Thread: Functional Analysis

So, I have always hated real and complex analysis (though I was required to learn them both for my degree, albeit at a very superficial level).

For reasons that do me no great credit, I feel the need to learn functional analysis in some depth (basically I have phys jock friends on other fora to whom this subject seems just like breathing; I want to keep up there - and also here, obviously).

My limited knowledge of the subject is gleaned from VERY general texts, and constantly trips me up in public

So I have just ordered Rudin's "Functional Analysis" (Amazon, used - 20 euros). I saw it recommended on another site.

Any good? Are there any better?

Originally Posted by Guitarist

So, I have always hated real and complex analysis (though I was required to learn them both for my degree, albeit at a very superficial level).

For reasons that do me no great credit, I feel the need to learn functional analysis in some depth (basically I have phys jock friends on other fora to whom this subject seems just like breathing; I want to keep up there - and also here, obviously).

My limited knowledge of the subject is gleaned from VERY general texts, and constantly trips me up in public

So I have just ordered Rudin's "Functional Analysis" (Amazon, used - 20 euros). I saw it recommended on another site.

Any good? Are there any better?

Rudin's book is a classic. There is no better.

There are other texts that are more specialized and go into more depth on some specific topics.

I can pretty well guarantee that the knowledge of your physics friends is no more deep, and likely quite a bit more superficial, that what you will find in Rudin's book.

Originally Posted by Guitarist

So, I have always hated real and complex analysis (though I was required to learn them both for my degree, albeit at a very superficial level).

BTW, if you want a good book on real and complex analysis, in addition to your book on functional analysis, you won't find one better than Real and Complex Analysis by the same Walter Rudin. Both of Rudin's books are very widely used and highly regarded graduate mathematics texts.

Thanks. I get that sinking feeling that I ought to study areas of math that I dislike in addition to those that I enjoy. Life is sooo hard!

In fact Rudin's "Functional Analysis" arrived over the weekend, but I haven't had much time to go into it too deeply (wedding going on here - no not mine nor any of mine!)

No wonder my copy was so cheap. It is battered, which is OK but also scribbled over with some seemingly poor attempts at proofs, which is not so good.

Ah well, I still have hopes of being invigorated.....

As far as obtaining used math books goes, I find alibris.com to be reliable in terms of delivering high-quality books that are in the condition the site says they're in. They also tend to be cheap if you're willing to order back an edition. I just bought a linear algebra book for $12.83 and definitely haven't paid over $30 for anything (although Intro to Real Analysis 3rd ed. by Bartle and Sherbert was the international edition). abebooks I think is also good, but I have not used it as often.

Originally Posted by AlexP

As far as obtaining used math books goes, I find alibris.com to be reliable in terms of delivering high-quality books that are in the condition the site says they're in. They also tend to be cheap if you're willing to order back an edition. I just bought a linear algebra book for $12.83 and definitely haven't paid over $30 for anything (although Intro to Real Analysis 3rd ed. by Bartle and Sherbert was the international edition). abebooks I think is also good, but I have not used it as often.

I have had the same experience. I look for books in "very good" or better condition.

Yes, I have used alibris and find it an excellent source for books "as described".

I will, however, admit to being a bit of a gadget-geek, so I thought of getting an eReader i.e. a hand-held device that allows you (for a fee) to read so-called books on such a device.

So I went to my local electronics outlet and looked at them all, and ended up thinking "Why?" Surely reading books is all about, like, feet up, beer on, and something to keep your hands busy, especially if, like me, you an ex-smoker. I call that bliss, whether it be a novel or something more technical.

e-reading (if that is a word) seems to bypass all the so-called "chill-out" bits of the experience of holding paper and cardboard in your hands, beer on, feet up. TV off etc (plus you need better eyes than I now have!!)

But then again, I am a dinosaur I guess

Originally Posted by Guitarist

Yes, I have used alibris and find it an excellent source for books "as described".

I will, however, admit to being a bit of a gadget-geek, so I thought of getting an eReader i.e. a hand-held device that allows you (for a fee) to read so-called books on such a device.

So I went to my local electronics outlet and looked at them all, and ended up thinking "Why?" Surely reading books is all about, like, feet up, beer on, and something to keep your hands busy, especially if, like me, you an ex-smoker. I call that bliss, whether it be a novel or something more technical.

e-reading (if that is a word) seems to bypass all the so-called "chill-out" bits of the experience of holding paper and cardboard in your hands, beer on, feet up. TV off etc (plus you need better eyes than I now have!!)

