Courses
MATH 211
Descriptive statistics; Probability; Random variables; Special distributions; Estimation; Hypothesis testing; Normal distribution; Two-Sample Inference; Regression.
MATH 303
Review of vector calculus; Fourier series and Fourier transform; Calculus of functions of a complex variable.
MATH 312
Decision theory; estimation; confidence intervals; hypotheses testing; large-sample theory; efficiency of alternative statistical procedures.
MATH 351
Detailed examination of current topics in Mathematics.
MATH 401
Complex numbers and functions; exponential and trigonometric functions; infinite series and products; limits, continuity and derivatives of complex functions; Cauchys theorem; Taylor and Laurent series; conformal mapping.
MATH 302
Normed and Banach spaces; linear operators; duality; inner product and Hilbert spaces; Riesz representation theorem; Hahn-Banach theorem; uniform boundedness principle; open mapping theorem; strong, weak and weak* convergence.
MATH 309
Classification of second order partial equations; well posed problems; method of separation of variables and applications; wave equation: D?Alambert?s solution; Laplace equation: Poisson?s formula, maximum principle, boundary value and eigenvalue problems; heat equation: Cauchy problem, maximum principle.
MATH 350
Detailed examination of current topics in Mathematics.
MATH 395
Investigation of one or more topics of interest with the guidance of an instructor. Presentation of a research proposal at the end of the term.
MATH 403
Basic principles of normed spaces. Normed and Banach spaces; Hilbert spaces; linear operators; dual spaces. Basic principles of functional analysis: Hahn-Banach theorem; open mapping theorem; uniform boundedness theorem, Krein-Milman theorem. Applications.
MATH 301
Metric spaces and their topology; continuity, compactness and connectedness in a metric space; completion of a metric space; differentiation and Riemann integration; sequences and series of functions; uniform convergence; Ascoli-Arzela theorem; Stone-Weierstrass theorem; Banach fixed-point theorem and its applications.
MATH 305
Fixed point iteration and Newton’s method for nonlinear equations, direct solution of linear systems and the least squares problem, symmetric positive definite and banded matrices, systems of nonlinear equations, the QR algorithm for the symmetric eigenvalue problem, Lagrange and Hermite polynomial interpolation, polynomial approximation in the infinity norm and the Chebyshev polynomials, approximation in the 2 norm and the orthogonal polynomials, numerical differentiation, Newton-Cotes and Gaussian quadratures for numerical integration.
MATH 320
Finite-dimensional real and complex vector spaces, bases of a vector space, linear maps, dual spaces, quadratic forms, self-adjoint and unitary transformations, eigenvalue problem, canonical form of a linear transformation, tensors, and applications.
MATH 390
Investigation of one or more topics of interest with the guidance of an instructor. Presentation of a research proposal at the end of the term.
MATH 402
Topological spaces, subspaces, continuous functions, base for a topology, separation axioms, compactness, locally compact spaces, connectedness, path connectedness, finite product spaces, set theory and Zorn?s lemma, infinite product spaces, quotient spaces, homotopic paths, the fundamental group,induced homomorphisms, covering spaces, applications of the index, homotopic maps, maps into the punctured plane, vector fields, the Jordan curve theorem.