» Please see the Schedule of Classes for the current semester’s offerings.
MAT 1122 History of Mathematics 3 credits Pythagorean Theorem; Commensurability; Archimedean Axiom; scientific revolutions; Euclidean and non-Euclidean geometries; circumference of the Earth; methods of exhaustion; theory of conics; geometrical optics; Ptolemaic and other kinematic models; Oresme; dynamic models; rational mechanics.
MAT 1160 Precalculus4 creditsNumber systems, functions, equations, and inequalities; algebra of polynomials, exponentials, and logarithms; analytic geometry of lines and circles; vectors, trigonometry, and complex numbers.Lecture: 3 hours; Recitation: 2 hoursPrerequisites: two years of high school mathematics and placement by examination.
MAT 1412, 1413 or 1413H Calculus I, II4 creditsFirst semester: limits, continuity, derivatives; applications to graphing, maxima and minima, and related rates; mean value theorem; integration, fundamental theorem of the calculus, integration by substitution. Second semester: applications of integration in geometry and physics; methods of integration; improper integrals; indeterminate forms; numerical integration; sequences, power series and Taylor series, polar coordinates; parametric equations.Lecture: 3 hours; Recitation: 2 hoursPrerequisites: three years of high school mathematics and placement by examination or MAT 1160.
MAT 1422 or 1422H Great Proofs in Mathematics3 creditsLandmark theorems from ancient to modern times. Geometry: Pythagorean theorem, Euler's formula, platonic polyhedra. Number theory: irrational numbers, infinitude of primes, unique factorization, Pythagorean triples. Set theory: sets, relations, functions, infinite cardinal numbers, Schroeder-Bernstein theorem. Probability: expectation, conditioning, independence, the law of averages. Theory of computation: Turing machines, decidable and undecidable problems.Prerequisite: permission of the instructor.
MAT 1504 Discrete Structures4 creditsBoolean algebra and predicate calculus; proof methods; sets, functions and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. (See COM 1504.)Lecture: 3 hours; Lab: 2 hoursPrerequisite: three years of high school mathematics.
MAT 1510 Multivariable Calculus4 creditsVectors, vector functions and curves; functions of several variables, partial derivatives; multiple integrals, Jacobians; vector fields, line and surface integrals; theorems of Green, Gauss, and Stokes.Prerequisite: MAT 1413.
MAT 1520 or 1521 Advanced Calculus I, II3 creditsReal numbers, limits, intrinsic properties of continuous functions, differentiability and integrability, uniform convergence, implicit and inverse function theorems, point-set topology, metric spaces, curves and surfaces.Prerequisite: MAT 1510.
MAT 1540 or 1541 Functions of a Complex Variable I, II3 creditsAnalytic functions, Cauchy-Riemann equations, Cauchy integral formula, residue theory; conformal mappings, normal families, Riemann mapping theorem, Weierstrass theorem, applications.Prerequisite: MAT 1510.
2105 Linear Algebra3 creditsSystems of linear equations,
Gaussian elimination, matrices, matrix algebra; vector spaces, linear
transformations, similarity; inner product spaces; determinants; eigenvalues and
eigenvectors, diagonalization; quadratic forms; canonical forms; spectral
theory; applications.Prerequisite: MAT 1412.
MAT 2215 or 2216 Modern Algebra I, II3 creditsBasic concepts of modern abstract algebra: groups, rings, and fields, with illustrations and applications, particularly in elementary number theory and the theory of equations.Prerequisite (with permission, corequisite): MAT 2105.
MAT 2251 Theory of Numbers3 creditsDivisibility, prime factorization, distribution of primes, linear and quadratic congruences, primitive roots, quadratic residues, quadratic reciprocity, Diophantine equations.Prerequisite: MAT 1413.
MAT 2461 Probability Theory3 creditsProbability spaces; combinatorics; conditional probability; discrete and continuous random variables; examples; density and distribution functions; independence; expectation and variance; multivariate distributions; moment-generating functions; applications.Corequisite: MAT 1510.
MAT 2462 Mathematical Statistics3 creditsFunctions of random variables; Central Limit Theorem; chi-square distribution; t-distribution; F-distribution; point and interval estimation; maximum likelihood; hypothesis testing; analysis of variance.Prerequisite: MAT 2461.
MAT 2471 Queuing Theory3 creditsClassification of queues; systems without memory; systems with losses; queues as birth-and-death processes; embedded Markov chains; networks; diffusion and Monte Carlo approximations.Prerequisite: MAT 2462.
MAT 2481 Topics in Actuarial Mathematics3 creditsPrerequisites: MAT 2461, MAT 2462.
MAT 2601 Differential Equations3 creditsClassification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods.Prerequisite: MAT 1413.
MAT 2611 Partial Differential Equations3 creditsSolution of parabolic, hyperbolic, and elliptic equations; initial and boundary value problems arising in physical situations such as heat conduction, wave propagation and gravitational potential; method of characteristics, separation of variables, Laplace and Fourier transforms.Prerequisites: MAT 1510, MAT 2601.
MAT 2651 Numerical Analysis3 creditsComputer-assisted analysis of differential and integral equations; applications of polynomial interpolation and numerical linear algebra to differential equations; error estimation, rates of convergence, extrapolation, multistep and implicit methods, stability, stiffness, ill-posed problems, chaos, and difference methods. Special attention is given to the analysis of boundary value problems by finite-element methods.Prerequisites: MAT 1510, MAT 2105.
MAT 2701 Geometry3 creditsEmbedded hypersurfaces; metrics, connections, and curvature; hyperbolic and spherical geometries; projective geometries; algebraic curves; applications to physics.Prerequisite: MAT 1510.
MAT 2901 Mathematics of Finance3 creditsDiscrete models for options, pricing derivatives, continuous stock price models, Brownian motion, the Black-Scholes formula, the Black-Scholes differential equation, hedging options, dynamic programming, bond price models, yield curves, forwards and futures, Keynes interest rate parity formula.Prerequisite: familiarity with differential equations and probability.
MAT 3301, 3302, 3303 or 3304 Topics in Modern Mathematics3 creditsSelected subjects in analysis, algebra, geometry, topology, and applied mathematics. Students may register for up to four semesters with permission of the senior professor.Prerequisite: permission of the instructor.
MAT 4931 or 4932 Seminar1-3 creditsSeminar in current problems and literature of mathematics.Prerequisite: permission of the instructor.
MAT 4933 or 4934 Problem Seminar1-3 creditsTechniques for solving problems in mathematics. Recommended for mathematics majors.Prerequisite: permission of the instructor.
Courses numbered 5000 or higher are listed at:
All graduate courses are open to qualified undergraduates with permission of
the Department of Mathematical Sciences.
500 West 185th Street
New York, NY 10033
500 West 185th Street
New York, NY 10033
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