. Mathematical topics covered: stochastic processes, partial differential equations and their relationship. No background in finance is assumed.
MATH 5460-001 Advanced Applied Probability Robin Pemantle MW 1:45 PM-3:14 PM The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). AMCS5461001
MATH 5700-401 Logic and Computability 1 Henry Piers Towsner TR 3:30 PM-4:59 PM The course focuses on topics drawn from the central areas of mathematical logic: model theory, proof theory, set theory, and computability theory. LGIC3100401, PHIL4721401, PHIL6721401 https://coursesintouch.apps.upenn.edu/cpr/jsp/fast.do?webService=syll&t=202430&c=MATH5700401
MATH 5800-001 Combinatorial Analysis James B. Haglund MW 10:15 AM-11:44 AM Standard tools of enumerative combinatorics including partitions and compositions of integers, set partitions, generating functions, permutations with restricted positions, inclusion-exclusion, partially ordered sets. Permission of the instructor required to enroll.
MATH 5861-401 Mathematical Modeling in Biology MW 1:45 PM-3:14 PM This course will cover various mathematical models and tools that are used to study modern biological problems. Mathematical models may be drawn from cell biology, physiology, population genetics, or ecology. Tools in dynamical systems or stochastic processes will be introduced as necessary. No prior knowledge of biology is needed to take this course, but some familiarity with differential equations and probability will be assumed. BIOL5860401
MATH 5940-401 Mathematical Methods of Physics Martin Claassen TR 10:15 AM-11:44 AM A discussion of those concepts and techniques of classical analysis employed inphysical theories. Topics include complex analysis. Fourier series and transforms, ordinary and partial equations, Hilbert spaces, among others. PHYS5500401
MATH 6000-001 Topology and Geometric Analysis Herman Gluck TR 1:45 PM-3:14 PM Differentiable functions, inverse and implicit function theorems. Theory of manifolds: differentiable manifolds, charts, tangent bundles, transversality, Sard's theorem, vector and tensor fields and differential forms: Frobenius' theorem, integration on manifolds, Stokes' theorem in n dimensions, de Rham cohomology. Introduction to Lie groups and Lie group actions.
MATH 6020-001 Algebra Danny Krashen MW 10:15 AM-11:44 AM Group theory: permutation groups, symmetry groups, linear algebraic groups, Jordan-Holder and Sylow theorems, finite abelian groups, solvable and nilpotent groups, p-groups, group extensions. Ring theory: Prime and maximal ideals, localization, Hilbert basis theorem, integral extensions, Dedekind domains, primary decomposition, rings associated to affine varieties, semisimple rings, Wedderburn's theorem, elementary representation theory. Linear algebra: Diagonalization and canonical form of matrices, elementary representation theory, bilinear forms, quotient spaces, dual spaces, tensor products, exact sequences, exterior and symmetric algebras. Module theory: Tensor products, flat and projective modules, introduction to homological algebra, Nakayama's Lemma. Field theory: separable and normal extensions, cyclic extensions, fundamental theorem of Galois theory, solvability of equations.
MATH 6080-401 Analysis Philip Gressman TR 10:15 AM-11:44 AM Complex analysis: analyticity, Cauchy theory, meromorphic functions, isolated singularities, analytic continuation, Runge's theorem, d-bar equation, Mittlag-Leffler theorem, harmonic and sub-harmonic functions, Riemann mapping theorem, Fourier transform from the analytic perspective. Introduction to real analysis: Weierstrass approximation, Lebesgue measure in Euclidean spaces, Borel measures and convergence theorems, C0 and the Riesz-Markov theorem, Lp-spaces, Fubini Theorem. AMCS6081401
MATH 6180-001 Algebraic Topology, Part I Jonathan Block TR 10:15 AM-11:44 AM Homotopy groups, Hurewicz theorem, Whitehead theorem, spectral sequences. Classification of vector bundles and fiber bundles. Characteristic classes and obstruction theory.
MATH 6240-001 Algebraic Geometry Florian Pop MW 12:00 PM-1:29 PM Algebraic geometry over algebraically closed fields, using ideas from commutative algebra. Topics include: Affine and projective algebraic varieties, morphisms and rational maps, singularities and blowing up, rings of functions, algebraic curves, Riemann Roch theorem, elliptic curves, Jacobian varieties, sheaves, schemes, divisors, line bundles, cohomology of varieties, classification of surfaces.
MATH 6260-001 Commutative Algebra MW 8:30 AM-9:59 AM Topics in commutative algebra taken from the literature. Material will vary from year to year depending upon the instructor's interests.
MATH 6340-001 Arithmetic Geometry Florian Pop MW 1:45 PM-3:14 PM Arithmetic Geometry
MATH 6480-401 Probability Theory Jiaoyang Huang MW 1:45 PM-3:14 PM Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times. AMCS6481401, STAT9300401
MATH 6600-001 Differential Geometry Davi Maximo-Alexandrino-Nogueir TR 12:00 PM-1:29 PM Riemannian metrics and connections, geodesics, completeness, Hopf-Rinow theorem, sectional curvature, Ricci curvature, scalar curvature, Jacobi fields, second fundamental form and Gauss equations, manifolds of constant curvature, first and second variation formulas, Bonnet-Myers theorem, comparison theorems, Morse index theorem, Hadamard theorem, Preissmann theorem, and further topics such as sphere theorems, critical points of distance functions, the soul theorem, Gromov-Hausdorff convergence.
MATH 6710-301 Topics in Logic Andre Scedrov TR 1:45 PM-3:14 PM Discusses advanced topics in logic.
MATH 6770-401 Topics in Logic Scott Weinstein TR 10:15 AM-11:44 AM This graduate course focuses on topics drawn from the central areas of mathematical logic: model theory, proof theory, set theory, and computability theory. LGIC4960401, PHIL4720401, PHIL6720401
MATH 6940-001 Mathematical Foundations of Theoretical Physics Ron Donagi MF 1:45 PM-3:14 PM Selected topics in mathematical physics, such as mathematical methods of classical mechanics, electrodynamics, relativity, quantum mechanics and quantum field theory.
MATH 7020-001 Topics in Algebra Ching-Li Chai MW 1:45 PM-3:14 PM Topics from the literature. The specific subjects will vary from year to year.
MATH 8100-010 Reading Seminar Ron Donagi Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member
MATH 8100-017 Reading Seminar Jonathan Block Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member
MATH 8100-021 Reading Seminar Florian Pop Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member
MATH 8100-024 Reading Seminar Tony G Pantev Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member
MATH 8100-039 Reading Seminar Henry Piers Towsner Reading of mathematical literature under the direction of a faculty member in a group of students. Hours and syllabus to be arranged with the supervising faculty member