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Real Analysis
This course in real analysis is 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 of value to specialists and nonspecialists alike. The text covers three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal, down-to-earth style, the author gives motivation and overview of new ideas, while still supplying full details and complete proofs. He provides a great many exercises and suggestions for further study.
- GenresMathematicsAcademic
416 pages, Paperback
Published August 21, 2008
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Displaying 1 - 3 of 3 reviews
April 24, 2016
This is my review on Amazon dated November 15, 2011:
I wish I had reviewed this REMARKABLE textbook 5 years ago when I had a lot of knowledge at my fingertips. Now I am not able to go "deep" anymore, which means you may not find this review (that much) helpful. Nevertheless, I am just happy to improve its overall rating (should have done long ago!)
What I still remember though is:
1) what appealed to me most: It was the COHERENCE of the material presented as well as the WAY it was presented. This, coupled with a very good choice of format (size, quality of paper, font, etc.), made it one of the MOST ENJOYABLE learning experiences for me!
2) the EXERCISES being VERY GOOD and interesting (no answers, but some of them had helpful hints).
3) the "WHY?s" thrown in the proofs. I liked this feature a lot. After all, when doing mathematics (proofs), you are not supposed to take anything for granted; on the contrary, you need to justify each and every statement/implication you make. This will make you think about things you considered "basic" or "obvious."
4) the author's PASSION for the subject being felt throughout the book, and being very CONTAGIOUS.
Lastly, let me share a couple of things with you:
1) The REAL ANALYSIS course I took back then was a 2-semester course. I took each semester at different place (within the University), with different professor and using different texbook. While I found the classes in the first semester lacking structure, the second semester made up for it BIG TIME!
2) I have always loved just about anything and everything about mathematics. That being said, I still had my FAVORITEs during the studies, and I can tell you real analysis was not among them. As many of you may guess, this has changed by the time I graduated...
I attribute both things to nothing else but THE TEXTBOOK used (and, of course, the professor and the right choice he made).
HIGHLY RECOMMENDED!
I wish I had reviewed this REMARKABLE textbook 5 years ago when I had a lot of knowledge at my fingertips. Now I am not able to go "deep" anymore, which means you may not find this review (that much) helpful. Nevertheless, I am just happy to improve its overall rating (should have done long ago!)
What I still remember though is:
1) what appealed to me most: It was the COHERENCE of the material presented as well as the WAY it was presented. This, coupled with a very good choice of format (size, quality of paper, font, etc.), made it one of the MOST ENJOYABLE learning experiences for me!
2) the EXERCISES being VERY GOOD and interesting (no answers, but some of them had helpful hints).
3) the "WHY?s" thrown in the proofs. I liked this feature a lot. After all, when doing mathematics (proofs), you are not supposed to take anything for granted; on the contrary, you need to justify each and every statement/implication you make. This will make you think about things you considered "basic" or "obvious."
4) the author's PASSION for the subject being felt throughout the book, and being very CONTAGIOUS.
Lastly, let me share a couple of things with you:
1) The REAL ANALYSIS course I took back then was a 2-semester course. I took each semester at different place (within the University), with different professor and using different texbook. While I found the classes in the first semester lacking structure, the second semester made up for it BIG TIME!
2) I have always loved just about anything and everything about mathematics. That being said, I still had my FAVORITEs during the studies, and I can tell you real analysis was not among them. As many of you may guess, this has changed by the time I graduated...
I attribute both things to nothing else but THE TEXTBOOK used (and, of course, the professor and the right choice he made).
HIGHLY RECOMMENDED!
September 28, 2022
Very insightful but also intense and emotional book. I am only on chapter 4 and it already made me cry a couple of times.
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May 17, 2010Read chapteers 3, 7, 13, 16.
Displaying 1 - 3 of 3 reviews