Course Descriptions

16:640:502 - Theory of Functions of a Real Variable II

Michael Kiessling

Course Description:

The course 502 is a continuation of Fall’s 501, but also offers outlook on applications in other fields of mathematics, and in mathematical physics and engineering. We will pick up where the course 501 ended, so 501 is a pre-requisite. The material is mostly from Folland’s book. We begin with some selected material from section 3 (Signed measures and differentiation), then hop to section 5 (Elements of functional analysis) and continue with sections 6 (L p spaces), 7 (Radon measures), 8 (Elements of Fourier analysis) and 9 (Elements of distribution theory). Since 502 is no longer a mandatory course (it used to be) there is also some flexibility as to the material, thus we may also look into some selected material of sections 10 (Probability theory) and 11 (Haar measure, Hausdorf measure) at the end of the course. I plan to occasionally supplement Folland’s book by “hand outs” of typed-up material. Given the pandemic situation, the course is currently planned to be taught in synchronous remote mode; a room in Hill Center has been booked for in-class instruction in case the situation improves significantly.


Textbook:

“Real Analysis” (2nd ed) by G.B. Folland

Prerequisites:

Mathematics 501 or equivalent

 

Schedule of Sections:

Previous Semesters:

Spring 2020 Prof. Sussmann
Spring 2016 Prof. Sussmann
Spring 2015 Prof. Nussbaum
Spring 2014 Prof. Chanillo
Spring 2013 Prof. Carlen
Spring 2012 Prof. Chanillo
Spring 2011 Prof. Nussbaum
Spring 2010 Prof. Han
Spring 2009 Prof. Carlen
Spring 2007 Prof. Goodman
Spring 2004 Prof. Goodman