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

Just going to brag a bit here...

Today I took a college placement test to evaluate my english and math skills. Spent 45 minutes on the english part, and about 2 hours and 15 minutes on the math. The way it works is you're given problems one by one with increasing difficulty, and they don't stop coming untill you get 5 wrong. Well one by one people dissapeared but me and one other guy were there untill time ran out and we still hadn't gotten 5 wrong! :-D The test has no time limit but the schedule only permited three hours max, so I have to go back to keep hitting what they throw at me till I strike out. Its nice to rise to the top for once! After the test I wanted to chat with the other guy who was there till the end with me but didn't get a chance. The questions started proably about 9th grade level and by the time I was done I was doing trig/precalculus. Even though I've gone beyond that I'm pleased, its easy to mess up here and there even on stuff you know. The worst of it was sometimes I got old problems I hadn't done in a long time. Like the equation of an elipse, etc. Also some imaginary number problems, combined rate problems and chemical mixture problems I hadn't done in quite some time were tricky.

But the best part was I found an incorrect question in the test. "sqrt (500) + sqrt ( 180) = ?" and they had a list of five integer answers. 300 was listed which would be the answer if "+" was replaced with "*" I called the instructor over and pointed out that clearly it was a mistake. She laughed when I showed her and said "no one's EVER pointed that out to me!" which seems to suggest the test has been used for some time! and when I remained unbeaten when time ran out she said "we should have you write the tests!" lol. At the end of the test they passed out a survey paper asking questions about what you thought of the test and gave a space for comments. I left them a note about the incorrect problem there. They'd better send me some cash!

Sorry for bragging, just feelin' pretty happy about the whole thing.

*Last edited by mikau (2006-06-28 09:58:37)*

A logarithm is just a misspelled algorithm.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,660

Bask in the glow, mikau! You deserve it.

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

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Psh, that's not bragging. Congratulations. As MIF said, you certainly deserve it. Just curious, do you know how many questions you answered?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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

I wish I knew! They weren't numbered they just kept comin'! I feel like I was somewhere between 40 and 50, maybe even 60? I can't be sure I wasn't keeping track. At any rate I survived the whole time and wasn't moving at a snails pace. But it said it was not a timed test so I took my time with the problems, double checking as not to make silly mistakes.

What does irritate me though, I didn't know about the 5 question thing and most people started packing up before me. "how come everyone's getting done before me? I must be a n00b!" when "20 minutes left" was announced I got nervous. It said the test was time limit free! I started rushing questions trying to get done but more and more kept coming! But I found out when time was called it just keeps going untill you get 5 wrong. SOOOOooo on the next test I'm going to take my time with each question and be sure I get it right even if time is running low. Take as many tests as I need till I reach strike 5. (they're free afterall) Hopefully I'll fall out when I get to problems I truely don't know how to solve, instead of don't remember, or mess up on. I want to try hard to get to and through the calculus problems so i can start more advanced calculus in fall and not have to retake it.

*Last edited by mikau (2006-06-28 12:04:44)*

A logarithm is just a misspelled algorithm.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Cool to hear about that test taking!! Neat mikau!!

**igloo** **myrtilles** **fourmis**

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

actualy I believe there was a second problem that was incorrect.

Find the range of 1/(x^2 - 4) now if you factor the denominator into (x + 2)(x-2) you'll find it has asymptotes at 2 and -2, but as for range, as far as I can tell this range includes all real numbers but zero. For large absolute values of x it will approach the x axes from the positive side, slide up to infinity on the outsides of 2 and -2, and jump to negative infinity inbetween, sliding up to -1/4 in the middle and bending back down. So we have positive and negative infinity. It approaches zero as an assymptote at both ends but never touches or crosses. So it should be everything but zero. But this was not one of the multiple choice answers. It had the stipulation everything but 2 and -2 so I THINK they said state the range of the function when they meant DOMAIN!

*Last edited by mikau (2006-06-28 15:19:25)*

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

You're right, that is domain, not range. The range is in fact everything but 0.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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

I know, I'm just wondering if that was in fact the problem. Thats how I remember it. I'm pretty sure it was in which case it was also wrong.

APPALLING! Students are loosing points on these questions! How are these errors getting into placement tests? 1? Okay.. it happens, but 2? NEGLIGENCE! I COULD HEAR EUCLID TURNING OVER IN HIS GRAVE!

