analysis

So I've started to study for real analysis, which at the moment I am planning to take in the fall.  This may be a stupid idea*, but I'm being stubborn about wanting to take it... well, just because I'm curious, and it sounds cool, and I've spent enough time around people for whom it is common knowledge to feel like I ought to know the stuff.  (The people in question were mathematicians and physicists, if that wasn't clear.)

I've been using the videos from Francis Su's online course, which at least for the two lectures I've watched is pretty comprehensible.  It's cool stuff.  Rudin (a classic analysis book), on the other hand, is incredibly dense, but Dr. Su's lectures have done a pretty good job of unpacking the proofs and have enabled me to follow the text.

I am stuck on page 2 (ha!), trying to write a proof without resorting back to the textbook.  I will look... but maybe tomorrow.

Despite coming to all this math very late, I'm glad I've had some exposure to trying to figure problems out because I think it helps me understand where the results came from, and what kind of work it took to produce them.  In my previous research, I remember that those rare, amazing moments of insight only came after marinading myself in the math and ideas for months and months.  And in one day - or maybe was it over three days? - everything flashed together, and I wrote and wrote and finally proved what had eluded me for so long.  I think that the magic happened less than a handful of times in the whole two years I worked on this project, at least in the sense where things actually panned out.

The point being, I suspect that many of the proofs in Rudin were the results of months and years of work, blind alleys, and seemingly endless futile attempts that ultimately did lead to the gorgeous, concise proofs presented  - or at least that they weren't for the most part written in the first five minutes in which the writer encountered the problem.  I don't know.  But at least it makes me feel less stupid.

* as I need to maintain a certain GPA to keep getting paid!