The official help me get a degree thread

[Supergrunch]

I hope it's not a problem to ask this kind of question in this thread:

 

I'm reading a book ("The Colossal Book of Mathematics") and I'm having a problem with some wording:

 

The topic is "The Calculus of Finite Differences", I won't go into detail with the exact procedure...

 

I don't get the following:

 

"The coefficient of x is obtained by taking half the bottom number from the first number of the middle row."

 

The first number of the middle row is 8. And half the bottom number from 8 has to be 3.

 

The problem I have: What is half the bottom number?

 

I know that the bottom number in a fraction is the denominator. But I just can't figure out what half the bottom number means and how you get 3 as a result...

I googled it, I tried dictionaries, wikipedia and blah blah.

To cut it short: I'm not able to translate "half the bottom number" and therefore I'm confused (I bet it's simple and embarrassing for me after someone has explained...)

Without the actual question and/or example, that's totally meaningless to anyone, but it doesn't seem to make much sense as it stands. If you post the question I might be able to help out though.

 

Edit: Having googled for the quote you gave, it seems you're following this (or something very similar), with page 7 being the relevant bit. If this is the case, then you've misterpreted what they mean - "bottom number" refers not to part of a fraction but to the lowest number in the inverted pyramid. For instance, the example they give is formed from y = 3x^2 - 2x + 5. You substitute in x = 0, 1, 2, put these in the top row and write the differences below, giving (ignore the colours for now, they're there so I can refer to the numbers in a bit):

 

5_6_13

_1_7

__6

 

This allows you to work out the coefficients, which is useful when you have the y values but not the equation, such as when you're trying to find the (quadratic) equation underlying a pattern. The x^2 coefficient is the bottom number (6, in blue above) halved (i.e. 3), the x coefficient is the bottom number (the blue one again) divided by two (giving you 3) and subtracted from the first number of the middle row (1, in red above), i.e. 1 - 3 which is -2. And the constant is just the first number in the top row (in green above), which is 5.

 

Hope that helps - if not or I'm addressing the wrong problem entirely try elaborating on yours.

 

Edit 2: I think this problem is perhaps really a language one. In colloquial English, we sometimes say "taking away" instead of "subtracting" - for instance, "5 take away 3 is 2," meaning "5 - 3 = 2." This gets further shortened to "take," e.g. "take a from b" means "b - a." Hence "taking half the bottom number from the first number of the middle row" means "((bottom number)/2) - (first number of the middle row)," with "bottom number" referring to the number in the lowest row. It is a slightly confusing way of phrasing things - I didn't interpret it correctly out of context. This is all the more reason for the use of formal notation as opposed to natural language.

 

Final (unimportant) aside: It annoys me how these things get taught to people as a kind of process they have to follow without knowing why it works, which is what the book I linked to seems to be doing. Maths is what it is because it make sense, and therefore any maths done should make sense to the people doing it.

Edited December 14, 2009 by Supergrunch

[chairdriver]

Yeah, I really hate how Calculus is taught. You just get told what to do, and not why or how it works. At school Calculus was always my worst thing because it's so unintuitive if you haven't looked at it properly.

[Supergrunch]

Yeah, and I even get annoyed by simple things like "move it to the other side of the equation and the sign changes." Sure, it's descriptively accurate, but it's just confusing and doesn't give people any sensical foundations to build on.

[Dannyboy-the-Dane]

I feel the same way. I never liked being told "that's just the way it is". But WHY?! Everything in maths has a logical explanation - so give it to me!

 

And dr4hkon's problem above is indeed worded confusingly. Why can't they be precise when instructing what to do? People don't stand a chance if they don't

[Slaggis]

I have an exam tomorrow, and I've got one of the questions down (Are pressure groups good for democracy) but the other "Does membership of the European Union make the British parliament irrelevant?". I'm a bit stumped after going through the basics. I need more.

 

Anyone have an suggestions? I will love you long time.

Edited January 10, 2010 by Slaggis

[jayseven]

our parliament acts as a forum for the representatives of The People to, together, make up our country's mind on whatever decisions are on the table at the EU.

 

Similarly, if we have a british government why do we need local establishments, like councils, to exist? Because there are simply matters too trivial for MPs to waste their time with.

 

Of course none of this is referenced/researched, just my general opinion

[Ellmeister]

No of course not, the Eu doesn't do care about the everyday runnings of the UK.

 

The parliament still needs to make laws, and keep order etc etc.

[Slaggis]

No of course not, the Eu doesn't do care about the everyday runnings of the UK.

 

The parliament still needs to make laws, and keep order etc etc.

 

Thanks But, it's basic stuff like this that I'm fine with. It's trying to get other sources of info/opinons/ideas to stretch to about 5 A4 sides that's the issue. Other than basically what you said, I'm stumped.

[MoogleViper]

Show that the production function

Q = 10 x K^(2/5) x L

is homogeneous.

State its degree of homogeneity. and comment on its returns to scale

 

I've worked out the degree of homogeneity (1.4). But what is the return to scale?