- Paperback: 416 pages
- Publisher: Cambridge University Press; 1 edition (August 15, 2000)
- Language: English
- ISBN-10: 0521497566
- ISBN-13: 978-0521497565
- Product Dimensions: 7 x 0.9 x 10 inches
- Shipping Weight: 2 pounds (View shipping rates and policies)
- Average Customer Review: 16 customer reviews
- Amazon Best Sellers Rank: #296,321 in Books (See Top 100 in Books)
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Real Analysis 1st Edition
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'... extremely well written: very entertaining and motivating.' Adhemar Bultheel, Bulletin of the London Mathematical Society
'The author writes lucidly in a friendly, readable style and he is strong at motivating, anticipating and reviewing the various themes that permeate the text ... The overwhelming impression is that Real analysis was a labour of love for the author, written with a genuine reverence for both its beautiful subject matter and its creators, refiners and teachers down the ages. As such - and high praise indeed - it will sit very happily alongside classics such as Apostol's Mathematical analysis, Royden's Real analysis, Rudin's Real and complex analysis and Hewitt and Stromberg's Real and abstract analysis.' The Mathematical Gazette
This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists alike, including historical commentary, carefully chosen references, and plenty of exercises.
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Top customer reviews
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This book is like taking a course from one who loves the subject and knows it very well.
And what is more, she wants to communicate her knowledge to you.
She has anticipated your difficulties and is prepared to guide you.
The material is well motivated; the historical asides help you understand and appreciate the material even more.
There are a lot good exercises.
One caveat is that analysis is on R not R^n.
I particularly liked the discussion on the Cantor set.
The material is pitched at the senior level.
I wish I had this book when I was studying this subject.
What I do like is how the exercises are weaved in the sections per chapter. It makes it obvious to the student that this set of problems is heavily related the material that was just read. Nonetheless, after I went through the first four chapters of this book, I gave up on trying to follow it. It's a good thing I had also been reading Rudin. Through the rest of the course, I just ended up using Rudin's book, which I think is much more clear. I also like that Rudin goes through more proofs and examples, instead of just listing them off. It's no wonder why Rudin's book has been used for so long and at so many universities.
I wish I was able to appreciate this book as much as the other viewers had. It's not as if I have a personal gripe with Carothers, but this was not a happy experience.
This book is great if you've had a reasonable real analysis course and want to review what you've learned while simultaneously going into a little more depth or if you want to teach yourself basic Lebesgue theory. For the former, its coverage of function spaces and topics like Stone-Weierstrass is excellent (imagine Ch. 7 of Baby Rudin expanded to several chapters). For the latter, it offers the most intuitive and systematic (step-by-step) development of the Lebesgue integral I've seen. This book is worth getting just for that part. Also, if you're really smart, this book is gentle enough to conceivably be used as a first text in real analysis, provided you've already seen epsilon-delta, difference quotients, Riemann sums, etc. in a rigorous calculus book (Apostol or Spivak), or don't care if you learn things "out of order".