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No doubt this is trivial, but I don't have handy access to a measure theory text and web searching has availed me nothing. Is there a tidy expression for the Lebesgue measure μ(Rn \ S) of the complement of an arbitrary measurable subset S of Rn in terms of the measure μ(S) of S? My guess is that if μ(S) = c is finite, then μ(Rn \ S) = ∞, and if not then there is nothing in general we can say about μ(Rn \ S).— PaulTanenbaum ( talk) 01:03, 28 February 2008 (UTC)
here's my question:
so i do, i get [3, -6].
but then the question asks
huh? i have no idea how to do this; none of my notes tell me how. i thought about finding its magnitude √(x2+y2), but you end up with √45. i checked the answer at the back of my textbook and it says 3√5. can anyone help me here? -- 24.109.218.172 ( talk) 01:51, 28 February 2008 (UTC)
oh wait... i think i figured it out. √45 equals about 6.708; 3√5 equals about 6.708. does anyone know how they got 3√5?-- 24.109.218.172 ( talk) 01:52, 28 February 2008 (UTC)
√45=√(9x5)=√9√5=3√5 should make it totally clear.. (another √2√2=√(2x2)=2) or √72=√2x36=√2√36=6√2 .. it helps if you spot that the value in the root has a factor that is a square eg 4,9,16 etc is a factor
87.102.84.112 (
talk) 10:27, 28 February 2008 (UTC)
What is the formula for generating the reflection curve for a point to point reflection (not formula for ellipse)?
I think Ive managed to do the previous question:
(<---Plus 4 to the top of the fraction and 1 to the bottom)
The next one proved a little more difficult:
(lowest common denominator)
And Something Goes next.. im not sure what
Im not sure how to do the questions like these because the numbers are different on both sides.
I'm having trouble trying to determine some of the language in the following problem:
Consider the following set C, a subset of the set of all bitstrings:
Basis step:
where is the empty string.
Recursive step:
Where...
given by
given by
given by
(Note and are character and string concatentation respectively.)
My question is as follows:
Evaluate
Now what does this mean? Do I just generate the set using just on three seperate steps and concatenate?:
Then I suppose that's wrong. I'm fairly certain I have to concat the (0) at the end. Trouble is there is no mention of the operator and there is no indication of what means. Last time I checked it was the function composition operator. Help start me off with this one! Damien Karras ( talk) 13:16, 28 February 2008 (UTC)
is a constant. Is there a closed-form solution for ? — Keenan Pepper 16:34, 28 February 2008 (UTC)
I'm looking for a website that would contain information on how the amount of tourists in Japan (or another country) varies periodically throughout the year. Tuesday42 ( talk) 16:46, 28 February 2008 (UTC)
There's no doubt that mathematics is important to humanity. Engineering depends on it, along with statistics, and other fields. But why do they teach complicated math to the average highschool student who may or may not intend to go into those fields? If such a person decides to become a writer, historian, or go into business, he would never need something like geometry, calculus or pre-calc. So why? 64.236.121.129 ( talk) 19:18, 28 February 2008 (UTC)
Of all the mathematics which I had learn in high school, I hated geometry and statistics the most. It's not that I cannot do geometry but that I just can't see myself solving real world problem in geometry and that real world engineers uses vectors to solve problems rather than using geometry.
As for statistics, it's useful but just not taught right to me in highschool. Furthermore as I didn't have computers in highschool, doing a statistics problem which I made up myself is excruciating painful (because adding lots of numbers together is very painful without a computer). Hence my dislike for statistics. 202.168.50.40 ( talk) 21:19, 28 February 2008 (UTC)
Why learn math? Because solving problems is fun and joy and satisfaction. Most math courses teach some theory first and then presents you with exercises to check that you understand the theory. In my opinion that is a mistake. It would be better first to present some problems, which you can understand but not solve, and then teach the tools which enables you to solve the problems. Most problems have two solutions, a elementary brute force method, and an elegant shortcut. You do not appreciate the shortcut unless you know the elementary method. Bo Jacoby ( talk) 01:52, 29 February 2008 (UTC).
One thing I wish highschool math teachers would do is tell students what the maths they are teaching is actually used for. In my entire time in HS, or even middleschool, they never told us what these maths they were teaching us, were for. I remember a student asked a teacher what are we going to use these complicated algebra theories she was teaching us for, and she said "absolutely nothing". I had to learn on my own, what maths was for. Physics, engineering, etc.
