first post here so sorry if this question is answered somewhere, but I couldn't find it.
I'll start with some background before the question: I've recently completed an undergraduate math degree, with all the standard courses including real analysis from Baby Rudin. Although I'm taking a few years off before graduate school to make some money, I found an inexpensive paperback version of Big Rudin and decided to self-study from it before grad school.
So, on to the main question:
If you've ever conducted self-study from Big Rudin, how did you structure your program, and did you feel as if that method was effective?
For example, did you simply choose to read the chapters and work through the exercises, choose to emulate the syllabus of some existing course, etc.? Also, how did you go about verifying your solutions to the exercises? (Perhaps a solution manual or ProofWiki?)
Any experiences, advice, tips, etc. would be greatly appreciated. Cheers!
( 5 months ago )
I worked my way through Big Rudin and thought it was a great experience; the book is exceptionally well-written.
Walter Rudin has a great gift in his ability to lay things out in logical order, step-by-step, somehow without making any of the consecutive ideas he introduces either too simple or too complicated based upon what has been covered. So I can't think of a better book to self-study.
I did it without a syllabus, just working my way through the material in the order he presented it; I attempted most of the exercises, and was able to solve many of them. I was working in isolation which was a disadvantage--it's generally better to have companions to share ideas with--but was able to find plenty of co-students to talk Big Rudin with when I returned to university. Of course, many of the solutions can be solved with the aid of the web.
My experience was that, when I was able to solve a problem, the answer became so clear that it was self-evident it was correct. I think Rudin lays out his problem sets very intelligently, so that solving one leads naturally to better luck with later problems.
My suggestion would be to read the text thorougly, do what exercises you can, and try to find a group of like-minded individuals with whom you may share ideas.