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#1 2007-03-12 15:44:14

MathsIsFun
Registered: 2005-01-21
Posts: 7,659

Degree of an Expression

I am still working on creating some pages on Limits, and along the way I made this page:

Degree (of an Expression)

Is it correct? And easy? And enough?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2007-03-12 19:59:12

MathsIsFun
Registered: 2005-01-21
Posts: 7,659

Re: Degree of an Expression

I am thinking of adding that you can also work out the Degree by taking the limit of log(f(x))/log(x) as x goes to infinity.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#3 2007-03-12 20:04:13

lightning
Real Member
Registered: 2007-02-26
Posts: 2,060

Re: Degree of an Expression

its fine and i tottaly agree (top one)

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#4 2007-03-12 22:46:38

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Degree of an Expression

Nice job on that page, I never knew about the fractions thing. Well... there isn't really much to talk about regarding degree apart from what you've already said... and perhaps that limit thing... so yeah

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#5 2007-03-12 22:51:53

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Degree of an Expression

I agree with Toast. You've pretty much said everything you can say about degree, and explained it very well.

I'm not sure whether you should include the bit about loggy limits, because it's on a substantially higher level than the rest of the page.

Why did the vector cross the road?
It wanted to be normal.

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#6 2007-03-13 15:35:57

MathsIsFun
Registered: 2005-01-21
Posts: 7,659

Re: Degree of an Expression

Thanks People!

Have a look now, I added "loggy limits" ... should I keep it?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2007-03-13 15:39:13

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Degree of an Expression

Hey, just thought I might mention. I recall reading that in multivariable equations, the degree of each term is the sum of the exponants of the variables in the term, and the degree of the expression or equation is equal to the degree of its highest degree term.

At least thats what I recall. I might have forgotten the precise definiton.

A logarithm is just a misspelled algorithm.

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#8 2007-03-14 02:10:50

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Degree of an Expression

So, xy would be order 2 then? That makes sense.

I think the loggy limits addition looks good. I was a bit worried that it would be too advanced, but it's explained very well so people could probably follow along anyway. I was confused by your example for a bit before I realised that you were using logs with base e, but that's probably just me. I usually use log = log(10) and ln = log(e).

Why did the vector cross the road?
It wanted to be normal.

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#9 2007-03-14 05:41:11

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Degree of an Expression

So, xy would be order 2 then? That makes sense.

especially if you consider a system of equations such as xy = 2 and y = 2x + 3, substituting you get y = 4/y + 3 which becomes y^2 - 3y - 4 = 0 which is obviously a 2nd degree equation.

A logarithm is just a misspelled algorithm.

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#10 2007-03-14 09:41:03

MathsIsFun
Registered: 2005-01-21
Posts: 7,659

Re: Degree of an Expression

mathsyperson wrote:

I usually use log = log(10) and ln = log(e).

Is that because you were mostly taught that? Do you think I will also confuse most people?

(PS: there does seem to be conflicting standards on this!)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#11 2007-03-14 10:04:40

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Degree of an Expression

Hmm... in my math books "ln" was always used for base e, and "log" was assumed to be base 10 when no base was given. However, in programming "log" itself tends to go by base e. So I guess it depends on what you're familiar with. At any rate, I think people from both fields will recognize "ln" so maybe you should use that. Or at least display what base you are using.

A logarithm is just a misspelled algorithm.

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#12 2007-03-14 10:55:14

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Degree of an Expression

MathsIsFun wrote:
mathsyperson wrote:

I usually use log = log(10) and ln = log(e).

Is that because you were mostly taught that?

Pretty much. That's what I was taught when I was first introduced to logs, and I've just stuck to it. I don't know which is used most throughout the world though.
Don't worry too much, anyone who knows enough about logs to understand that section will be able to figure out what base you're using pretty quickly.

Why did the vector cross the road?
It wanted to be normal.

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#13 2007-03-14 11:04:14

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Degree of an Expression

In "advanced" texts I notice that "log" is used instead of "ln". I'm not sure why they don't save themselves a letter and stick with "tradition", but I can see how they justify replacing the base 10 log notation with base e: base 10 logarithms just aren't that commonly used farther down the road. I think that ln is the clearest notation though. Is ln used in England?

Last edited by Zhylliolom (2007-03-14 11:05:00)

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#14 2007-03-14 12:16:46

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Degree of an Expression

I'm from England, so yes.

Why did the vector cross the road?
It wanted to be normal.

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