omg I just took a look at Apostol's "Mathematical Analysis"

InquilineKea
Wed, 11 Jul 2007 22:36:29 +0000

It allows the reader to explore the missing parts on his own, giving him a more thorough understanding of the topic. If you think “Hold up. How did he go from that step to that one?” and work it out by yourself [and understand everything correctly], it is very satisfying [and even enlightening].



That’s contingent upon the assumption that you can work everything out by yourself. However - it is flawed pedagogy. It assumes that the student can do everything that mathematicians took decades to develop, which isn’t very realistic. yes you will get a more thorough understanding of the topic if you can work everything out - however - that is contingent upon the assumption that the reader is able to explore all the missing parts on his own - and most students won’t - so they’d be better served by books like Apostol (at least initially). They can work out Rudin later. Most real analysis textbooks don’t have much fluff anyhow (even Apostol is very succinct)

If you merely want light and enjoyable reading and don’t want to derive everything yourself, then you probably don’t want Rudin. Yes some math books can be light and enjoyable reading - it’s an excellent habit to pick up. ^_^

For a course syllabi, try
http://www.math.caltech.edu/courses/06ma108a.html

Caltech uses Carothers. ^_^

http://www.amazon.com/gp/cdp/member-reviews/ATN0BSFQQTEQI?ie=UTF8&display=public&sort_by=MostRecentReview&page=3



this book was written by an expert in analysis, whose goal in writing a book is to provide the most concise possible proof of every result. This is what many expert analysts revere, but unfortunately is not what most students appreciate nor benefit from.

Hence this book remains the text of choice for most analysis professors, but not for most students learning the topic.

George Simmons’ books are much better liked by learners, and for very strong students the books of Dieudonne are much more highly recommended.



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