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 » 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 Precalculus
4 credits

Number 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 hours
Prerequisites: two years of high school mathematics and placement by examination.

MAT 1412, 1413 or 1413H Calculus I, II
4 credits

First 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 hours
Prerequisites: three years of high school mathematics and placement by examination or MAT 1160.

MAT 1504 Discrete Structures
4 credits

Boolean 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 hours
Prerequisite: three years of high school mathematics.

MAT 1510 Multivariable Calculus
4 credits

Vectors, 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, II
3 credits

Real 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, II
3 credits

Analytic functions, Cauchy-Riemann equations, Cauchy integral formula, residue theory; conformal mappings, normal families, Riemann mapping theorem, Weierstrass theorem, applications.
Prerequisite: MAT 1510.

MAT 2105 Linear Algebra
3 credits

Systems 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, II
3 credits

Basic 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 Numbers
3 credits

Divisibility, prime factorization, distribution of primes, linear and quadratic congruences, primitive roots, quadratic residues, quadratic reciprocity, Diophantine equations.
Prerequisite: MAT 1413.

MAT 2461 Probability Theory
3 credits

Probability 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 Statistics
3 credits

Functions 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 Theory
3 credits

Classification 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 Mathematics
3 credits

Prerequisites: MAT 2461, MAT 2462.

MAT 2601 Differential Equations
3 credits

Classification 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 Equations
3 credits

Solution 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 Analysis
3 credits

Computer-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 Geometry
3 credits

Embedded hypersurfaces; metrics, connections, and curvature; hyperbolic and spherical geometries; projective geometries; algebraic curves; applications to physics.
Prerequisite: MAT 1510.

MAT 2901 Mathematics of Finance
3 credits

Discrete 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 Mathematics
3 credits

Selected 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 Seminar
1-3 credits

Seminar in current problems and literature of mathematics.
Prerequisite: permission of the instructor.

MAT 4933 or 4934 Problem Seminar
1-3 credits

Techniques for solving problems in mathematics. Recommended for mathematics majors.
Prerequisite: permission of the instructor. 

Graduate Courses

Courses numbered 5000 or higher are listed at:http://www.yu.edu/academics/graduate-arts-sciences/mathematical-courses/
All first-year graduate courses are open to qualified undergraduates with permission of the Department of Mathematical Sciences.