Steben
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Here's some calculus, because I know it'll make your day. An engineering friend asked me if this problem was possible, I said I didn't think so, but I'm also incredibly dumb, so maybe you can? Here's what he asked.
Is it possible to simplify int[(u')^2]dx to an expression that doesn't use an integral symbol, where u is a function of x and u' is its first derivative?
Think of differential equations. In this case, the equation would be f' = (u')^2. I can't think of any generalized solution to this, can you?
Aggh.. diff eq was so long ago. I'm gonna pull out my text book from that class now..
And still no dice. Ah well.
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Is it possible to simplify int[(u')^2]dx to an expression that doesn't use an integral symbol, where u is a function of x and u' is its first derivative?
I don't think so because u is a generic function. Without any specifics, you can't determine the output of int[(u')^2]dx without resorting to just evaluating on a case-to-case basis. For example, there is no way to explain the following:
If u(x)=x then the function (int[(u')^2]dx) = x+C or possibly u'(x)*u(x)
If u(x)=ln(x) then the function = -1/x+C or possibly -u'(x)
Not really a proof, but it's what I say.
That's the reasoning I used.
I don't think calc 2 would teach you how to integrate that function; it doesn't look like integration by parts would simplify it. I'm intrigued though
It doesn't. Here's what happened when I tried integration by parts.
int((u')^2)dx = int(u'u')dx
= uu' - int(u''u)dx
= uu' - (uu' - int(u'u')dx)
= int(u'u')dx
= int((u')^2)dx -
Here's some calculus, because I know it'll make your day. An engineering friend asked me if this problem was possible, I said I didn't think so, but I'm also incredibly dumb, so maybe you can? Here's what he asked.
Is it possible to simplify int[(u')^2]dx to an expression that doesn't use an integral symbol, where u is a function of x and u' is its first derivative?
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Auburn University's basketball pep band played this last night, along with an arrangement of the Metal Mario theme I've done as well. They're going to play a shortened version of the Katamari theme as well as the Mario theme at basketball games. I'll try to get a recording sometime in the future.
Of course, if you want to hear the whole thing, you should get your marching band to perform it.
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The method I've been attempting to use is to prove that any infinite bounded set has a limit point, and constructing a sequence from that. Unfortunately, I'm having trouble proving any infinite bounded set has a limit point without using the fact that any infinit bounded set has a sequence which is increasing or decreasing. Whoops.
Any subset of the real numbers has a limit point - each element is a limit point. That doesn't help you at all though. I'd think more on this, but I got a test tomorrow so maybe tomorrow night I can think on that more.
The definition of a limit point we're using is that "x is a limit point of a set H iff any segment about x contains an element of H distinct from x". Any subset of the real numbers contains a limit point of the real numbers, but I need a limit point of the set itself.
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Oh wait you have an infinite set. The real numbers have the well-ordering property, so you can take that set and find a sequence and order it so that it is always increasing or decreasing then. This argument is quite strong though...(uses the Axiom of Choice)
But what if the sequence I chose was {1/4, 1/1, 1/6, 1/1930, 1/205, -4, 1/356!, ...}. I can't order it so that it is always decreasing, because of that -4. Eventually I'll have to use that -4, and then the next number will be greater than it. All that to say, the axiom of choice only lets me pick arbitrary numbers out of the sequence (I think?), and that -4 makes life difficult.
That, and, we haven't talked about the Axiom of Choice in class, so I can't use it. Dang.
The method I've been attempting to use is to prove that any infinite bounded set has a limit point, and constructing a sequence from that. Unfortunately, I'm having trouble proving any infinite bounded set has a limit point without using the fact that any infinit bounded set has a sequence which is increasing or decreasing. Whoops.
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I've been working on the same stupid theorem in Analysis for the past three weeks. I'm probably just being dumb and missing something obvious, but it's been really difficult... I'll type it below for you guys, at the risk of revealing my relative inexperience at proof-based mathematics.Show that if H is a bounded infinite set, then there exists some sequence made of distinct points of H which is always increasing or always decreasing.