I think the comment the ideology that, "we have to force everything on students whether they like it or not, just so they have a choice of what they want to do later in life" is not quite "right", in the sense that it's a good idea. There are basics to math that everyone should learn, sure. But the more complicated maths should be left to the future engineers, and such. Of course it isn't up to me, so things remain as they are. But yes, I agree that seems to be one of the reasons why they teach maths to students.
The critical thinking part definitely is a reason why they teach maths, I just don't think it works. Even in college, they make computer science students learn complicated calculus theories that they will probably never use. You don't need calculus to program in C++ (I think. I didn't get very far in my Comp Sci studies, so I don't know what the advanced classes encompass). So the only reason to learn calc for a comp sci student is for the critical thinking skills. But like I said before, you can ace a calc class just by memorizing formulas and recognizing patterns. "Oh this is the equation that we learned in lesson 5. I'll just follow the pattern they taught in lesson 5 to solve this equation". No critical thinking involved.
I remember at the end of one of our calc classes, my prof asked one student what a Derivative was. And the student just kept saying the derivative was the derivative. He had no idea a derivative was just the slope at a given point on a function. He just knew how to find the derivative, and solve the equation. He did well in the class, but he had no idea what the point of it was though. Another time another professor came into our calc class and asked us what the point of a math degree was. The only answer the students could give was "to teach math to other people". Amazing. 64.236.121.129 ( talk) 14:26, 29 February 2008 (UTC)
If you plot the Mandelbrot set with matrices instead of complex numbers, can you get interesting shapes with more than two dimensions? — DanielLC 23:18, 28 February 2008 (UTC)
COMPUTE: JUNE 18, 2008 + 31 WEEKS + 2 DAYS
THANK YOU.--
Goon Noot (
talk) 23:23, 28 February 2008 (UTC)
Here is a calendar, it shouldn't be hard to do. In the future, please avoid posting in all caps. It is the online equivalent of shouting. 134.173.92.241 ( talk) 23:58, 28 February 2008 (UTC)
Mathematics desk | ||
---|---|---|
< February 27 | << Jan | February | Mar >> | February 29 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
No doubt this is trivial, but I don't have handy access to a measure theory text and web searching has availed me nothing. Is there a tidy expression for the Lebesgue measure μ(Rn \ S) of the complement of an arbitrary measurable subset S of Rn in terms of the measure μ(S) of S? My guess is that if μ(S) = c is finite, then μ(Rn \ S) = ∞, and if not then there is nothing in general we can say about μ(Rn \ S).— PaulTanenbaum ( talk) 01:03, 28 February 2008 (UTC)
here's my question:
so i do, i get [3, -6].
but then the question asks
huh? i have no idea how to do this; none of my notes tell me how. i thought about finding its magnitude √(x2+y2), but you end up with √45. i checked the answer at the back of my textbook and it says 3√5. can anyone help me here? -- 24.109.218.172 ( talk) 01:51, 28 February 2008 (UTC)
oh wait... i think i figured it out. √45 equals about 6.708; 3√5 equals about 6.708. does anyone know how they got 3√5?-- 24.109.218.172 ( talk) 01:52, 28 February 2008 (UTC)
√45=√(9x5)=√9√5=3√5 should make it totally clear.. (another √2√2=√(2x2)=2) or √72=√2x36=√2√36=6√2 .. it helps if you spot that the value in the root has a factor that is a square eg 4,9,16 etc is a factor
87.102.84.112 (
talk) 10:27, 28 February 2008 (UTC)
What is the formula for generating the reflection curve for a point to point reflection (not formula for ellipse)?
I think Ive managed to do the previous question:
(<---Plus 4 to the top of the fraction and 1 to the bottom)
The next one proved a little more difficult:
(lowest common denominator)
And Something Goes next.. im not sure what
Im not sure how to do the questions like these because the numbers are different on both sides.
I'm having trouble trying to determine some of the language in the following problem:
Consider the following set C, a subset of the set of all bitstrings:
Basis step:
where is the empty string.
Recursive step:
Where...
given by
given by
given by
(Note and are character and string concatentation respectively.)