But then again, I am a dinosaur I guess

What about an Amazon Kindle? I hear they're good for that sort of thing...

Originally Posted by x(x-y)

[
What about an Amazon Kindle? I hear they're good for that sort of thing...

1. I agree with Guitarist.

2. The sort of mathematics and physics books that interest me are not available on Kindle.

3. I am not willing to pay what they want for a device that will eventually fail or become obsolete and for which content is extra. My library is permanent.

Originally Posted by DrRocket

Originally Posted by x(x-y)

[
What about an Amazon Kindle? I hear they're good for that sort of thing...

1. I agree with Guitarist.

2. The sort of mathematics and physics books that interest me are not available on Kindle.

3. I am not willing to pay what they want for a device that will eventually fail or become obsolete and for which content is extra. My library is permanent.

Well, I agree on most of that- however I have never actually used a Kindle so I cannot really comment. But my dad uses a Kindle for his business (carbon black consultancy) and he says that its very useful for reading scientific papers and such.

I'm not into the idea of e-readers at all. I think there's just something much more satisfying about having a library that takes up x number of shelves than x number of gigabytes. And I agree with DrRocket and Guitarist.

However, an e-reader is far more convenient for travel purposes than carrying a physical library with you!

Originally Posted by Guitarist

e-reading (if that is a word) seems to bypass all the so-called "chill-out" bits of the experience of holding paper and cardboard in your hands, beer on, feet up. TV off etc (plus you need better eyes than I now have!!)

I love my Kindle. It's great for reading on the bus, but equally satisfying for the "beer on, feet up. TV off etc " where the etc. part includes dog on lap, which makes page turning hard but button pressing is unaffected.

But then again, I am a dinosaur I guess

I thought I was one too, but it turns out that birds are dinosaurs so now I'm a bird. (No, not a dodo.)

(By the way I only looked in this thread because I thought by functional analysis you were referring to the procedure that is part of value engineering. Apparently there's a mathematical procedure of the same name that's unrelated.)

Originally Posted by Bunbury

(By the way I only looked in this thread because I thought by functional analysis you were referring to the procedure that is part of value engineering. Apparently there's a mathematical procedure of the same name that's unrelated.)

It is not a procedure, but rather a very large branch of mathematics. It includes topological vector spaces and things based on topological vector spaces such as:representation theory, Fourier analysis, the theory of distributions, operator theory, ...

"Analysis" is one of the major branches of mathematics, the others being algebra and topology. Sometimes geometry is included with algebra and topology and sometimes it is listed separately as a fourth branch. In reality all of mathematics is interconnected. Analysis is essentially "on beyond calculus".

Thanks for the clarification. You may already have figured out that I am not a mathematician. In the engineering field functional analysis is a useful part of the value engineering process, which is value analysis applied to new product design. Here's a link in case anyone's interested.

http://www.urenio.org/tools/en/value_analysis.pdf

The next stage of the VA exercise is to commence the analysis of the product by identifying systematically the most important functions of a product or service. This is known as functional analysis.

Originally Posted by Bunbury

Thanks for the clarification. You may already have figured out that I am not a mathematician. In the engineering field functional analysis is a useful part of the value engineering process, which is value analysis applied to new product design. Here's a link in case anyone's interested.

http://www.urenio.org/tools/en/value_analysis.pdf

The next stage of the VA exercise is to commence the analysis of the product by identifying systematically the most important functions of a product or service. This is known as functional analysis.

That depends on which branch of engineering one is dealing with. If you talk to someone involved with modern control theory or the foundations of finite-element analysis they will understand the mathematical perspective of functional analysis.

Originally Posted by Guitarist

e-reading (if that is a word) seems to bypass all the so-called "chill-out" bits of the experience of holding paper and cardboard in your hands, beer on, feet up. TV off etc (plus you need better eyes than I now have!!)

But then again, I am a dinosaur I guess

Actually weak eyesight is one reason I got a Kindle. You can increase the font size as much as you need.

Harold I hadn't realized that, thanks. But I still find reading electronic screens hard on the eyes.

But don't you just love the image of Alex sitting in his book-lined library, choosing a dusty old tome at random and spending the evening with a glass of good malt? I do!

Collecting books can become an obsession, however. Last year I took literally thousands of our books to a charity shop. Many were airport crap, some were probably collectable, and others had been very much enjoyed by either Mrs. G or myself or both, but not "deep" enough to be worth a second look.

