Scientific Computing
Science, Technology, Engineering, Arts & Math
Teaching & Learning Math & Science with Technology
Graphing Calculators, Numerical Methods, Computer Algebra Systems & Linux Clusters
Why Shadowfax? Our cluster is so fast that we named it after the Lord Of The Rings character!
Website once known as CalcPage.tripod.com (1988 – 2008)
As you can see, we had a full house today! Wow, thanx guys for the great turnout right before the holidays and all the trouble shooting you did! BTW, this meeting took the place of both meetings for this month as I had to cancel two weeks ago.
Anyway, we tried booting a single node of the cluster from a student station (AMD Athlon 64bit dual-core) using a pelicanHPC 64bit 2.1 CD. We ran the pelican_setup script and compiled flops.f
mpif77 -o flops flops.f
and ran it stressing only one core to see how many MFLOPS we could get
mpirun -np 1 --hostfile tmp/bhosts flops
and we got nearly 400 MFLOPS. Then we tried 2 cores and got a bit over 750 MFLOPS. Try as we might, we could not get two or more nodes of this type to boot up via PXEboot using the school Linux network. Then we tried a cross-over Ethernet cable and got 4 cores running flops up over 1500 MFLOPS! We tried the same thing with the 2 new Intel Xeon 32bit dual-core servers we just inherited. The difference here was we used a pelicanHPC 32bit 2.2 CD which compiles and runs flops automatically for a single node. Also, we got PXEboot to work over the school Linux network and got 4 cores running over 2200 MFLOPS!
We also tried hooking up some laptops to a private router via pelicanHPC 2.2 and mixed in some of the student stations. This worked well since it was off the school network. At one point we had 4 nodes running 8 cores at about 3400 MFLOPS. Thanx for bringing in your own laptops, routers and cables! Maybe we should get our own gigabit switches?
OK, so that's progress! I think we are sick of playing with the school network: public vs private, eth0 vs eth1, starting a DHCP server or not. So, the consensus now is to roll our own version of pelicanHPC (see research links above - last link is not HPC retated and is there just for fun). We'll remaster pelicanHPC without its own DHCP server to make use of the existing DHCP server on the public Windows network on eth0 since pelicanHPC seems to work best on eth0. Not to worry, pelicanHPC is based on debianLive which is supposed to be easy to remaster.
Let us proclaim it through out the land, our remaster shall be named shadowfaxHPC! OOPs, sorry to get all LOTRy there. Where's Gandalf when you need him?
WOW, this one is grand! Look what one of my students just did! Its mathematically correct and lyrically perfect, its got great piano, vocals, graphics and lyrics. This is a perfect example of a Calculus Carol, a Calculus Filk and a YouTube Production! In other words, it's got great production values and choreography! Enjoy:
As promissed, here's my preCalculus Carols SongBook! BTW, by preCalculus I mean any class before Calculus. I do you this songbook with my preCalculus class, but I also use it is other classes. I'm sure you could find one or two songs in here you could use in Algebra, Geometry or Trig.
What I did was, I added the "Oh Calculus, Oh Calculus" from my last blog post to my Calculus Carols SongBook. The "Program" song is now part of my preCalculus Carol SongBook. What follows are the remaining 11 preCalculus Carols in no particular order. I will include a 12th song here which is not a carol. It's a rap song recently written for me by my preCalculus students you may find amusing....
(1) Binomials! Binomials! (tune = "Jingle Bells")
Add and multiply!
Are the terms alike,
Or are they different?
Oh my!
Binomials! Binomials!
To multiply we toil!
Distribute the monomials,
Or multiply by FOIL!
(2) Exponents! (tune = "Jingle Bells") Exponents! Exponents! Powerful things! Raise you up, And root you down Are what logarithms bring!
Natural is e, Common is 10, E to the zero is one, Ten to the zero’s one again! To multiply, just add, To divide simply subtract, Be sure your bases match Or you’re on the wrong track!
Oh, Exponents! Exponents! Powerful things! Raise you up, And root you down Are what logarithms bring!
(3) Mathematics, My Favorite Subject! (tune = "Rudolf")
Mathematics, my favorite subject, is a very challenging class!
And if you ever take it, you will learn to love it fast!
In it we learn equations: Linear, Quadratic and more….
We always do our homework, it’ll never become a bore!
For some future college day, your professor just might say,
“Students, with your minds so bright, solve this problem right tonight!”