Is H a subset of the real numbers? If so, then with a bounded set, you have the least upper bound and greatest lower bound. There must exist sequences in H that converge to the least upper bound and greatest lower bound. Then, there exist subsequences of each sequences such that the subsequences are monotone and converge to the least upper bound and greatest lower bound, respectively.
Yeah, H is a subset of the reals.
I don't follow your argument, though. Let's say H is the union of {1-1/n|n is a natural number} and {1+1/n|n is a natural number}. It's bounded by 0 and 2, but I need a sequence that is always increasing or always decreasing, rather, x_n>x_n+1 always or x_n<x_n+1 always. No such sequence converges to 0 or 2... the only way I can find such a sequence is if it converges to 1... I can't see how talking about the least upper bound or greatest lower bound helps me..
Yes - I'm just talking about the existence, guaranteed by theorems. If you don't have the particular theorems that I'm referring to, then just prove them - if you have an element that is not the least upper bound or greatest lower bound, you can find another element closer, and keep constructing it that way.
Um. I need the sequence to be strictly increasing or strictly decreasing, not monotone. I think that's our delimma.
If the least upper bound and the greatest lower bound isn't in your sets (i. e. if it's an open bounded set), then my method works in constructing a strictly increasing or decreasing sequence.
That's true. But I need it in general. For instance, the example above. It's not open bounded, so that proof doesn't help me.
I've looked over various Putnam problems (with their solutions handy), but I've never actually taken the test. I should look into it. I probably wouldn't solve any of them, but it'd be fun to try.
I wouldn't feel too bad about not solving any of the problems. I've heard that some years the median score is a zero.
I need to go back and look at some of those problems now that I've taken a math classes where we do actual proofs... maybe I could halfway get one right, if I try real hard.
Of course, the real problem with Putnam is that it's on a Saturday during football season. With any luck, I'll be at the SEC tournament that weekend.
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I've been working on the same stupid theorem in Analysis for the past three weeks. I'm probably just being dumb and missing something obvious, but it's been really difficult... I'll type it below for you guys, at the risk of revealing my relative inexperience at proof-based mathematics.Show that if H is a bounded infinite set, then there exists some sequence made of distinct points of H which is always increasing or always decreasing.
Is H a subset of the real numbers? If so, then with a bounded set, you have the least upper bound and greatest lower bound. There must exist sequences in H that converge to the least upper bound and greatest lower bound. Then, there exist subsequences of each sequences such that the subsequences are monotone and converge to the least upper bound and greatest lower bound, respectively.
Yeah, H is a subset of the reals.
I don't follow your argument, though. Let's say H is the union of {1-1/n|n is a natural number} and {1+1/n|n is a natural number}. It's bounded by 0 and 2, but I need a sequence that is always increasing or always decreasing, rather, x_n>x_n+1 always or x_n<x_n+1 always. No such sequence converges to 0 or 2... the only way I can find such a sequence is if it converges to 1... I can't see how talking about the least upper bound or greatest lower bound helps me..
Yes - I'm just talking about the existence, guaranteed by theorems. If you don't have the particular theorems that I'm referring to, then just prove them - if you have an element that is not the least upper bound or greatest lower bound, you can find another element closer, and keep constructing it that way.
Um. I need the sequence to be strictly increasing or strictly decreasing, not monotone. I think that's our delimma.
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I've been working on the same stupid theorem in Analysis for the past three weeks. I'm probably just being dumb and missing something obvious, but it's been really difficult... I'll type it below for you guys, at the risk of revealing my relative inexperience at proof-based mathematics.Show that if H is a bounded infinite set, then there exists some sequence made of distinct points of H which is always increasing or always decreasing.
Is H a subset of the real numbers? If so, then with a bounded set, you have the least upper bound and greatest lower bound. There must exist sequences in H that converge to the least upper bound and greatest lower bound. Then, there exist subsequences of each sequences such that the subsequences are monotone and converge to the least upper bound and greatest lower bound, respectively.
