Opinions on textbooks on Analysis

[Mr.Husky]

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.

 

[fresh_42]

Here's an old poll of a book from the same author:

https://www.physicsforums.com/threads/functional-analysis-by-reed-and-simon.672090/

 

[Frabjous]

Here's an old poll of a book from the same author:

https://www.physicsforums.com/threads/functional-analysis-by-reed-and-simon.672090/

I think that is part of a different series.

 

[Mr.Husky]

Here's an old poll of a book from the same author:

https://www.physicsforums.com/threads/functional-analysis-by-reed-and-simon.672090/

Thanks fresh_42, the poll indicates same author but not same series.

 

[fresh_42]

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.

 

[Mr.Husky]

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.

 

[Frabjous]

Here‘s a review
https://www.maa.org/press/maa-reviews/real-analysis-a-comprehensive-course-in-analysis-part-1

 

[Frabjous]

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.

 

[Mr.Husky]

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!

 

[fresh_42]

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).

 

[vanhees71]

As a physicist you should also never forget to study some (Lie-)group and representation theory!

 

[fresh_42]

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.

 

[Mr.Husky]

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?

 

[fresh_42]

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."

 

[vanhees71]

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 :-).

 

[Frabjous]

Usually you sit down with paper and pencil working

Confession time: I have a favorite pencil.
https://www.amazon.com/gp/product/B017BDDZ7I/?tag=pfamazon01-20

Paper too, but I need to keep an edge …

 

[Mondayman]

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.

 

[Mr.Husky]

Thanks everyone for your replies!

I changed my plans. Rather than working with Simon's analysis 5 volume set, I choose to study the following little and fun book with reference to that set.
https://www.amazon.com/dp/0821827839/?tag=pfamazon01-20