But I seem unable to stop myself from book-buying. Is there a BB Anonymous? (Figure it out!) Or maybe I could rent space in Alex's library......?

Originally Posted by Guitarist

Harold I hadn't realized that, thanks. But I still find reading electronic screens hard on the eyes.

But don't you just love the image of Alex sitting in his book-lined library, choosing a dusty old tome at random and spending the evening with a glass of good malt? I do!

Collecting books can become an obsession, however. Last year I took literally thousands of our books to a charity shop. Many were airport crap, some were probably collectable, and others had been very much enjoyed by either Mrs. G or myself or both, but not "deep" enough to be worth a second look.

But I seem unable to stop myself from book-buying. Is there a BB Anonymous? (Figure it out!) Or maybe I could rent space in Alex's library......?

I do! haha. I'm not really obsesssed, but I do casually collect old books, and newer books on interesting topics. Recently I bought Experiments in Physical Chemistry by Shoemaker, Garland, and Steinfeld, not because I intend to learn physical chemistry anytime soon (though I wouldn't mind) but there's still just something about having it on the shelf and being able to casually peruse it that's satisfying.

My favorite book is 10 Place Logarithms Including Wolfram's Tables of Natural Logarithms, Reprint of the Rare Edition of 1794. (Reprinted in 1958) by Georg Vega

All the math in it that comes before the logarithm tables is in both Latin and German, split down the middle of the page. It's a beautiful book, more so because it's completely obsolete today.

Originally Posted by AlexP

not because I intend to learn physical chemistry anytime soon (though I wouldn't mind)

Well you should. It may surprise you to learn that my first degree was in Chemistry (I have forgotten most of it), and just loved Phys Chem.

Math is involved in Phys Chem, and as you seem to have a genuine desire to learn math I strongly suggest you go for it. There is nothing really hard about the math used here (or wasn't, when dinosaurs ruled the Earth), but with your chemistry intuition, it should be an easy portal into the very rich world of mathematical physics or even pure mathematics.

Originally Posted by Guitarist

But I seem unable to stop myself from book-buying. Is there a BB Anonymous? (Figure it out!) ......?

I hope not. If there is my wife may commit me.

Originally Posted by Guitarist

Originally Posted by AlexP

not because I intend to learn physical chemistry anytime soon (though I wouldn't mind)

Well you should. It may surprise you to learn that my first degree was in Chemistry (I have forgotten most of it), and just loved Phys Chem.

Math is involved in Phys Chem, and as you seem to have a genuine desire to learn math I strongly suggest you go for it. There is nothing really hard about the math used here (or wasn't, when dinosaurs ruled the Earth), but with your chemistry intuition, it should be an easy portal into the very rich world of mathematical physics or even pure mathematics.

I found a nice set of lecture notes online on it that I leisurely looked through, and it certainly does seem interesting. I probably will learn it at some point...but for now I'm just trying to get through a lot of math. I'd also like to learn classical physics (never had to take calc-based), QM, maybe GR and SR, etc.... But I figure I might as well get a lot of the mathematical prerequisites down first.

Originally Posted by AlexP

I found a nice set of lecture notes online on it that I leisurely looked through, and it certainly does seem interesting. I probably will learn it at some point...but for now I'm just trying to get through a lot of math. I'd also like to learn classical physics (never had to take calc-based), QM, maybe GR and SR, etc.... But I figure I might as well get a lot of the mathematical prerequisites down first.

Have you changed majors and schools ?

I have not. I will have my B.S. in Conservation Biology in August, and I plan to do my Master's in the same area. We'll see where things go from there. I am considering the idea of taking a couple years for a Master's in Mathematics, because it is (obviously) a major interest of mine and I would love to have a formal education in it. If that happens it will be after the Master's in Con Bio but before my PhD if I decide to go that route. I realize that a Master's in math isn't super-useful, but I don't intend to work in the field and I'm not willing to devote the time a PhD would take because it would take too much time away from the field I intend to work in.

For now I am just continuing my self-study. I just finished the course in real analysis and abstract algebra that I mentioned to you a while ago, and I'm continuing to work on the algebra. I also have purchased a linear algebra book to start working from, and I'd like to do topology soon as well but that might wait until after the algebra and linear.

I've decided to take a year off before going back for my Master's, so I will have plenty of time to work on the math. Then hopefully when I go back I'll be able to work out an independent study course again. And I plan to return to this same school for my Master's.