Yeah, H is a subset of the reals.
I don't follow your argument, though. Let's say H is the union of {1-1/n|n is a natural number} and {1+1/n|n is a natural number}. It's bounded by 0 and 2, but I need a sequence that is always increasing or always decreasing, rather, x_n>x_n+1 always or x_n<x_n+1 always. No such sequence converges to 0 or 2... the only way I can find such a sequence is if it converges to 1... I can't see how talking about the least upper bound or greatest lower bound helps me..
Anyone else taking the Putnam this year?I'm nervous. It's going to be my first.
I've looked over various Putnam problems (with their solutions handy), but I've never actually taken the test. I should look into it. I probably wouldn't solve any of them, but it'd be fun to try.
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you can export as a wav in Finale 06.
Ha, I'm dumb. I found the option under Save Special.
I'll post a recording asap.
EDIT: http://steben.noplaceforatoaster.com/music/kotr.mp3
There you go. Unfortunately, it has more than its share of pops and crackles... I'm not sure how to fix the problem, but you can tell what it's supposed to sound like now.
EDIT EDIT: Okay, now it sounds better. Woo.
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I've been working on the same stupid theorem in Analysis for the past three weeks. I'm probably just being dumb and missing something obvious, but it's been really difficult... I'll type it below for you guys, at the risk of revealing my relative inexperience at proof-based mathematics.
Show that if H is a bounded infinite set, then there exists some sequence made of distinct points of H which is always increasing or always decreasing. -
Y'know, the original was never high on my list of favorite themes from Final Fantasy games. Your arrangement is freaking awesome, though... something I'd love to play myself. I especially like having the beginning portion being similar to the original version, then breaking into a jazz style for the rest of the song.
The only issue I'd have is the ending is very... underwhelming. I'd prefer ending the piece on more of an upbeat note than what you've got there. Perhaps at the end of the section at around 3:15, you could transition back into something like what you've got at 2:28, and go for a big finish at the end of that phrase? Or maybe you could just finish it up at 3:01ish. Just a thought, anyway.
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http://steben.noplaceforatoaster.com/music/
I am done, folks. I feel.. as if I'm a more complete person now. Or something! I dunno.
Unfortunately I don't have a MIDI or other form of recording to showcase the final version of this arrangement, because Finale refuses to properly convert the piece into MIDI format. (The percussion is screwy when I do that... perhaps I'll get a version with just the winds up.) Ideally I want an MP3, but that's a feature found in Finale '07, and I have '06. We'll see if I can't work something out, because I'm sure the majority of you just want to know what it sounds like, and have no plans to get a marching band to play it.
Thanks guys, especially to Rainman DX. I think it's time I got started on homework for class tomorrow... I've kind of been putting it off to get this finished by the end of the weekend.
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I hate math in all forms, although imaginary numbers are easy, THEY ARE POINTLESS AND MAKE ME ANGRY AND TYPE IN CAPLSOCK
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I'm on the final stretch of finishing this stuff. I did something weird with the key in the middle section (right after the 3-3-2-3-3-2 pattern part), which I'm trying to undo, since it sounds dumb now.
Also, KOTR lyrics!
Na na na...Don't worry, do your best
It's picnic time, feel so good
A lovely afternoon
Then a wild midnight, yeah
Rolling it all forward, I love you, always a smile for you
It's a love moon just for you, hey so! You gotta keep going
Compression, compression
Matching T-shirts
Hand-knit mufflers
A heart-warming crowd milling about
Soak up the joy! Say goodbye (bye-bye)
Let's all roll forward, give it all you got
On a day like this let's dance and sing, I've got the leading role
It's my way, it's my way
*Na na na na na na na na na katamari damashi
Na na na na na na na na na katamari damashi
Na na na na na na na na na katamari damashi
Na na na na na na na na na katamari damashi
Drunk on feelings of peace
Yearning for the twinkling heavens
It's wonderful, that head
The deafening clamor of the festival
This is just like the big bang, I'm painting myself the color of you
If you need a reason, I just want to party
I'm rolling on, I'm rolling on
* repeat x 2
Source: http://www.chudahs-corner.com/lyrics/index.php?catalog=COCX-32760&id=4
EDIT: This game does not endorse drug use in any way, subtle or otherwise. Nope.
