This looks great based on my quick perusal. I'd be very surprised if the notes could teach these subjects to anyone who didn't have significant prior exposure. The notes seem better suited for reviewing and contextualizing material you already know rather well. My favorite book of this type is Shafarevich's Basic Notions of Algebra.
The stated prerequisites are also more advanced than the submission title implies. At my university we didn't have a dedicated course in complex analysis until our third semester, and that was in Denmark, where students will study nothing but mathematics from day one. In the American system where even mathematics majors have a mixed course of study for their first several years, it's not unusual for rigorous complex analysis to be a final year subject. Even Harvard's infamous Math 55b second-semester honors course only treats complex analysis very superficially.
I'd be very surprised if the notes could teach these subjects to anyone who didn't have significant prior exposure.
I'm self-taught, and these notes are probably the most useful resource I've yet come across.
It's hard not having anyone to work through physics problems with. Learning in-person is much higher bandwidth. But thus far OCW has done a fair job in supplementing this.
The problem is that there isn't a unifying thread across courses. Each course is isolated from every other course. That's a good way to build a toolkit, but it makes it rather difficult to understand how and why certain knowledge will be useful later on, and how to apply that knowledge.
So these notes are the unifying thread I've wanted.
But it's true that notes aren't a substitute for courses. Perhaps books are, though. These have served me well so far: http://dl.dropbox.com/u/315/books/list.html and recommendations would be great.
I don't think it's implied that complex analysis is required for reading these notes. The author writes that he expects students will take a course on complex analysis "at some point" but as far as I can tell he doesn't do anything requiring complex analysis in these notes (e.g. every search for "complex" turns up something unrelated to complex analysis, and the word "contour" (as in contour integral) doesn't appear in the notes at all).
I'll take your word for it. In that case, the notes can't very well be said to take you to the graduate level. There's no point in skating over arguably the most beautiful and interconnected area of mathematics (by which I mean complex analysis) in an effort to get to some nominal level of mathematical advancedness.
The stated prerequisites are also more advanced than the submission title implies. At my university we didn't have a dedicated course in complex analysis until our third semester, and that was in Denmark, where students will study nothing but mathematics from day one. In the American system where even mathematics majors have a mixed course of study for their first several years, it's not unusual for rigorous complex analysis to be a final year subject. Even Harvard's infamous Math 55b second-semester honors course only treats complex analysis very superficially.