Why maths textbooks when you can have Wikipedia?

[Cincinnatus]

I recall that there was something of a controversy on wikipedia a while back over the appropriateness of mathematical proofs for that setting. Was anyone here involved in that? Or remember what was decided anyway?

 

[kenewbie]

As a person doing self study, I would rather have a bad textbook than wikipedia. It is better for certain subjects than it is for others, but learning math of wikipedia alone would be nigh impossible.

The problem as I see it is this: The editors are in competition, there is constant nitpicking on posts, and finding an error in something written by others is used to elevate your own status. You would think that this is a good thing, since it gives accurate articles? Well, the problem is that you end up with math articles and definitions that are so careful and technical that they only make sense *if you already know* the subject.

Another thing is the ordering of the material. It does not exist in many cases. Say you want to learn algebra using wikipedia. First off there is elementary algebra, which contains a few examples and descriptions. The next article is Abstract Algebra. Since wikipedia is not a textbook, there is no information on the plethora of stuff you need to learn in between those two things. The information is not structured for learning a subject, it is structured for finding a single specific bit of information.

Wikipedia gives a lot of really cool history on subjects, which may not be included in textbooks. That's always fun to read. And it is a good resource for looking up definitions or formulas you might have forgotten. If you do not know what a term means, wikipedia usually does (although again, you need to be familiar with the related material for it to make sense). But wikipedia is certainly no place to go if you want to learn a field or a subject which cannot be contained in a single article.

k

 

[Gib Z]

kenewbie's comment is a good echo of what I said in this thread before - They have completely different purposes. Why are we comparing them like this? Why have a rubber when you can have a stapler?

 

[ekrim]

wikipedias great to have open while you look through your textbooks. Any term you're not familiar with is accessible with the push of a button

 

[KennyCivE]

What's to prevent me from intentionally putting up subtle wrong information on wikipedia? It might not get noticed before somebody learns the incorrect thing.

 

[Phy6explorer]

Why?

Nothing is going to prevent you from doing it, but why do it?
I,mean, I know you won't do it, will you?Why will someone want to pollute a good source of information?

 

[kenewbie]

Nothing is going to prevent you from doing it, but why do it?
I,mean, I know you won't do it, will you?Why will someone want to pollute a good source of information?

For the same reason people kick lampposts' until the streetlight goes out I guess. Because they can.

k

 

[leon1127]

Quoted from Wiki

Proof of the central limit theorem

For a theorem of such fundamental importance to statistics and applied probability, the central limit theorem has a remarkably simple proof using characteristic functions. It is similar to the proof of a (weak) law of large numbers. For any random variable, Y, with zero mean and unit variance (var(Y) = 1), the characteristic function of Y is, by Taylor's theorem,

\varphi_Y(t) = 1 - {t^2 \over 2} + o(t^2), \quad t \rightarrow 0

where o (t2 ) is "little o notation" for some function of t that goes to zero more rapidly than t2. Letting Yi be (Xi − μ)/σ, the standardized value of Xi, [it is easy to see] that the standardized mean of the observations X1, X2, ..., Xn is

Z_n = \frac{n\overline{X}_n-n\mu}{\sigma\sqrt{n}} = \sum_{i=1}^n {Y_i \over \sqrt{n}}.

By [simple properties] of characteristic functions, the characteristic function of Zn is
<br /> \left[\varphi_Y\left({t \over \sqrt{n}}\right)\right]^n = \left[ 1 - {t^2 \over 2n} + o\left({t^2 \over n}\right) \right]^n \, \rightarrow \, e^{-t^2/2}, \quad n \rightarrow \infty.<br /> [\latex]<br /> But, this limit is just the characteristic function of a standard normal distribution, N(0,1), and the central limit theorem follows from the Lévy continuity theorem, which confirms that the convergence of characteristic functions implies convergence in distribution.<br /> --------------------------------------------------------------------------------<br /> <a href="http://en.wikipedia.org/wiki/Central_limit_theorem" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://en.wikipedia.org/wiki/Central_limit_theorem</a><br /> <br /> Look at the squared bracket, and see if they are trivial

 

[jtbell]

Why will someone want to pollute a good source of information?

Because he sincerely believes that he is right and most everybody else is wrong.

 

[kuahji]

I'll have to admit, wikipedia has come a long way since it first came out with mathematics. With things like statistics, you do have to be careful with the different notation for variables. I still however would take a decent textbook any day over wikipedia because a textbook will "teach" you the material while wikipedia usually just lists it quick. Also textbooks have practice problems, while wikipedia does not.