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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

I have just completed a large project ... my complete College Algebra course.

I want volunteers to use it to learn College Algebra, and give me feedback while doing it, so that I may improve it for other people.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi Maths;

I am taking your course, I have had 3 College algebra courses already but I am glad to help you check it. Hope people that are being exposed to it for the first time take it also.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Bless you

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi Maths;

I am here at the bottom.

http://www.mathsisfun.com/rational-numbers.html

Is that the newest Pythagoras story. I have read at least 6 or 7 different renditions of that. I think this one is pretty good. Hippasus got what he deserved. If only they hadn't discovered those darn irrational numbers. Why couldn't they have just defined that hypotenuse as almost 3 / 2 units? Probably wouldn't have needed square roots and all that i jazz either.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

that's pretty interesting!

i guess i'll take the course soon!!

thanks for taking such a pain... MathsIsFun!

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi MathsisFun;

I am here:

http://www.mathsisfun.com/algebra/degre … ssion.html

Near the bottom:

You can sometimes work out the degree of an expression by dividing ...

I like the idea of numerical experimentation as a means of getting an answer that can later be proved rigorously.

I noticed that you use 2,4,10,100,1000... to try to determine the limit of ln (3 + √ x) / ln(x). I got embarrassed once when I did the same procedure to guess at a limit. Because I used all even numbers my limit appeared to converge on 1 / 2. What I didn't see was that for odd values it converged to - 1 / 2. Using all even numbers for x ( doesn't matter in your example ) can cause sign errors. So putting some odd numbers in there eliminates that possibility.

Really nice animations!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Thanks. And good point. Maybe I should throw an odd one in.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

The decomposing the cube into 4 cuboids was really cool. So far, so good.

http://www.mathsisfun.com/algebra/zero- … perty.html

The "Zero Product Property" says that if a times b is 0, then a or b has to be 0:

You could include "or both."

http://www.mathsisfun.com/algebra/theorems-lemmas.html

A Lemma is a small results (less important than a theorem)

Possible typo; results -> result

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi Maths;

I am here at the bottom.

http://www.mathsisfun.com/sets/function … iling.html

You probably were aware of this but I was not.

There is a controversy, some books and CAS say that frac(-3.65) is not .35. it is -.65.

Please Check this link:

http://mathworld.wolfram.com/FractionalPart.html

And waterloo (maple) agrees with their definition:

While the rest agree with yours.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Gee, I prefer the normal definition ... it works the same above and below zero.

Wolfram say their definition "has the benefit that frac(x)+int(x)=x". Well the normal definition has the benefit that frac(x)+floor(x)=x. Seems like they are trying to justify a mistake.

Thanks for pointing this out. I may need to make a special note.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Re **frac(x) where x = -3.65**:

I tested this on my two scientific calculators that have the *frac *function...an HP 48SX and a Canon F-802P.

Both say this:

frac(x) = -.65

int(x) = -3

int(x) + frac(x) = -3.65

My first inclination, which no doubt stems from my use of these calculators, is that both the *frac *and *int *functions should simply select their particular side of the decimal point and maintain the sign. I don't know what is generally thought or taught, but to me it seems the intuitive approach.

Excel, OOoCalc and my Sharp PC-1500A BASIC pocket computer say:

-3.65-INT(-3.65) = 0.35

Two other software calculators (BCalc and Microsoft Calculator for XP) say:

-3.65-INT(-3.65) = -0.65

*Last edited by phrontister (2010-04-18 13:59:37)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi all;

There isn't any general agreement on how to handle frac(-3.65). Most calculators and CAS are in favor of -.65 while most books and sites are favoring .35. A small note to warn the reader about the ambiguity would be a good idea.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

I added a comment ... and a small section on the "Int" function.

http://www.mathsisfun.com/sets/function … iling.html

How is that do you think?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi MathsisFun;

I think that is enough.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi MathsIsFun,

The comment that you added:

HOWEVER: many calculators and computer programs actually give the answer:

frac(-3.65) = -0.65

Because they use frac(x) = x - int(x) instead.

