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Originally Posted by werther
Hi, I'm sure TMians here know a lot about RA than what I know -- I am considering taking an analysis course in the future but one is taught using Rudin and the other, Royden. Can someone plese tell me the difference between the two; I understand one is more difficult than the other, but I don't know which one is which. Thanks very much.
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Which Rudin are you talking about, the baby Rudin (principles of Math analysis) or Rudin's "Real and Functional Analysis" text?
I assume that you're talking about the baby Rudin. Anyways.
Royden and baby Rudin are tough books to read if that's your first pure math course. Royden is more advanced, more abstract, and covers more of the advanced topics in subjects like measure theory or topology. Royden is usually used in a graduate level analysis course while Rudin is standard for undergraduate analysis. I'd just take this course with Rudin's book because it covers more ground in terms of subjects like elementary functions, and even this little book is impossible to cover in a one semester course. If you read Rudin cover to cover and master the subject, then you will be already be well prepared to enter a graduate economics program in terms of real analysis preparation (of course, if you also study things like optimization, statistics, etc, that'd be even better). I also think that Rudin can be handier as a reference because it covers differential calculus in R^n while Royden doesn't.