User talk:Amir Aliev

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[edit] Your MathCOTW nomination won!

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Twice! James S. 07:47, 16 April 2007 (UTC)

[edit] Tanaka's formula

Hi, Amir!

I just spent some time on this article, to make the displayed formulas and symbols look better (and to polish up the English idiom a bit, as well). You might want to take a look and see if it reads more smoothly now.

I happen to agree with the concerns you expressed over here, about standard notations in probability and statistics. Personally, the only notations I've encountered regularly are

for probability measure, and

for the expected value operator. But then, I don't have any really new books lying around, just old stuff like Feller. Anyway, I'd like to help introduce more regularity into the probability notation used on Wikipedia, and I'll be happy to discuss it with you at any time. Together we may be able to get something written into the manual of style and at least limit the proliferation of different notational systems that way.

Have a great day, Amir!  ;^> DavidCBryant 00:27, 24 February 2007 (UTC)

Hi, David!

Thanks for your corrections, I've forgotten about the articles again :-)

Frankly speaking I have absolutely no idea where those guys take their notations, I've also seen only P & E (sometimes italic, sometimes bold though). I have a couple of modern books also to look in. Being a probability student, I have also a lot of probability articles. I'll look and count different notations in them (if any) and write here in a couple of hours.

And yes, in the end we should write something for manual of style because it seems this notational systems are propagating fast, for example I've encoutered only recently the

I promise I will write soon about the probability articles I have. Amir Aliev 09:49, 24 February 2007 (UTC)

I found 53 articles on Wikipedia that use

by running a Wiki-search ... I just entered "\mathbb{P} probability" (no quotes, though) in the search box, then hit the "Search" button. I looked at a few of them, and they mostly seem to be fairly abstract articles dealing with definitions of probability space, etc. There's no need to be in a rush about it, Amir … I just think it's something we can help each other with, and maybe improve Wikipedia a little bit in the process. (Oh – if I were going to propose a standard, and rely on authorities, I'd probably pick Kolmogorov & Feller as the most important authors of the 20th century.) DavidCBryant 14:41, 24 February 2007 (UTC)

So, I've looked through my articles and found this:

P, E come first, with 10,5 cases (a half is the article that used Pr and E)

P, E comes second, with 6,5 cases

\mathbb{P, E} comes third with 2,5 cases

and the last are two uses of Pr

Notice that those are articles in English; I have numerous articles in Russian and they all write P, E as it is taught by Russian school of probability. Among the books I have one writes P,E, one \mathbb{P,E} and two \mathrm{P, E} - but one of the two is written and the other co-written by my supervisor, A.N.Shiryaev, and he is obviously an adept of Russian school :-) . I don't have the translations of the Kolmogorov works, only in Russian and he also prefers P and E, but writes M for the expectation, as it was called mean value then. All this said, I should admit that my position (\mathrm) is pretty weak. Nevertheless, we should present the problem because, as I've already said, wikipedia is one piece of work and should stick to one notational system. If the public will choose P, E let it be. Amir Aliev 22:07, 24 February 2007 (UTC)

[edit] Kolmogorov

Sorry I put m on my changes - I made quite a few and virtually all were wikilinks and such - I forgot about this sentence removal. On the matter - I think this sentence makes very little sense. There are hundreds of areas and sub-areas in mathematics. What constitutes an area is unclear. Same for original paper - often they lie in several fields, more in some than others. There is no way to quantify this. Why try, anyway? To make a point, it's clear for example that Kolmogorov made no contributions to finite groups theory. Same for commutative algebra. In summary, the statement is either too vague or misleading, if not wrong outright. Mhym 19:01, 27 February 2007 (UTC)

In fact it's pretty clear what constitutes an area and what doesn't - BUT I don't want to argue because it drifts to the original research. I have taken this remark from two sources, this one and the biography of Kolmogorov (1991-93. Selected works of A.N. Kolmogorov, 3 vols. Tikhomirov, V. M., ed., Volosov, V. M., trans. Dordrecht:Kluwer Academic Publishers. ISBN 9027727961), both cited in the article. The first one says

In over 300 research papers, textbooks and monographs, Kolmogorov covered almost every area of mathematics except number theory.

The other one also something like that, but I have it in Russian. So probably it is not so vague after all? Amir Aliev 21:47, 27 February 2007 (UTC)

Not that I can settle this question, but I would like to make a few observations. The article areas of mathematics divides the entire subject into five broad categories: Foundations, Algebra, Analysis, Geometry, and Applied Math (which includes probability & statistics as a subhead). I made my own review of Kolmogorov's contributions to mathematics. While concentrated in the area of probability and statistics, his results do touch on Geometry (specifically, fractal geometry), Analysis (Landau-Kolmogorov inequalities, ergodic theory), Algebra (specifically, measure theory on sigma-algebras), and Foundations (algorithmic information theory, and "BHK" interpretation of intuitionistic logic). So Amir's observation, while possibly non-encyclopedic, is probably true, at least from the perspective of a moderately well-informed reader. DavidCBryant 21:12, 28 February 2007 (UTC)

If you want to say "Kolmogorov made contributions in the following areas: 1, 2, 3, ... N" - that's fine. Otherwise this sounds ambiguous as well as OR (your refs make blank unsupported and unexplained statement). Even if you are talking MSC2000, there are about 60 "areas", numerous sub-areas (like 5E, 60C, etc.) and sub-sub-areas (like 5E99, 60C20). I see no place for sentences "all areas but .. " Did he work on graph theory? (5C) Galois theory? I can go on... Mhym 03:55, 1 March 2007 (UTC)

Exactly! You can go on. But this is called original research, as you perfectly know. The are two independent sources that state something but then comes Mhym and wow! he can go on. Probably that was a litte bit too rude, but still I see no reason why we should erase key phrase (supported by two references) only because you pretend not to understand it. Amir Aliev 21:19, 1 March 2007 (UTC)

You are confused. OR is writing something into WP that constitutes a new and original thought. It is not removing from WP something that was written in two sources. Say, I can find more than two literature sources which claim that Earth is flat (all of the sources would be fairly old). So what? Surely you don't think we should include that in the Earth article. Maybe some historical article, but not this one. Same logic applies here. The claims in the WP should be both clear, true and supported by references. If one of these conditions fails - don't include such claim. Mhym 19:57, 2 March 2007 (UTC)

It's not the same logic. You won't find any reputable sources claiming that the Earth is flat, will you? Amir Aliev 22:09, 2 March 2007 (UTC)