Then you’ll use this background, that other students have missed,
With math you’ll solve the problem, and be named to the Dean’s List!
(4) Oh Number PI! (tune = "Oh Christmas Tree")
Oh, number PI,
Oh, number PI,
Your digits are non-ending!
Oh, number PI,
Oh, number PI,
No pattern are you sending?
You’re three point one four one five nine,
And even more if we had time!
Oh, number PI,
Oh, number PI,
For circle lengths unbending.
Oh, number PI,
Oh, number PI,
You are a number very sweet!
Oh, number PI,
Oh, number PI,
Your uses are so very neat?
There’s 2 PI r and PI r squared,
A semi-circle and you’re there!
Oh, number PI,
Oh, number PI,
We know that PI’s a tasty treat!
(5) On The First Day of Math Class (tune = " On The First Day of XMas")
On the first day of math class,
My teacher said to me,
“The assignment is on page three!”
On the second day of math class,
My teacher said to me,
“Get xtra help! The assignment is on page three!”
On the third day of math class,
My teacher said to me,
“Are there any questions? Get xtra help! The assignment is on page three!”
On the fourth day of math class,
My teacher said to me,
“We’ll have a test on Friday. Are there any questions? Get xtra help! The assignment is on page three!”
On the fifth day of math class,
My teacher said to me,
“Please study hard! We’ll have a test on Friday. Are there any questions? Get xtra help! The assignment is on page three!”
(6) Rudolph the Statistician. (tune = "Rudolph")
Rudolph the statistician, had a cool 83,
And if you ever saw him, he would be simulating!
All the other reindeers used to laugh and call him NERD!
They never let poor Rudolph play in any of their math games...
Then, one foggy Christmas Eve, Santa came to say,
“Rudolph, could you do a SRS and tell me what toys I should make?”
Then, how the reindeers loved him, generalizing his sample data!
Rudolf, the statistician, is the reason you get toys!
(7) Rudolph the Statistician 2 (tune = "Rudolph")
Rudolph the statistician
Sampled data everywhere!
Mean heights and heart conditions
Calculated with great care!
All the population
Living from coast to coast
Sought out his data samples
He would always give the most!
Then one foggy Xmas Eve
Santa came to say,
“Rudolph, with your pencil write,
What gifts I should bring tonight.”
Quickly, he polled the children,
And Rudolph shouted with glee,
“Stats did provide the answer:
Give Nintendos and Barbies!
(8) On The 12th Day of Math Class (tune = " On The 12th Day of XMas")
On the 12th day of Math Class, my teacher gave to me:
12 mean averages,
11 equations regressing,
10 graphs plotting,
9 surveys polling,
8 experiments failing,
7 random numbers,
6 crazy teachers,
5 preCalculus problems!
4 charts and data,
3 wrong assumptions,
2 assignments whinning
And a brand new TI-83!
(9) Oh Algebra! (tune = "Oh Christmas Tree")
Oh Algebra! Oh Algebra!
How lovely are your properties!
Oh Algebra! Oh Algebra!
How lovely are your properties!
They show us how to operate,
Our feeble minds they stimulate…
Oh Algebra! Oh Algebra!
How lovely are your properties!
(10) Jingle Algebra! (tune = "Jingle Bells")
Dashing through my text,
It’s really not complex!
But, if my mind runs slow,
It gives me lots of woe,
Oh, Oh, Oh!
I study Algebra.
My brain runs, I say, “Go!”
So much I do not know,
And so very far to go.
Yo!
Properties, Quantities,
Factors into play!
Points to plot,
I think a lot,
Success should come my way!
Rational n’ Radical,
Equations have a say!
Slopes and Lines,
I’ll make the time,
Math Power’s here to stay!
Yea!
(11) Conic Section Carol (tune = "God Rest ye Merry Gentlemen")
God rest ye merry ellipses
And hyperbolae too!
Parabolas and Circles,
All curves of degree two!
Degenerate and involute,
The mathematician’s toy,
Oh sections of conics and joy,
Conics and joy, etc.
Of symmetry and foci
And fun directrices!
Both smooth and sharply pointed curves
Can have some vertices.
To prove this Polar Mode
Is such a clever ploy!
Oh sections of conics and joy,
Conics and joy, etc.
(Rap) PreCalc Exclusive! (not a holiday tune = just rap it, dude)
Mike and Nik, chillen in PreCalc,
Got mad work, solvin’ them problems out.
