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 http://CalcPage.tripod.com (1988 – 2008)
With Chapter 9 finished our 8 Week Trig Boot Camp studying Polar Graphs and Vector Arithmetic. We found Polar Coodinate systems to be most useful when plotting none functions: Roses, Cardioids and Lemniscates. We then went on to adding, subtracting and multiplying 2D and 3D Cartesian Vectors! Remember: Dot Products and Cross Products are not the same! After Midterms we played with Chapter 10: Conic Sections! We talked about General vs. Standard Form Conics for Parbolas, Ellipses and Hyperbolas! We even used Polar Coordinates when rotating conics. We played around with Parametric mode too. Gotta love those Parabolic Mirrors, Elliptical Planet Orbits, Whisper Gallery, LORAN and Projectile Motion problems!
XTRA CREDIT FILKS RUBRIC (1 video = up to 5 bonus points):
1) Use a recognizable tune.
2) Karaoke entire song changing up the words (about STEAM).
3) You are Singing, Dancing or Playing an instrument.
4) You upload your video to YouTube and provide the url.
5) YouTube Description includes the lyrics.
XTRA CREDIT ARTICLES RUBRIC (up to 5 articles = 1 bonus point each):
We studied UNIT08 Advanced Integration Techniques and UNIT09 Special DiffEqus. These used to be two separate units, but now I just lump them all into UNIT08. We start with L'Hopital's Rule and the famous scene from Mean Girls. We're gonna need that rule soon. Then we go on to integrating inverse trig functions as well as exponential and logarithmic functions not necessarily of base e. We also covered trig powers, trig sub, by parts and partial fractions. Last, but not least, we worked with DiffEqus requiring these techniques such as Logistics! We played with Exponential Growth and Decay, Exponential Approach and Logistic Growth and Decay models. We solved these DiffEqus analytically as above and graphically using Slope Fields and Euler's Method with our own program for the TI nSpire we called eulern(). We're loving our class set of TI nSPire CX CAS Graphing Calculators from Donorschoose!
This month we tackled LAB06 which was all about iteration: for & while loops! Before we could start each project, the first thing we had to do was to decide when to use a for loop over a while loop. For loops are useful when you know exactly how many times you have to iterate. Watch out for that "off by 1 error!" In other words, there's 3 kinds of for loops: the one you want, the one that loops once too many times and the one that doesn't get to the last iteration you needed! Use a while loop when you need a Boolean to decide when to stop iterating, aka a sentinel. Again, there's 3 kinds of while loops: the one you want, the one that never starts and the one that never ends. Gotta hate those infinite loops. Watch those loop invariants! Don't forget to prime your while loops! We even played with our own iterator classes as well as java.math.BigIntegers and java.math.BigDecimals! BTW, we're loving our new cs50.io, aka c9.io, ide from the Amazon Cloud (AWS)! Don't forget about the Processing IDE! We just started using OpenProcessing online as they've just added Processing.js which is more compatible with Processing's IDE. The default mode is P5.js (javascript) but we switch to Processing.js (java) and all is well! So, we're computing in the cloud even when we use Processing! IDK, is OpenProcessing is on AWS or the Google Compute Platform (GCP)?
RECOMMENDED AP COMPSCI REVIEW:
CRIB SHEET (given during exam) REVIEW BARRONS BOOK (see me) REVIEW BARRONS ONLINE REVIEW APCENTRAL (past FRQs) REVIEW EDX REVIEW MOOC01
We un-boxed all the stuff we got from BOCES and Donorschoose and figured out how to boot up 1 RPI per student. We are playing around with these micro-board PCs as replacement PCs at home until our next meeting.
USB Power Supplies
NOOBS Sims
HDMI To VGI Converters
DECEMBER UPDATE: (meeting 3)
We downloaded the latest pelicanHPC ISO and burned a DVD for each of us. Then we booted our PCs from the DVD drive and ran openMPI from RAM. We used flops.f to test our "clusters." flops.f is a FORTRAN program that uses mpirun to stress a cluster by calculating PI using reimann sums for 1/(1+x^2) from a=0 to b=1.
BTW, I call our PCs "clusters" since they have quadcore processors and openMPI can run on multicore just as well as on a grid. We can't set up a grid based (multinode) Linux cluster anymore as we are not allowed to setup our own DHCP server anymore. We got about 2 GigaFLOP/s per core, so 8 GigaFLOP/s per PC. If we could setup our own DHCP server, we'd get 100 cores running in parallel for about 200 GigaFLOP/s!
Compile:
mpif77 -o flops flops.f
Execute multicore:
mpirun -np 4 flops
Execute multinode:
mpirun -np 100 --hostfile machines flops
Enter pelicanHPC as a our first solution! We demoed an old DVD we had to show how to fire up the cluster. Our experiment demonstrated that we could not boot the whole room anymore, as we used to, as PXE Boot or Netboot requires we setup our own DHCP server. When you boot the DVD on one PC, it sets up a DHCP server so all the other PCs can PXE Boot the same OS. However, our new WimpDoze network uses its own DHCP server. These two servers conflict, so we cannot reliably connect all the Worker bees to the Queen bee. We can't setup grid computing or a grid cluster, but we can still setup SMP. In other words, boot up a single PC with the pelicanHPC DVD and run multicore applications on all the cores on that one PC.
So, here's your homework. Download the latest pelicanHPC ISO file and burn your own bootable DVD. Don't worry if your first burn doesn't boot. You can use that DVD as a "Linux Coaster" for your favorite beverage the next time you play on SteamOS. If you can make this work at home, try to run Hello_World_MPI.py from John Burke's sample MPI4PY (MPI for Python) code.
NOVEMBER UPDATE: (meeting 2)
See below for our Raspberry PI project. We have been waiting for funding for some extra hardware from DonorsChoose and we just got it! Yeah! In the mean time we're playing with PelicanHPC and BCCD DVDs to see how openMPI works so we can set it up the same way on our new Linux Cluster.
OCTOBER UPDATE: (meeting 1)
We've decided to make a Linux Cluster out of Raspberry Pi single board computers! Our school district has been kind enough to purchase 25 RPIs plus some USB and Ethernet cabling, so now we just need some power supplies, routers and SD cards. So here comes DonorsChoose to the rescue! We started a campaign to raise the money to purchase all the remaining equipment from Amazon!
What we want to do is to replace our Linux Lab of 25 quadcore PCs, where we used to do this project,with 25 networked RPI 3.0s. The Raspbian OS is a perfect match for our project! Raspbian is linux based just like our old lab which was based on Ubuntu Linux. Also, python is built-in so we can just add openSSH and openMPI to code with MPI4PY once again! With the NOOB SD card, we start with Linux and python preinstalled!
Once we get all the hardware networked and the firmware installed, we can install an openMPI software stack. Then we can generate Fractals, MandelZooms, POV-Rays and Blender Animations!
So, what's all this good for aside from making Fractal Zoom or Shrek Movies?
SETI Search
Econometrics
Bioinformatics
Protein Folding
Beal Conjecture
Scientific Computing
Computational Physics
Mersenne Prime Search
Computational Chemistry
Computational Astronomy
Computer Aided Design (CAD)
Computer Algebra Systems (CAS)
These are but a few examples of using Computer Science to solve problems in Mathematics and the Sciences (STEAM). In fact, many of these applications fall under the heading of Cluster Programming, Super Computing, Scientific Computing or Computing Science. These problems typically take too long to process on a single PC, so we need a lot more horse power. Next time, maybe we'll just use Titan!
