Real Analysis III: MATH4001
Academic Year 2015-2016
Instructor: Dr. Youness Lamzouri.
Office: N515 Ross Building.
Time and location : Monday, Wednesday and Friday 1:30-2:30 pm in VH 1020 (Vari Hall).
Office hours: Wednesdays and Fridays 11:30 am-12:30 pm,
or by appointment.
Textbook: "Real Analysis"
by N. L. Carothers. Cambridge University Press.
Course Description :
This course aims to broaden and deepen the student's knowledge in real analysis. It provides an essential basis for further study in several mathematical areas including functional analysis, probability theory and harmonic analysis. The first part of the course covers the topology of metric spaces and normed vector spaces with the objective of generalizing several notions including continuity and limits to a more abstract setting. The second part serves as a transition from the discussion of abstract spaces to concrete spaces of functions including a study of the Riemann-Stieltjes integral and Fourier analysis. The third and last part of the course concerns Lebesgue measure and integration on the real line.