Real Analysis and Fourier theory
It’s interesting that “questions of Fourier series convergence are largely responsible for seeding the subject of real analysis” according to one source, and Fourier theory “with all its generalizations and ramifications, may well be said to occupy a central role in the whole of analysis” according to Rudin himself, yet we spent only three days talking about Fourier series in class, and Rudin’s book only has 8 pages on them. I guess that’s what comes of relegating Lebesgue integration to the last chapter.
Possibly relevant posts:
- Real Analysis (11/1/2006)
- Upcoming analysis test (3/27/2005)
- Auditing a Fourier course (6/9/2005)
Real analysis was probably born with the space L_2. L_2 is very rich in that respect. For instance, two functions in L_2 are identical if they differ in their definition by a set of Lebesque measure zero.
Of course, since I like to be a contarian, I’ll think real analysis began with Newton. Or going back even futhur, it began with whoever “discovered” the irrationals.
Comment by Z — 3/4/2005 @ 2:08 pm
I guess it depends on whose definition you’re going by, but I think it makes sense to place real analysis as coming strictly after the two calculi. Although the two are similar, there is a definite emphasis on precision in real analysis that was lacking in the original formulation of the calculi.
Comment by Alex — 3/5/2005 @ 7:00 pm