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Never heard of it. But now I know. Thank God for Bahamut and Wikipedia.
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This topic is back and badder than ever.
Here's the question I have for you kids. In Intro to Topolgy, we were asked if the intervals (0,1) and (0,1] were homeomorphic, that is, if there is a bijective continuous function f:(0,1)->(0,1] whose inverse was also continuous.
The problem was solved by talking about continuity - assuming such a function exists, and coming to a contradiction from its continuity. Therefore, they weren't homeomorphic. But what I'm wondering is, is there a bijection between the two spaces, regardless of continuity? I want to say no, but perhaps someone here can think of one?
Well, I can't explicitly construct one, but one can talk about cardinality. The cardinality of [0, 1] = the cardinality of the real numbers (which is uncountably infinite). The cardinality of (0, 1) = [0, 1] - {0, 1} is also equal to the cardinality of [0, 1] by cardinal arithmetic. Similarly, the cardinality of (0, 1] = [0, 1] - {0} is also the cardinality of [0, 1]. Now, by definition of cardinality, two sets have the same cardinality if there exists a bijection between the two.
Fair enough. I've never heard cardinality be defined that way, but it certainly makes sense. And now that I'm thinking about it, I guess we want there to be a bijection intuitively anyway. We'll let f-inverse(1)=1/2, and let the inverse function map the rest of (0,1) evenly on either side of 1/2. If that makes any sense...
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This topic is back and badder than ever.
Here's the question I have for you kids. In Intro to Topolgy, we were asked if the intervals (0,1) and (0,1] were homeomorphic, that is, if there is a bijective continuous function f:(0,1)->(0,1] whose inverse was also continuous.
The problem was solved by talking about continuity - assuming such a function exists, and coming to a contradiction from its continuity. Therefore, they weren't homeomorphic. But what I'm wondering is, is there a bijection between the two spaces, regardless of continuity? I want to say no, but perhaps someone here can think of one?
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Get a tutor. The vast majority of math professors range from mediocre to crappy teachers (at least at my school), and don't understand how to explain math to someone who's not naturally mathematically inclined. I'm a math major, yet for over half my math classes so far I've pretty much just taught myself everything I need to know from books. (Granted, that's getting a little bit harder now that I'm taking Senior-level classes, many of which don't have books.)
However, if you get a good tutor (or make a friend in the class who knows what's going on), you can get that person to explain things to you in a way that you can understand. Of course, if you don't need math for your major, and you're struggling, then get out. No need to sweat out a difficult class that you'll never use that'll only hurt your GPA.
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Guys. Check back a couple pages, and you can see the score for the percussion parts that Rainman wrote back in the early summer/late spring.
I have a MIDI which combines my stuff and Rainman's percussion, but because of the way Finale notates stuff, and the way percussion music is actually read, there's no easy way (to my knowledge) to convert the written Finale part into a MIDI where the percussion instrumentation is correct. We're talking slide whistles instead of bass drums.
Anyway, my first priority in finishing this piece is to get it written correctly. I have it all in a Finale file right now, but I lost all my articulations when converting from Noteworthy to MIDI back to Finale. Also, there's some tweaking to the overall arrangement I need to do.
Once I'm happy with the written arrangement, I'll publish the score and some sort of recording here, and if you like it, you can PM me and I'll send you the individual parts. (I'd post the parts themselves, but I'd like to have an idea of who's playing my arrangement.)
Also at that point, I'll look into finding someone who might want to take the arrangement and create a synthesized verison for OCR/VGMIX/ThaSauce submission, since getting a marching band to create a decent recording of the piece that I'd have permission to submit to any of those places would be difficult. (I'll look into AU Marching Band, but even if we play it, the chances of us recording it and allowing me to submit it are slim.)
