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Real Analysis, by N. L. Carothers
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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. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.
- Sales Rank: #1331664 in eBooks
- Published on: 2000-08-15
- Released on: 2000-08-15
- Format: Kindle eBook
Review
'... 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
About the Author
Carothers is Professor of Mathematics at Bowling Green State University in Bowling Green, Ohio.
Most helpful customer reviews
26 of 27 people found the following review helpful.
Excellent textbook for review, but this is not a first course.
By G. Basilio
In the author's preface, he states that the prerequisites are "one semester of advanced calculus or real analysis at the undergraduate level". So, this book cannot be judged as an 'intro to real analysis'.
I just want to comment on how I have experienced this book. Let me mention that I am using this for self-study after completing a course using Rudin's Principles of Mathematical Analysis (we covered every chapter except Ch. 10 on integration in R^n). I picked this up to review analysis with the goal of covering function spaces and measure theory with more emphasis that Rudin. This book does just that! But, I also wanted a book that stays in R for the Lebesgue measure. Having read the first 3 chapters of Folland, I didn't really think I 'understood' the material even though I could do the exercises (but not without a lot of sweat and coffee). (At one point I felt I became a function: [input] facts, assumptions then [output] proofs, ie hw exercises.) Folland does everything for abstract measures and treats the Lebesgue measure as a corollary.
Having said that, this books hits the spot.
A previous reviewer said this book was informal, unprofessional, and chatty. I do agree with him on that the book is very informal in the exposition and is chatty. I feel that this might be very distracting for those who do not wish to be specialists in analysis, or to those who are seeing analysis for the first time. However, for someone who has finished, say Baby Rudin, this book IS AMAZING. His chatty 'foreshadowing' is the best part, since by now you are trying to see the 'big picture'. In this respect, the chattiness tells of the shortcomings of the previous theory and points one to the right questions to ask.
I think this book shines for the purpose of an intermediate course between Baby Rudin and graduate real analysis ala Folland. As such, the exercises are at the perfect level and include standard, important, and interesting results and extensions. I don't think this book is rigorous enough for a real course at the graduate level, however.
A final note, the editorial (why?)'s placed throughout do get annoying but I feel they make sure you do not take results for granted, an all too common habit when reading advanced math.
0 of 0 people found the following review helpful.
Five Stars
By SANAT KUMAR PANDEY
Joy to read and good solved example. Used it for self study.
2 of 4 people found the following review helpful.
Highly Recommended
By Indikos
I highly recommend this text, especially for self-study.
This book is like taking a course 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.
The material is pitched at the senior level.
I wish I had this book when I was studying this subject.
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