Btw, Ricky, I might find out how many I got right when I get the results. Not sure though..

*Last edited by mikau (2006-06-28 15:58:27)*

A logarithm is just a misspelled algorithm.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

What's domain and range of a function?

**igloo** **myrtilles** **fourmis**

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

The domain of a function is the set of acceptable input values. For instance, take the function f(x) = sqrt(x) the domain of this function is positive real numbers (and zero). Theres a formal way to say it but I'd probably mess it up. D = Subset of reals | x >= 0 something like that. Anyways, its basicly the set of input values the function can work with. A negative number would not be in that functions "domain" because you can't take the square root of a negative number.

In a function like f(x) = 1/x, the domain would be all real numbers except zero, because division by zero is undefined.

Next there's range. Take a function like f(x) = x^2, the domain of the function would be any real number (positive or negative) but the range of this function would be all positive real numbers (And zero) simply because if x is positive or negative, it will always be positive when squared.

You could also take a function like f(x) = -x^2, the range (output) of this function would always be all real numbers less then or equal to zero. Or a function like f(x) = x^2 + 4, the range of this function would be all real numbers greater then or equal to 4. And you get the idea...

What happened here, if you have a function like f(x) = 1/( x^2 - 4) you can factor the denominator to get 1/(x + 2)(x - 2), since division by zero is undefined, you cannot select any values of x that will cause any of these factors to equal zero (then the whole denominator becomes zero) if the factor x + 2 = 0 then x would equal -2, if the factor x - 2 were to equal zero, x would be 2. Therefore the numbers 2 and -2 are not in the domain of the function since they would cause the function to "crash". In the test they mistakenly asked me to find the range of the function but actually they wanted the domain which was all real numbers except 2 and minus 2, which was one of the answers listed. The range of that function is actually all real numbers except zero, but that was not one of the multiple choice answers. So I figured they mixed up the definition.

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

The domain of a function is the set of acceptable input values. For instance, take the function f(x) = sqrt(x) the domain of this function is positive real numbers (and zero). Theres a formal way to say it but I'd probably mess it up.

Be careful there, mikau. That is a common misconception.

Because we like functions that we can use calculus, we almost always talk about functions over the real numbers. But there are many kinds of functios. There are those only over the naturals, or integers, or rationals, and the list goes on.

All functions are defined with a domain in range. Keep that word in mind. Functions doen't *have* domains, they are *given* them. While that may seem like a nit-pick, it's a big difference.

For example, I can talk about the function f: [0, 2] -> R such that f(x) = 2x. Or I can talk about a *different* function f: [0, 3] -> R such that f(x) = 2x. The first set given is simply the domain, the second set is the range.

Now, when you are asked for the domain of a function, what is assumed is that:

1. You are talking about all real numbers

2. The domain is such that the function goes into a real number

If I define a function f: R -> C(omplex) such that f(x) = sqrt(x), then we say the domain is all real numbers. If I define a function f: R->R such that f(x) = sqrt(x), then I can redefine the domain to be all nonnegative numbers, since all the other ones don't lead into the range, and thus, aren't in the domain.

So to sum up, it is a misconception, but one that works most of the time, especially in calculus.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,660

For reference: Plot of 1/(x^2-4)

Ricky wrote:

Functions don't have domains, they are given them

So, you would normally say that f(x) = sqrt(x) has the domain of positive reals (because it is assumed that the result must be a real),

but if someone said the range was complex, then does the domain become:

a) the complex numbers (because you can take the square root of a complex number if the result can be complex), or

b) whatever you say it is?

If it is b), then that makes exams easier!

(Maybe the answer is a and b together )

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

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

Yes the domain and range could include imaginary numbers, in which case the range would incluse positive real numbers and imaginary numbers. I was aware of that and thought someone might point it out. But heck I didn't want to confuse John E. Franklin too much. One thing I wasn't really aware of was functions are given domains. Still certain functions won't be able to execute their algorithms with certain input values, regardless of how the domain was defined by the creator.

A logarithm is just a misspelled algorithm.

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

interesting question mathsisfun....

