I am currently self-studying Apostol's Calculus, and I am able to grasp what he's teaching. I've also read a proof based books and feel comfortable with proofs. Will baby Rudin be too hard to self-study from? People say he is terse. People also say Apostol is dry, but I don't think it is so bad.
Rudin is a little long-winded but it probably wouldn't be too bad. You might try another (undergraduate) real analysis book first. How far are you into Apostol? I assure you, the end sections are very different from the earlier ones but your success in both hinges almost entirely on how thoroughly you understand the arguments and logic presented in all the sections you've read before it, so be careful.
I'm at polynomial approximations in Apostol volume 1. The estimates for polynomial errors are a little cryptic--I cannot do most of the problems in that section--so I'm supplementing with an international edition of Courant. Also I'm right now looking on the web for information on little o notation, because I'm not seeing how the o's add together. Will a book like Shilov's be a good intro to make way for Rudin? I have both Shilov's Linear Algebra and Elementary Real and Complex Analysis. I want to do Rudin because I want to be well-prepared for graduate level math, and I have to self-study because I cannot get a math or physics bachelor's degree. Also I read that Rudin goes into multivariable analysis, something that sounds interesting. I could probably order an international edition quite cheap, so money's not a problem here. I just want to be at graduate school level after a few years while I'm pursuing a less demanding degree.
Rudin's book is horrible. He gives almost no intuition on the subject and treats mant things ad hoc. His treatise on multivariable calculus is so bad that it causes me to cry. And the chapter on Lebesgue integration is a mutilation of such a beautiful subject. Most of the time, Rudin just wants to impress you with how smart he is... I highly recommend the books by Berberian which are simply lovely books.
Hey, the infamous mathwonk approves too. I'll give it a try when I'm there. What book lucidly explains Complex Analysis?
I feel that the book by Bak and Newman is very good! I originally learnt complex analysis from the book of Freitag & Busam, but somehow, I feel that the book is a bit too chaotic...
you're missing the point of rudin and maybe books in general. they shouldn't give you "intuition" but should force you to develop it on your own and that's exactly what rudin does. besides who's to say what kind of intuition you should have for whatever concept eg you might intuitively understand something geometrically while i intuitively understand something analytically. this amazon review says everything about rudin better than i can: http://www.amazon.com/review/R23MC2...&ASIN=007054235X&nodeID=283155&tag=&linkCode= "Book should be called "Tada! You're a mathematican!""
One could equally ask: who's to say that "forcing you to develop your own intuition" is the most efficient way to learn for everyone? It obviously is not, and that's why there are many different books out there. I don't think Rudin's book is horrible - in fact, I think the first eight chapters are wonderful once you have a certain level of "analysis maturity" - but I also believe that many students are not going to gain an intuition for the material by self-studying Rudin, no matter how long they struggle with it. (Rudin's book plus a good instructor is another story.)
Certainly not. You should develop intuition on your own, that's right, but Rudin is really bad for that. He never motivates any result and places them in historical context, and for me that's essential. I like reading why and how people came up with things and I think that's what people need to develop their intuition. Don't get me wrong, I like rigourous books. Books may be very technical and terse for me. But they should at least give some kind of motivation for the results! Professional math papers do that, so math books should do that too. Never, in his entire book does Rudin even mention that Lebesgue measure is just a formalization for "length" or "area". As a result, I understood nothing of Rudin's treatise. If he at least mentioned something like that, then I would be fine. (OK, maybe I was stupid for not seeing that, but still). The chapter on multivariate calculus is bad too. Basically, he says that Stokes' theorem is true by definition. I don't find that very satisfactory... True, and that is why there are so many math books out there. Every author presents his own intuition, and you should choose the intuition that's most comfortable with you. EDIT: If I read Rudin right now, it's a wonderful book and I like to read it. But that's only because I know the material already and I know what Rudin is trying to do. So I feel that Rudin should be used to refresh some results and to prepare you for later courses. But certainly not as a first course...
i have a fairly radical view of education in the sciences so bear with me: i think forcing you to develop your own intuition is the most efficient way to learn for everyone because the point of a course of study in a science is not to learn the material but to learn how to solve problems (at least in undergrad). and the only way to truly learn how to solve problems, instead of memorizing algorithms for already solved problems, is to struggle on your own and find out what kind of thought experiments work for you. i think baby rudin paired with something like polya's "how to solve it" would make for a hell of an education in basic analysis. yes it's true i had a very good instructor for rudin BUT i believe he was good because he made us struggle with the material on our own and didn't spoon feed it to us. i'll admit there was at least one time i remember seeing him fill in a gap in a proof after which i remarked that there was no way in hell i could have seen the need to do that/been able to. but i also think that that's a weakness of mine i need to shore up (spotting gaps in proofs). here i can't but agree with you; there should be more of a narrative in all math books. this is mainly the reason i've gone back to physics after an undergrad degree where i focused mostly on pure math. when you read a physics book you're seduced by the material (someof the time) because you feel like you're working on grandiose things that pertain to somehow magical phenomena. i've felt like that in regards to math once in my education and that was when zeno's paradox was resolved in calc using the geometric series.
Ah yes, the magical moment You can't be a scientist without having at least one of those. I had my first moment when I first learned about complex numbers. It's then that I knew I would pursue mathematics.