Put me to the test, I solve the best,
Don’t even front, we’re better than the rest!
Graphing that line, on my Ziggy 83,
Let’s take that test, you won’t do better then me.
Move your work, not the keyboard,
Mr. García might just slap you with a cord!
Get off your phone, this class is no joke,
Mr. García’s on FaceBook with a poke.
Homework, pre-test, a piece of pie,
That’s how it works if you want your grade high!
No Regents, but we still go hard,
Tryin’ get a 100 on my report card.
PreCalculus, is the best class,
All the other subjects can kiss my @$$!
Mr. García is the man,
Rather be here than playing in the band.
PreCalc 2011, we can pass right through,
Calc 2012, we’re ready for you!
My students gave me 2 more holiday filks, this time based on Chanukah tunes! The first one I'm adding to my "Calculus Carol Song Book" (see last blog post). The second one I'm adding to my "preCalculus Carol Song Book" which I will post next week, so stay tuned! I'm having my computing classes sing too. My AP Computer Science is singing Calculus Carols and my Computer Math is singing preCaclulus Carols. Enjoy!
OK, its that time of year again! These are my favorite filks. These songs are what got me filking in class in the first place. We take a recognizable holiday tune and change up the words so it has something to do with Calculus. We sing one song a day all December long for practice. Then, the last day before break we go Calculus Caroling all over the school, every period, bothering our favorite teachers! So, here's some of our favorite Calculus Carols in no particular order, hope you enjoy them. BTW, there's only 11 of them, I need a 12th one, so if you have something, please share! Oh, and the last one is really not a song, you'll see....
On the 12th day of Calculus, Newton gave to me twelve homework problems,
11 differential equations,
10 feuds with Hooke,
9 orbiting planets,
8 tides of water,
7 spectrum colors,
6 reflecting telescopes,
5 optic rings,
4 flying comets,
3 Laws of Motion,
2 refracting prisms
and an apple falling from a tree.
11) An Engineer’s Xmas!
There are approximately two billion children (persons under 18) in the world. However, since Santa does not visit children of Muslim, Hindu, Jewish or Buddhist (except maybe in Japan) religions, this reduces the workload for Christmas night to 15% of the total, or 378 million (according to the population reference bureau). At an average (census) rate of 3.5 children per household, that comes to 108 million homes, presuming there is at least one good child in each.
Santa has about 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming east to west (which seems logical). This works out to 967.7 visits per second. This is to say that for each Christian household with a good child, Santa has around 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the stocking, distribute the remaining presents under the tree, eat whatever snacks have been left for him, get back up the chimney, jump into the sleigh and get onto the next house.
Assuming that each of these 108 million stops is evenly distributed around the earth (which, of course, we know to be false, but will accept for the purposes of our calculations), we are now talking about 0.78 miles per household; a total trip of 75.5 million miles, not counting bathroom stops or breaks.
This means Santa’s sleigh is moving at 650 miles per second--3,000 times the speed of sound. For purposes of comparison, the fastest man made vehicle, the Ulysses space probe, moves at a poky 27.4 miles per second, and a conventional reindeer can run (at best) 15 miles per hour.
The payload of the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium sized LEGO set (two pounds), the sleigh is carrying over 500 thousands tons, not counting Santa himself. On land, a conventional reindeer can pull no more than 300 pounds. Even granting that the "flying" reindeer can pull 10 times the normal amount, the job can’t be done with eight or even nine of them---Santa would need 360,000 of them. This increases the payload, not counting the weight of the sleigh, another 54,000 tons, or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch).
600,000 tons traveling at 650 miles per second creates enormous air resistance—this would heat up the reindeer in the same fashion as a spacecraft re-entering the earth’s atmosphere. The lead pair of reindeer would adsorb 14.3 quintillion joules of energy per second each. In short, they would burst into flames almost instantaneously, exposing the reindeer behind them and creating deafening sonic booms in their wake. The entire reindeer team would be vaporized within 4.26 thousandths of a second, or right about the time Santa reached the fifth house on his trip.
Not that it matters, however, since Santa, as a result of accelerating from a dead stop to 650 m.p.s. in .001 seconds, would be subjected to acceleration forces of 17,000 g’s. A 250 pound Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by 4,315,015 pounds of force, instantly crushing his bones and organs and reducing him to a quivering blob of pink goo. Therefore, if Santa did exist, he doesn’t anymore!