My question is as follows:
Evaluate
Now what does this mean? Do I just generate the set using just on three seperate steps and concatenate?:
Then I suppose that's wrong. I'm fairly certain I have to concat the (0) at the end. Trouble is there is no mention of the operator and there is no indication of what means. Last time I checked it was the function composition operator. Help start me off with this one! Damien Karras ( talk) 13:16, 28 February 2008 (UTC)
is a constant. Is there a closed-form solution for ? — Keenan Pepper 16:34, 28 February 2008 (UTC)
I'm looking for a website that would contain information on how the amount of tourists in Japan (or another country) varies periodically throughout the year. Tuesday42 ( talk) 16:46, 28 February 2008 (UTC)
There's no doubt that mathematics is important to humanity. Engineering depends on it, along with statistics, and other fields. But why do they teach complicated math to the average highschool student who may or may not intend to go into those fields? If such a person decides to become a writer, historian, or go into business, he would never need something like geometry, calculus or pre-calc. So why? 64.236.121.129 ( talk) 19:18, 28 February 2008 (UTC)
Of all the mathematics which I had learn in high school, I hated geometry and statistics the most. It's not that I cannot do geometry but that I just can't see myself solving real world problem in geometry and that real world engineers uses vectors to solve problems rather than using geometry.
As for statistics, it's useful but just not taught right to me in highschool. Furthermore as I didn't have computers in highschool, doing a statistics problem which I made up myself is excruciating painful (because adding lots of numbers together is very painful without a computer). Hence my dislike for statistics. 202.168.50.40 ( talk) 21:19, 28 February 2008 (UTC)
Why learn math? Because solving problems is fun and joy and satisfaction. Most math courses teach some theory first and then presents you with exercises to check that you understand the theory. In my opinion that is a mistake. It would be better first to present some problems, which you can understand but not solve, and then teach the tools which enables you to solve the problems. Most problems have two solutions, a elementary brute force method, and an elegant shortcut. You do not appreciate the shortcut unless you know the elementary method. Bo Jacoby ( talk) 01:52, 29 February 2008 (UTC).
One thing I wish highschool math teachers would do is tell students what the maths they are teaching is actually used for. In my entire time in HS, or even middleschool, they never told us what these maths they were teaching us, were for. I remember a student asked a teacher what are we going to use these complicated algebra theories she was teaching us for, and she said "absolutely nothing". I had to learn on my own, what maths was for. Physics, engineering, etc.
I think the comment the ideology that, "we have to force everything on students whether they like it or not, just so they have a choice of what they want to do later in life" is not quite "right", in the sense that it's a good idea. There are basics to math that everyone should learn, sure. But the more complicated maths should be left to the future engineers, and such. Of course it isn't up to me, so things remain as they are. But yes, I agree that seems to be one of the reasons why they teach maths to students.
The critical thinking part definitely is a reason why they teach maths, I just don't think it works. Even in college, they make computer science students learn complicated calculus theories that they will probably never use. You don't need calculus to program in C++ (I think. I didn't get very far in my Comp Sci studies, so I don't know what the advanced classes encompass). So the only reason to learn calc for a comp sci student is for the critical thinking skills. But like I said before, you can ace a calc class just by memorizing formulas and recognizing patterns. "Oh this is the equation that we learned in lesson 5. I'll just follow the pattern they taught in lesson 5 to solve this equation". No critical thinking involved.
I remember at the end of one of our calc classes, my prof asked one student what a Derivative was. And the student just kept saying the derivative was the derivative. He had no idea a derivative was just the slope at a given point on a function. He just knew how to find the derivative, and solve the equation. He did well in the class, but he had no idea what the point of it was though. Another time another professor came into our calc class and asked us what the point of a math degree was. The only answer the students could give was "to teach math to other people". Amazing. 64.236.121.129 ( talk) 14:26, 29 February 2008 (UTC)
If you plot the Mandelbrot set with matrices instead of complex numbers, can you get interesting shapes with more than two dimensions? — DanielLC 23:18, 28 February 2008 (UTC)
COMPUTE: JUNE 18, 2008 + 31 WEEKS + 2 DAYS
THANK YOU.--
Goon Noot (
talk) 23:23, 28 February 2008 (UTC)
Here is a calendar, it shouldn't be hard to do. In the future, please avoid posting in all caps. It is the online equivalent of shouting. 134.173.92.241 ( talk) 23:58, 28 February 2008 (UTC)