Opinions on textbooks on Analysis

In summary, the conversation discussed the opinions on Barry Simon's "A Comprehensive Course in Analysis" 5 volume set and whether it would be worth studying. The individual had purchased the books at a discount but was unsure if they should go through them, considering they had 4 years and could spend 12 hours a week. They were currently studying real analysis and planned to start complex analysis in 7 months. They also mentioned being a physics major and studying math for fun and curiosity. The conversation then led to discussing other areas of mathematics that the individual could look into, such as algebra, topology, number theory, differential geometry, linear algebra, functional analysis, and PDE's. The individual was recommended some books from the GTM series
  • #1
Mr.Husky
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What are your opinions on Barry Simon's "A Comprehensive Course in Analysis" 5 volume set. I bought them with huge discount (paperback version). But I am not sure should I go through these books? I have 4 years and can spend 12 hours a week on them.

Note- I am now studying real analysis from Bruckner couples two books. Next complex analysis by Greenleaf. So I will start after 7 months. And I am a physics major who studies math for fun and curiosity.
 
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  • #5
Ganesh Mammu said:
Thanks fresh_42, the poll indicates same author but not same series.
That's what I said. At least it provides some confidence in the author's writing.
 
  • #6
fresh_42 said:
That's what I said. At least it provides some confidence in the author's writing.
Okay. I am sure that Barry Simon is an excellent author but I want to know how pure math grads or professionals view/review this series. I can't find reviews anywhere.
 
  • #8
Just an observation. There are other areas of mathematics (algebra, topology, number theory, differential geometry, linear algebra, functional analysis, PDE’s, etc.) that you might want to look into before doing another round of analysis.
 
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  • #9
caz said:
Just an observation. There are other areas of mathematics (algebra, topology, number theory, differential geometry, linear algebra, functional analysis, PDE’s, etc.) that you might want to look into before doing a second round of analysis
Math wonk is guiding me about algebra. For general topology I just started munkres. Simon's volume 2B covers analytical number theory. But I am not interested in number theory. I decided to start spivak's differential geometry along with Simon's analysis. For PDE's I will take a numerical PDE course. So that's it. I think this plan will keep me busy for next 6 years(12-15 hours a week only). I want to study pure math on par with my "Idiosyncratic" path to study physics.

Thank you for replying!
 
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  • #10
If you are looking for a book about analysis, that is more along the lines of measure theory, then you should have a look at Hewitt / Stromberg: Real And Abstract Analysis. (GTM 25).
 
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  • #11
As a physicist you should also never forget to study some (Lie-)group and representation theory!
 
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  • #12
vanhees71 said:
As a physicist you should also never forget to study some (Lie-)group and representation theory!
P.J. Olver, Applications of Lie Groups to Differential Equations (GTM 107)

The easiest way to representation theory is
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory (GTM 9)

whilst a more sophisticated version is
V.S. Varadarajan, Lie Groups, Lie Algebras, and Their Representation (GTM 102)

And yes, I'm a fan of the GTM series. It guarantees a certain level of quality. Otherwise, you have either to know somebody who recommends good books which also fit you, or do a long search in the library to find out what is best.
 
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  • #13
fresh_42 said:
P.J. Olver, Applications of Lie Groups to Differential Equations (GTM 107)

The easiest way to representation theory is
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory (GTM 9)

whilst a more sophisticated version is
V.S. Varadarajan, Lie Groups, Lie Algebras, and Their Representation (GTM 102)

And yes, I'm a fan of the GTM series. It guarantees a certain level of quality. Otherwise, you have either to know somebody who recommends good books which also fit you, or do a long search in the library to find out what is best.
Do you physicists do your research like shown on movies(always writing equations on board, thinking deeply etc.) Or how is it?
 
  • #14
Mr.Husky said:
Do you physicists do your research like shown on movies(always writing equations on board, thinking deeply etc.) Or how is it?
I had hoped that @vanhees71 would have answered this. He is a) a physicist and b) doing research.

Your question has so many levels that it is hard to answer. I guess a lot of time takes place in the library, to study references, see what others have done so far, and getting inspiration. I personally love chalk and blackboard, but others might not. Paper and pencil are probably important for everybody. Well, with exceptions. Euler was blind in his late days and still produced mathematics. He only needed someone to write it down. But scientists as Euler are definitely the exceptions. I don't know whether thinking deeply always applies. A friend of mine once said: "The genius might have the brilliant idea at night, but he is only a genius if he sits down at his desk the very next morning and elaborates his idea."
 
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  • #15
Mr.Husky said:
Do you physicists do your research like shown on movies(always writing equations on board, thinking deeply etc.) Or how is it?
I'm a theoretical physicist working in the field of relativistic heavy-ion collisions. In terms of theory what I'm using most of the time is relativistic many-body quantum field theory, relativistic transport theory (derived from there), relativistic hydrodynamics. Usually you sit down with paper and pencil working out your ideas and then use some numerics to evaluate the resulting equations.

Of course, there's also a lot of discussion with colleagues, including students, and these are indeed mostly done on the black board :-).
 
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  • #16
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  • #17
caz said:
Confession time: I have a favorite pencil
Same. I've used the same mechanical pencil throughtout my education so far, starting with high school upgrading in 2014. A Zebra M100 0.5mm. Every single assignment and exam has been written with it.
 
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  • #18

Related to Opinions on textbooks on Analysis

1. What is the importance of using textbooks in the study of Analysis?

Textbooks serve as a valuable resource for learning and understanding the concepts and principles of Analysis. They provide a structured and systematic approach to the subject, as well as additional practice problems and examples to reinforce learning.

2. How do I choose the best textbook for studying Analysis?

Choosing the best textbook for studying Analysis depends on your personal learning style and the specific topics covered in the textbook. It is recommended to read reviews and compare different textbooks to find one that suits your needs and preferences.

3. Are newer editions of textbooks better than older ones?

Newer editions of textbooks may have updated content and include new developments in the field of Analysis. However, older editions may still be relevant and useful. It is important to consider the specific changes and updates made in the newer edition before deciding which one to use.

4. Can I rely solely on textbooks for studying Analysis?

While textbooks are a valuable resource, it is recommended to supplement your learning with other materials such as lecture notes, online resources, and practice problems. This will provide a more well-rounded understanding of the subject.

5. How can I make the most out of using textbooks for studying Analysis?

To make the most out of using textbooks for studying Analysis, it is important to actively engage with the material by taking notes, asking questions, and practicing problems. It is also helpful to seek guidance from a teacher or tutor if you encounter any difficulties.

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