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October 15th, 2018, 08:01 PM   #1
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Math Focus: Frame Theory is pretty awesome, and it's ripe for undergraduate research!
Reading older literature

I'd like to read the book Measure Theory by Paul Halmos, but is that a bad idea since it is so old? Is reading these books from the 50's okay or do you think it's super outdated?

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October 15th, 2018, 08:45 PM   #2
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Math Focus: Frame Theory is pretty awesome, and it's ripe for undergraduate research!
I have read the first chapter, and the notation is really different. That was the first thing I really noticed.
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October 15th, 2018, 09:15 PM   #3
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I don't know the book but it was pretty standard back in the day. I can't imagine measure theory changing all that much, at least at the introductory level. I could be wrong. But Halmos is known as a clear writer. His Naive Set Theory is a classic and well worth reading today.

So I would say that without actually knowing the book in question, I would recommend that book. At least start working with it and decide for yourself.

Can you say how his notation was different? A sigma algebra is a sigma algebra I'd think.

ps -- Your first sentence said, "I'd like to read the book!" That's the best possible reason to read it. If all you want is a simple introduction to basic measure and integration theory, I'd suggest Royden (the classic) or Folland (the modern classic).

But if what you want is to read Halmos's book ... then you should read it! I'm sure such an enterprise would be richly rewarding.
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Last edited by Maschke; October 15th, 2018 at 09:26 PM.
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October 16th, 2018, 12:25 AM   #4
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Quote:
Originally Posted by ProofOfALifetime View Post
I'd like to read the book Measure Theory by Paul Halmos, but is that a bad idea since it is so old? Is reading these books from the 50's okay or do you think it's super outdated?

Sidenote: I just realized I'm a senior member now!!! thank you mymathforum, I don't know what to say! :')
Halmos won't lead you wrong. But whether it is the book for you, that is not so clear. Maybe you should tell us your knowledge at this point and why you want to learn measure?
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October 16th, 2018, 03:15 AM   #5
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Older the better I always say
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October 16th, 2018, 03:30 AM   #6
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Older the better I always say
Bah, that's just a crazy prejudice, but one that is sooo common. A book should be judged on its own merits. A book being older doesn't automatically make it better than a new book. Likewise, a newer book isn't necessarily better than something old. In fact, old vs new is just not a useful criterion that should be used when seeking the right book for you.
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October 16th, 2018, 03:45 AM   #7
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Bah, that's just a crazy prejudice, but one that is sooo common. A book should be judged on its own merits. A book being older doesn't automatically make it better than a new book. Likewise, a newer book isn't necessarily better than something old. In fact, old vs new is just not a useful criterion that should be used when seeking the right book for you.
Yeah yeah. Pinch of salt obviously.
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October 16th, 2018, 04:08 AM   #8
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Yeah yeah. Pinch of salt obviously.
My apologies, I didn't taste the salt! It's actually a very common (serious) opinion that you posted...
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October 16th, 2018, 04:28 AM   #9
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My apologies, I didn't taste the salt! It's actually a very common (serious) opinion that you posted...
Yes I even posted about it once (funnily enough, I was clear on the salt proportions there).

Personally, I often find that the literature on a given topic which is published closer to the time of said topic being conceived or discovered, is the most insightful. It's as if the ideas are presented in their simplest forms without obfuscation.
Of course, current discoveries and the literature on them aren't without their bugs and in many cases it may actually be counterproductive reading older literature for this reason. Also, 'old' is relative here.

But certainly it is ridiculous to hold such a one-sided view on any black and white comparison such as this. The point is, as you suggest, find the book which is right for you!
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October 16th, 2018, 05:01 AM   #10
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Personally, I often find that the literature on a given topic which is published closer to the time of said topic being conceived or discovered, is the most insightful. It's as if the ideas are presented in their simplest forms without obfuscation.
Hmm... Maybe. I'm not convinced. When I read Riemann's habilitationsverdrag on manifolds (the first ever text talking about abstract differential geometry), I understand nothing. Maybe it's because I'm just not too familiar with the math done at those times?

Or keep with differential geometry. Earlier books, like Kreyszig, often presented differential forms or tensors in a very unintuitive way. I much prefer the more modern point of view here. Sure, it's personal.

On many other works, I agree though. Take special relativity, there is no modern book that comes close to the presentation of Einstein's original paper.

And then some works I'm ambivalent about. Take Grothendieck's work on schemes. Reading the original sources, EGA, didn't really help me much. But neither did modern books...
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