Fourier Analysis
A continuation of MIT's Analysis I (18.100), this course splits roughly in half between the theory of the Lebesgue integral, with applications to probability, and the study of Fourier series and Fourier integrals. Topics include measure and integration theory, convergence theorems, and the construction of the Lebesgue integral on one side, and orthogonality, convergence of Fourier series, and Fourier transforms on the other, including their use in solving differential equations and analyzing signals. Materials come from MIT OpenCourseWare and include lecture notes, problem sets, and exams covering both halves of the subject. The course assumes background in real analysis and is aimed at students who want a rigorous grounding in the mathematical tools underlying probability theory and harmonic analysis. No instructor interaction or certificate is offered, consistent with MIT's OpenCourseWare model.