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School's kicking my butt. In additon to all my performing groups (symphonic band, marching band, men's chorus, low brass studio), I have three maths and a music history to worry about. Bleh. However, I don't have a football game to worry about this weekend, so I plan on installing Finale and transfering the song over.
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Sorry for the lack of updatage. You should have sent me a PM yelling at me, Rainman.
Here's the deal - director of bands here at AU has ignored my email about playing this piece this fall, so I guess it was an empty suggestion. I'm kind of annoyed, but not terribly surprised.
My birthday is Saturday, and I'm hoping to get Finale from my parents. If not, I'm going to buy it myself. Time to get caught up with the times.
I'm really not happy with the instrumentation, so I'm going to rewrite it once I get Finale. Rather than just trying to write out the whole thing, this time I'm going to start with a condensed score, so I'll have a reference when assigning parts to different instruments
I'm hoping to finish this up before the thick of football season, so people who requested copies for their bands can play it in the stands. Depends on the difficulty of my classes this semester, I guess.
I apologize for taking so freaking long with this... I think it's been half a year since I started. I've been distracted this summer with work and another sideproject of mine. The arrangement will be finished, but not before I'm happy with the results.
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Oh, and about AU's drumline... I think I remember hearing something about them being really young this year. I dunno, though. I've been away from the whole band scene all summer, so I only hear bits and pieces.
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Please post sheet music.
QFT
This just came up in iTunes. I don't remember if I listened to it when I first downloaded it (I must have..), but I'm really digging this. I'm a mediocre piano player, but I always love trying out stuff like this anyway. I have a simplified version of klutz's 600 AD in Piano memorized.
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Kthx.
My plan is to order Finale Academic, and redo the music I did in Noteworthy in Finale, then combine that with the drumline stuff that Rainman DX was awesome enough to arrange. Once I've done that and have a final version, I'll definitely send you a MIDI if you want to make a good sounding version. I'll send you a PM. (Hopefully I'll have it done by mid July... depends how long it takes me to get Finale I guess.)Could somoene post a midi? I wanna stick it through reason and make it sound slightly more real.If I'm on holiday It's not my fault.
Whatever. If you're on holiday I'll hate you forever.
(omg jay slash kay you're a cool guy for offering)
Louie's Rush for pep band (from Sonic Rush)
in Post Your Game ReMixes!
Posted
So, been playing a lot of Sonic Rush lately. Pretty fun, and I'm really digging the music.
Those who've played it may have noticed the similarity of the Water Palace music ("Back 2 Back") to the bane of many pep bands, "Louie Louie". Well, it's my bane, anyway.
So, I've spent way too much time this weekend trying to adapt Hideki Naganuma's version of Louie Louie for marching band (adding in a bit of the title theme, "A New Day", as well). I've sort of got what I want for the wind parts, notewise. Listen to it below.
Clips of original songs for reference:
http://steben.noplaceforatoaster.com/wip/louiesrushref.mp3
My WIP:
http://steben.noplaceforatoaster.com/wip/louiesrush%2010_29.mp3
Right now it's really falling flat of capturing the energy of the original. I'm chalking that up to the fact that I have no articulations, dynamics, or percussion at the moment. I hope! However, let me know what you think of what I've got so far. (I'd post a WIP score, but I know that the ranges on a lot of the instruments aren't exactly realistic... I don't quite have ranges memorized for non-low-brass instruments yet, so I have to check them against a reference I have. I'll post a score hopefully later in the week.)
This is going to be my third addition to a collection of video game songs I'm adapting for marching/pep bands. (The second is the Metal Mario theme, which I haven't put up a WIP for yet.) My goal is to arrange a bunch of them by the time next fall rolls around, so you guys who are in marching bands can download PDFs of the score and individual parts, and can convince your band to play some video game music at football games (or basketball or whatever). You can check out my site where I've got an arrangement of Katamari on the Rocks already posted, below.
http://steben.noplaceforatoaster.com/music/
Hope you like what I've got so far!