MATH 417 - Real Analysis

3 units (fi 6)(EITHER, 3-0-0)

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisite: MATH 317 or 414.

MATH 514 - Measure Theory I

3 units (fi 6)(EITHER, 3-0-0)

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisites: Math 317.

MATH 542 - Fourier Analysis

3 units (fi 6)(EITHER, 3-0-0)

Review, theory and extension of Fourier series for square integrable functions; orthonormal systems, Bessel's inequality, completeness, Parseval's identity, Riesz-Fischer Theorem. Extension to Fourier series for functions in other Lebesgue classes; Fejer means, conjugate series, Dirichlet, Fejer and Poisson kernels. Norm convergence; remarks on pointwise convergence. Fourier transforms and series in several dimensions; inverse transform, Plancherel formula, Poisson Formula, maximal functions, Riesz-Thorin Theorem and applications. Elementary distribution theory; D, D', S, S' and some elementary results, Fourier transforms of tempered distributions. Examination of some earlier results with tempered distributions instead of functions and getting familiar with basic concepts. Prerequisite: MATH 418.

MATH 600 - Reading in Mathematics

3 units (fi 6)(EITHER, 3-0-0)

Students registered in this course are supervised by individual staff members in areas of interest of the staff members. Students will be allowed to take this course only in exceptional circumstances and with the permission of the Chairman of the Department. This course shall not be counted against the minimum course requirement for graduate students.