Wikipedia:Reference desk/Archives/Mathematics/2010 February 27

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February 27

Feedback help?

An editor asked for feedback on an article covering an aspect in differential algebra here. My algebra is quite rusty, as is my DifE, and I never studied differential algebra. I made a couple small suggestions, but I thought maybe some of the visitors here would be in a better position to opine in a useful way.

I also be curious to hear some math gurus weigh in on my observation that so many math articles do not follow WP referencing guidelines—is this considered acceptable going forward, or should it be discouraged?--SPhilbrickT 02:05, 27 February 2010 (UTC)

I have not read the article yet (P-derivations), but I will do so if possible (and perhaps comment on the article as well). With regards to your second point—namely, the lack of references in specific mathematics articles—it can occassionally be a problem. However, if the article in question is "advanced", I think that it is a safe assumption that whoever wrote it is correct in that which he/she has written (in most cases, one would not learn about Bott periodicity (for instance), unless one has a good amount of experience with algebraic topology and the like; therefore, if someone does write a significant chunk of the article on Bott periodicity (in good faith), we can trust that the chunk in question is accurate). On the other hand, of course, even experienced mathematicians make mistakes, and that is why it is useful to reference non-trivial claims in articles. Referencing can also be useful to the person reading an article, because he/she may want to delve deeper into the topics in question. But as a general rule of thumb, it is most important to write a decent article, after which the first priority is to reference non-trivial claims (another alternative is to add references as you are writing the article). PST 03:56, 27 February 2010 (UTC)

I have to disagree here. I've seen plenty of math articles with questionable information so the theory that math articles don't need to be verifiable doesn't hold water.--RDBury (talk) 04:42, 27 February 2010 (UTC)

I never said that mathematics articles do not need to be verifiable; all I said was that the problem of "verifiability" is not that significant for "advanced mathematics articles". PST 05:01, 27 February 2010 (UTC)

One thing that does come to mind (and which I am sure will come to Michael Hardy's mind as well), is that the title of the article is "P-derivations" and not "P-derivation" which contradicts WP:MOS. Perhaps someone else can fix this. PST 03:58, 27 February 2010 (UTC)

I moved the article.--RDBury (talk) 04:46, 27 February 2010 (UTC)

(ec)On the first question, the subject as defined in the article seems to specific to Buium's work, at the least it's not something that many people are going to be familiar with.

On the second question, you should probably raise it at Wikipedia talk:WikiProject Mathematics. I will say that about 10% of math articles don't list any references at all, which is about the same as Wikipedia over all.--RDBury (talk) 04:28, 27 February 2010 (UTC)

Multiplication of a random variable

Suppose a normally distributed random variable x has a mean μ and standard deviation σ. If the variable is multiplied by n, what is the mean and standard deviation of the new variable in terms of n, μ and σ?--220.253.101.232 (talk) 09:40, 27 February 2010 (UTC)

Come to think of it, the new mean would be nμ. Not sure about the standard deviation though.--220.253.101.232 (talk) 09:42, 27 February 2010 (UTC)

Presuming this is homework, you could try working through an example, or seeing how the variance is affected (that will tell you what happens to the s.d.). Our article on the normal distribution is pretty good, by the way. 75.62.109.146 (talk) 09:44, 27 February 2010 (UTC)

This is not actually homework, I'm just interested. Specifically I was reading Modern portfolio theory, and I was wondering what the expected return and standard deviation would be of n shares given the expected return and standard deviation of one of those shares. —Preceding unsigned comment added by 220.253.101.232 (talk) 09:54, 27 February 2010 (UTC)

Is it (nσ^2)^0.5 ? --220.253.101.232 (talk) 10:02, 27 February 2010 (UTC)

If n is constant, the mean is nμ and the standard deviation is |n|σ, and it's easy to see why if you look at the definitions of mean and standard deviation. Michael Hardy (talk) 16:31, 27 February 2010 (UTC)

...and expressions involving √n occur in sums of n independent random variables. If you multiply a random variable by n, that's a sum of n copies of the same random variable—as far from independence as you can get. Michael Hardy (talk) 16:33, 27 February 2010 (UTC)

The quick way to see what happens to mean and SD is to realise that multiplying (or dividing) all values by a constant is equivalent to a change of units - a mean of 5cm and an SD of 1cm, for example, represent physical measurements which could be expressed alternatively as 50mm and 10mm respectively. If all values are expressed in mm rather than cm, they are still the same size as before, and so must be their mean and SD - everything will be ten times greater in the different units.→86.152.79.95 (talk) 19:18, 27 February 2010 (UTC)

For a random variable x having mean μ and standard deviation σ, the notation x ≈ μ±σ has the benefit that the formulas for adding a constant or multiplying by a constant take the familiar forms of associative and distributive rules: a+x ≈ a+(μ±σ) = (a+μ)±σ and ax ≈ a(μ±σ) = aμ±aσ. Bo Jacoby (talk) 22:18, 1 March 2010 (UTC).

What do I need to learn...

I have an interest in biostatistics and bioinformatics, but my maths background is mostly limited to a few semesters of college calculus and whatever (very) basic statistics I have been able to pick up since. Recently, this paper (which has a corresponding PPT presentation) caught my eye as something that could help me with a side project I've been considering on and off for a few years, but I'm not familiar with some of the notation that's used. What do I need to learn to manage a basic understanding of the algorithms presented in that paper? – ClockworkSoul 18:49, 27 February 2010 (UTC)

The notation (and all of the algorithms) in that paper are standard for a computer science algorithms class. If you don't want to take a class, but want the standard textbook that most universities use, get Introduction to Algorithms (commonly referred to as CLRS). -- kainaw™ 21:18, 27 February 2010 (UTC)

Also note, bioinformatics is heavy on database algorithms, not really mathematics. My job (in bioinformatics) is mostly taking algorithms other have written that will take a year or two to complete and reworking them to run in a day or two. It requires extensive knowledge of data organization, parallel processing algorithms, and statistical approximations. As a bonus, you should study a lot of medical jargon since the data is all medical data. It makes it much easier to know how to identify TIA in the data instead of being held up waiting for a doctor to explain it to you. -- kainaw™ 21:22, 27 February 2010 (UTC)

Thank you for your help, Kainaw! Fortunately, that's where my formal training is, so at least I've made some progress on that front! – ClockworkSoul 22:06, 27 February 2010 (UTC)

That article is about combinatorial graph algorithms and also some linear algebra (the part where it discusses least squares) that you'd probably find out about in either a numerical analysis or a statistics class. 75.62.109.146 (talk) 09:42, 28 February 2010 (UTC)