Elementary analysis text

  • #1
thrill3rnit3
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Introduction to Analysis by Maxwell Rosenlicht
https://www.amazon.com/gp/product/0486650383/?tag=pfamazon01-20&tag=pfamazon01-20

Elementary Real and Complex Analysis by Georgi Shilov
https://www.amazon.com/dp/0486689220/?tag=pfamazon01-20&tag=pfamazon01-20

Introductory Real Analysis by Kolmogorov
https://www.amazon.com/gp/product/0486612260/?tag=pfamazon01-20&tag=pfamazon01-20



Which one is best suited for self-studying introduction to analysis? Opinions on each one of them would be greatly appreciated.
 
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Answers and Replies

  • #3
thrill3rnit3
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opinions on any of the books listed above?
 
  • #4
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I have Shilov, and it's certainly adequate for self-study assuming this is for a first go at analysis. I would say kolmogorov is more advanced and not necessarily adequate for a first exploration. Kolmogorov goes all the way into measure whereas Shilov doesn't go beyond metric spaces. Alternatively, if you want a gentle introduction, try Michael J Schramm though there aren't any hints or solutions as opposed to Shilov's. It's Dover too.
 
  • #5
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What background do you have in analysis? Calculus at the level of Stewart, or something more advanced?
 
  • #6
thrill3rnit3
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I have Shilov, and it's certainly adequate for self-study assuming this is for a first go at analysis. I would say kolmogorov is more advanced and not necessarily adequate for a first exploration. Kolmogorov goes all the way into measure whereas Shilov doesn't go beyond metric spaces. Alternatively, if you want a gentle introduction, try Michael J Schramm though there aren't any hints or solutions as opposed to Shilov's. It's Dover too.
Would you recommend Schramm's over Shilov's?
 
  • #7
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Hard to say, I guess it depends on your learning style. I really liked Schramm's style over Shilov, they're both roughly on the same level of difficulty as far as problems. Schramm is a bit chattier and elaborates on consequences of theorems and their importance. It's nice for students like me who haven't yet reached enough mathematical maturity. I also think his progression is a bit more natural. I certainly like Schramm better than Shilov, but either is good, and Shilov has hints/answers.
 
  • #8
thrill3rnit3
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How about depth? Which book covers more depth?
 
  • #9
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I suspect Schramm has more depth since Shilov's book spends a lot of room on some theorems and results of complex analysis. Once Schramm covers the basic theorems of differentiation and integration he moves on to questions of continuity of special functions (dirichlet, and van de waerden) and then the briefest glimpse of measure theory. At the end he constructs the real numbers via dedekind cuts. Also, Shilov spends some time on certain topics that are usually covered in calculus such as arc length and surfaces of revolution.
 
  • #10
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I recommend Analysis: With an Introduction to Proof by Steven Lay as a starter in analysis. The analysis book by Creighton Buck is very good as well.
 
  • #11
jasonRF
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I second the nomination of Analysis: with an introduction to proof, by Lay. I recently worked through the 2nd edition of this book and felt like it was at the perfect level for me - I had never taken analysis. It starts you off with logic an proof, goes through sets, functions and cardinality in detail before moving on to the real numbers, continuity, etc. It is not as advanced as some intro books (my wife used Rudin as a math major - not so easy for a beginner!) but will give you a pretty solid understanding of elementary analysis. I thought that the 2nd edition was fine - it was also pretty cheap used online.

Good luck.

Jason
 

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