*Last edited by mikau (2006-07-01 12:54:21)*

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

The most common standard is to assume both the domain and range are real, unless otherwise specified. So if someone specifies a complex range but not the domain, assume it's real numbers.

At least that's the way I've seen it.

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

true. And in the real world, that assumption will rarely (possibly NEVER) be a bad one.

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I said it once and I'll say it again: Screw the real world. Want proof that the math world is better? Read my signature...

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

As a matter of fact I was going to ask you about that. Its rather funny. Is that some sort of famous quote?

A logarithm is just a misspelled algorithm.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,660

Ricky's current signature: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

I think it is somewhere here on this forum, but an Engineer, Scientist and Mathematician were given a fixed quantity of fencing and asked to enclose the largest area they could. The Engineer built a square, the Scientist built something close to a circle, but the Mathematician placed all the fencing in a tight bundle and said "the area is outside this".

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

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

No, it's something one of my math professors actually said during a lecture.

The class was called Modern Algebra, but it should have been called An Introduction to Abstract Algebra. We were going over rings, and in a ring, it's possible to have:

ab = 0, where a ≠ 0 and b ≠ 0.

known as zero divisors. My professor said, "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." and we went on to integral domains, which are pretty much just rings without zero divisors.

He has some other good quotes too. I think my favorite was, "It's like when you're on Mars and you see spiderman." For what he was talking about, it made complete sense. But out of context, it just sounds crazy.

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

hahaha...

I was asking because me and my friend write a series of short stories to entertain ourselves and eachother. The stories involve ourselves acting crazy and saving the world. Its kind of a mix between the three muskateers and the three stooges. Anyway, my character "mikau" is protrayed a somewhat eccentric, often overly enthusiastic fellow whos common sense has been compromised for mathematical brilliance. He looks at even the simplest things mathematically but usually produces results that are obviously off. "According to my calculations the rain actually flows UP the mountains... Wierd huh?"

another story...

Someone threw out a baby! mikau cried with a pail face.

Boboli didnt move as mikau stepped inside, instead he continued staring at the space where mikau had been. Mikau put the baby on a small scale and gapsed. IMPOSSIBLE! He is EXACTLY 2pi pounds! Im going to name you Radian!

Whoah whoah! boboli gasped. name him? I suppose that means- keep him? We cant keep a baby! We havent the time! Or even the know how!

how hard can it be? mikau asked leafing through the pages on his clipboard. If my calculations are correct all we need is a cage and some food.

What do they eat? boboli asked.

Mikau pushed a few buttons on his calculator, then looked up Toys. he replied "and possibly milk, but I'm pretty sure the latter solution is just a result of quadratic ambiguity."

lol Anyways, the quote would fit one line perfectly.

One seen where they're falling from a plane in a giant toystore, my comrad asks me "hey mikau, if jordan and mikau are falling from a plane at three thousand miles an hour, and they left their parachutes on the plane, how do they reduce they're impact velocity with the ground to less then 10 miles an hour?"

"Now there's an interesting problem!" mikau smiled looking down at his clipboard. "hmm... in the REAL world, this would be a problem, but in mathematics we can just define a place where the problem does not exist so we'll go ahead and do that now!"

SLAM! They leave giant craters in the floor.

*Last edited by mikau (2006-07-02 05:47:59)*

A logarithm is just a misspelled algorithm.

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

muahahaha! I just got a date for when to continue this math placement test, july 25th, which happens to be my birthday! Horaay! What better way to celebrate then to take a math test? This is gonna be the best B-day, EVER! :-D

My only concern is time. It took me nearly a week to get ahold of them again and the next placement test isn't till three weeks. What if I survive that one as well? I might have to wait to get in the college because my placement test finishes late. Oh the irony...

*Last edited by mikau (2006-07-05 05:59:07)*

A logarithm is just a misspelled algorithm.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,660

Maybe you can ask them what normally happens in cases like that, and what you could do to secure your place.

Anyway, have you decided what you want to do?

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

Computer science, and I want to sort of specialize in math. I'd like to get involved in the really mathsy aspects of programming and be the go to guy for math related programming problems at work.

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Applied Discrete Math is the way to go them. I'm actually majoring in ADM and computer science myself. It's great because most of the computer science courses cover math electives, and most of the math courses cover the computer science electives.

How old are you, mikau? And if you're of age, where are you going to college?

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