Playing with WolframAlpha and musing.
 

As someone who really struggles with maths I am interested in what a person with a 'good mathematical understanding'* sees when they look at something like this.

Do they look at this and just understand or is this not obvious to such a person?

:smile:
*Define as appropriate.

WolframAlpha is really good for one-offs: say you don't want to derive (and don't remember by heart) Sum(0<=i<=n)i^3, then it will tell you!
However, with a little more obscure requests, it gives you some fluff, i.e. it [I]tries[/I] to be helpful and applies every possible diversion, and every once in a while is been almost sarcastic (it would seem ;-) to the point of being absurd.

I have an advanced degree in math(s), if that counts, and I can tell you that the "simplification" provided by Alpha is something that no one (outside of a student trying to be a smart aleck) would ever make serious use of. It would be akin to asking for a glass of "aqueous dihydrogen monoxide" rather than "water". I suspect that it is an example of the computer's AI scheme running amok.

On the other hand, at least it didn't reply to 64!/32! by loudly chanting "SIXTY-FOUR! over THIRTY-TWO!". There was a guy in a *college* class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.

Breaking it down, I first notice that [TEX]-1+\cos(128\pi)[/TEX] and [TEX]-1+\cos(64\pi)[/TEX] are both 0, so those terms drop out. Then, [TEX]2^{-64}/2^{-32} = 1/2^{32}[/TEX]. Next, [TEX]\sin(64\pi)[/TEX] and [TEX]\sin(32\pi)[/TEX] are both 0, so [TEX]\pi^0[/TEX] is simply 1. Thus we conclude that this was constructed by a joker trying to be cute.

We are then left with [TEX]\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}[/TEX]. This becomes clear one you write out a few terms of the expansion.

[QUOTE=NBtarheel_33;319770]There was a guy in a *college* class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.[/QUOTE]

(this is cool, I have to remember it! :smile:)

[QUOTE=frmky;319771]
We are then left with [TEX]\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}[/TEX]. This becomes clear one you write out a few terms of the expansion.[/QUOTE]

According with the former, the last should be [SIZE=6]ONE HUNDRED TWENTY EIGHT!! [/SIZE]etc...
:rofl: :razz: :ouch2:

I pronounce these as 'sixty-four [I]pling[/I]', like a rather depressed microwave. Don't know where I picked that up.

Many people would maybe use a '[URL="http://en.wikipedia.org/wiki/Alveolar_click"]click[/URL]' (although probably not English speakers), for example, the [URL="http://en.wikipedia.org/wiki/%C7%83Kung_language"]!Kung[/URL].

So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?

[QUOTE=NBtarheel_33;319870]So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?[/QUOTE]

[tex]\prod_{i=33}^{64}i[/tex] :smile:

Generalizing to any m! with n least terms missing:

[TEX]\prod_{i=m-n+1}^{m}i[/TEX]

:smile:

Relevant to PE 403, try this:
Sum(over odd d from d[SUB]1[/SUB] to d[SUB]2[/SUB]) (2 + (d[SUP]3[/SUP]+5d)/3)
and the same for even d values.

Here's what we're looking for: [URL]http://mathworld.wolfram.com/RisingFactorial.html[/URL]. The "rising factorial" a.k.a. the "Pochhammer symbol". There is an analogous notation for the "falling factorial" as well (as opposed to the n! that we all know and love).

We could write [TEX]$\frac{64!}{32!}=33^{<64>}$[/TEX], using the rising factorial. Wonder why Alpha isn't smart enough to use *that* notation, considering that there is a Pochhammer[x, n] command in Mathematica!

(Side note: This is an example of where mathematics and its terminology reminds me of the study of medicine. Doesn't the "Pochhammer symbol" sound like some scary medical term a doctor would throw around? I can just imagine the advertisement: "Are your factorials frequently incomplete? Do you suffer from frequent factorial dysfunction? Ask your mathematician today whether the Pochhammer symbol is right for you. Side effects of the Pochhammer symbol can include increased CPU temperature and calculator overflow.")

[QUOTE=NBtarheel_33;319915](Side note: This is an example of where mathematics and its terminology reminds me of the study of medicine. Doesn't the "Pochhammer symbol" sound like some scary medical term a doctor would throw around? I can just imagine the advertisement: "Are your factorials frequently incomplete? Do you suffer from frequent factorial dysfunction? Ask your mathematician today whether the Pochhammer symbol is right for you. Side effects of the Pochhammer symbol can include increased CPU temperature and calculator overflow.")[/QUOTE]Oh yeah, the NA public TV advertising. I remember the first time I saw one of these obnoxious advertisements and thought what a messed up system the NA medical people are involved in.

I was kind of expecting to see some leeches advertised at some point also. And was half disappointed not to see any such advertisements. That would have been hilarious.