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Department of Mathematics at FAS, AUB
 
Graduate Courses

COURSES / PROGRAMS 

Mathematics

  • MATH 301/302 Graduate Tutorial Courses 1-3 cr.
    Prerequisite: graduate standing or consent of instructor.
  • MATH 303 Measure and Integration 3.0; 3 cr.
    A first course in measure theory, including general properties of measures, construction of Lebesgue measure in Rn, Lebesgue integration and convergence theorems, Lp-spaces, Hardy-Littlewood maximal function, Fubini's theorem, and convolutions.
    Prerequisite: MATH 223 or graduate standing. Annually.
  • MATH 304 Complex Analysis 3.0; 3 cr.
    A second course in complex analysis, covering the homotopy version of Cauchy's theorem, the open mapping theorem, maximum principle, Schwarz's lemma, harmonic functions, normal families, Riemann mapping theorem, Riemannian metrics, method of negative curvature, Picard's theorem, analytic continuation, monodromy, and modular function.
    Prerequisite: MATH 227 or graduate standing. Annually.
  • MATH 305 Functional Analysis 3.0; 3 cr.
    Vector spaces, Hamel basis, Hahn-Banach theorem, Banach spaces, continuous linear operators and functionals, Hilbert spaces, and weak topologies.
    Prerequisite: MATH 223 or graduate standing. Annually.
  • MATH 306 Calculus on Manifolds 3.0; 3 cr.
    Prerequisite: MATH 223. Offered Occasionally
  • MATH 307 Topics in Analysis 3.0; 3 cr.
  • MATH 314 Algebraic Topology I 3.0; 3 cr.
    Closed surfaces, categories and functors, homotopy, the fundamental group functor, and covering spaces.
    Prerequisites: MATH 214 and MATH 241 or graduate standing. Annually.
  • MATH 315 Algebraic Topology II 3.0; 3 cr.
    Singular homology with applications to Euclidean spaces and an introduction to cohomology theory.
    Prerequisite: MATH 314. Offered Occasionally
  • MATH 316 Topics in Topology 3.0; 3 cr.
  • MATH 341 Modules and Rings 3.0; 3 cr.
    Fundamental concepts of modules and rings, projective and injective modules, modules over a PID, Artinian and Noetherian modules and rings, modules with composition series, semi-simplicity, and tensor products.
    Prerequisite: MATH 241 or graduate standing. Annually.
  • MATH 342 Modules and Rings II 3.0; 3 cr.
    A course covering more advanced topics in modules and rings.
    Prerequisite: MATH 341. Annually.
  • MATH 343 Field Theory 3.0; 3 cr.
    Prerequisite: MATH 242.
  • MATH 344 Commutative Algebra 3.0; 3 cr.
    Prerequisites: MATH 242 and MATH 341.
  • MATH 345 Topics in Algebra 3.0; 3 cr.
  • MATH 350 Discrete Models for Differential Equations 3.1; 3 cr.
    A detailed study of methods and tools used in deriving discrete algebraic systems of equations for ordinary and partial differential equations: finite difference and finite element discretization procedures; generation and decomposition of sparse matrices, finite-precision arithmetic, ill-conditioning and pre-conditioning, scalar, vector, and parallelized versions of the algorithms. The course includes tutorial immersion sessions in which students become acquainted with state-of-the-art scientific software tools on standard computational platforms. Prerequisite: Linear Algebra and the equivalent of Math of MATH/CMPS 251 (which can be taken concurrently) or consent of instructor. Same as CMPS 350. Annually.
  • MATH 351 Optimization and Non-Linear Problems 3.1; 3 cr.
    A study of practical methods for formulating and solving numerical optimization problems that arise
    in science, engineering, and business applications. Newton’s method for nonlinear equations and
    unconstrained optimization. Simplex and interior-point methods for linear programming. Equality and
    inequality-constrained optimization. Sequential Quadratic Programming. Emphasis is on algorithmic
    description and analysis. The course includes an implementation component where students develop
    software and use state-of-the-art numerical libraries. Prerequisite: MATH/CMPS 350 or consent of
    instructor. Same as CMPS 351. Annually.
  • MATH 358 Introduction to Symbolic Computing 3.0; 3 cr.
    Introductory topics in computer algebra and algorithmic number theory that includes fast
    multiplication of polynomials and integers, fast Fourier transforms, primality testing and integers
    factorization. Applications to cryptography and pseudo-random number generation. Linear algebra
    and polynomial factorization over finite fields. Applications to error-correcting codes. Introduction
    to Grobner bases. Prerequisite: Good background in programming, linear algebra, discrete mathematics
    or consent of instructor. Same as CMPS 358. Annually.
  • MATH 360 Special Topics in Computational Science 3.0; 3 cr.
    A course on selected topics in computational science that changes according to the interests of visiting
    faculty, instructors, and students. Selected topics cover state-of-the-art tools and applications in
    computational science. Prerequisite: Consent of instructor. Same as CMPS 360. Annually.
  • MATH 395A/395B Comprehensive Exam 0 cr.
    Prerequisite: Consent of adviser
  • MATH 399 MA or MS Thesis 6 cr.

 

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