What I said in my other post:

phrontister wrote:

Excel, OOoCalc and my Sharp PC-1500A BASIC pocket computer say:

-3.65-INT(-3.65) = 0.35Two other software calculators (BCalc and Microsoft Calculator for XP) say:

-3.65-INT(-3.65) = -0.65

In the first example, INT(-3.65) = -4, while in the second INT(-3.65) = -3.

I think it is the way that INT handles negative decimal numbers in different calculators etc that gives the differing results, not necessarily that they use frac(x) = x - int(x).

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

phrontister wrote:

I think it is the way that INT handles negative decimal numbers in different calculators etc that gives the differing results, not necessarily that they use frac(x) = x - int(x).

Oh yeah. How about this:

*The "Int" function (short for "integer") is like the "Floor" function, BUT some calculators and computer programs show different results when given negative numbers:*

** Some say int(-3.65) = -4 (the same as the Floor function)*

** Others say int(-3.65) = -3 (which is the integer closest to zero)*

*So be careful with this function!*

And under "frac" I have:

*HOWEVER: many calculators and computer programs use frac(x) = x - int(x), and so their result depends on how they calculate int(x):*

*Some say frac(-3.65) = 0.35*

*Others say frac(-3.65) = -0.65*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi MathsisFun;

I finished up to here:

http://www.mathsisfun.com/algebra/mathe … odels.html

Interesting page. On the bottom:

If you become an expert in any of those you will have a job for life!

Maybe not entirely true. Depends on how costly the first error you make is.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

MathsIsFun wrote:

* Others say int(-3.65) = -3 (which is the integer closest to zero)

I reckon this might be better:

** Others say int(-3.65) = -3 (the same as the Ceiling function)*

It mirrors the bracketed comment for the -4 case, giving better consistency.

Furthermore, for negative numbers, -1 "is the integer closest to zero", not -3.

MathsIsFun wrote:

Some say frac(-3.65) = 0.35

Others say frac(-3.65) = -0.65

I'd prefer this, which I think ties it in more clearly with the part that *int *plays in this:

*Some say frac(-3.65) = 0.35 ...... i.e., -3.65 - (-4)*

*Others say frac(-3.65) = -0.65 ...... i.e., -3.65 - (-3)*

*Last edited by phrontister (2010-04-20 12:47:22)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi MathsisFun;

http://www.mathsisfun.com/algebra/expon … ithms.html

Near the bottom: The description of ph is slightly off, but for the purposes of the page it is fine.

This is read ph = - log of the molar concentration of the hydronium ion (or hydrogen ion). Confusing because in chemistry the [ ] have a specific meaning.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Thanks phrontister,

I went for most of your suggestions, but instead of "(the same as the Ceiling function)" I went with "(the rule is: neighbouring integer closest to zero, or "just throw away the .65")", as that is the rule they follow for positive and negative.

We have kept it short, sweet and hopefully accurate

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

bobbym wrote:

This is read ph = - log of the molar concentration of the hydronium ion (or hydrogen ion). Confusing because in chemistry the [ ] have a specific meaning.

What do you recommend I change? I don't want to be inaccurate.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi;

I was just mentioning it so that you would know, if you think you should change it then:

The relationship looks like this:

So when [H+] is 10^(-7) then - log (10^-7) = 7 a neutral ph. As [H+] goes up [OH-] goes down.

You can use either of these for accuracy.

Use either of those just as long as in your opinion it does not confuse the reader.

Just phrase it as - log of the molar concentration of the hydronium ion or the hydrogen ion for H30+ or H+ respectively. You see in math [ ] is for grouping but in chemistry [ ] this means molar concentration( moles per liter ).

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

KTHX

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi MathsisFun;

Went through it. Excellent as a refresher course and for first timers. This was my favorite lesson.

http://www.mathsisfun.com/algebra/circle-equations.html

I was doing it wrong, thanks for helping here.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

College Algebra in 5 Days! (But only if you have done it before.)

Thanks very much bobby. Now we can let more people know about it.

Any suggestions on the order of the pages?

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