Modernizing the Mathematics Classroom - How we deliver Calculus

BTW, I've been talking about this stuff for quite sometime!  I'm a long time contributor to several forums: ap-calculus, ap-compsci and www.linux.net just to name a few.

For example, take a look at the following thread:
http://mathforum.org/kb/thread.jspa?forumID=63&threadID=1815581&messageID=6385533#6385533


and other threads I've contributed to:
http://mathforum.org/kb/profile.jspa?userID=32552
http://mathforum.org/kb/profile.jspa?userID=32552
http://www.knoppix.net/forum/profile.php?mode=viewprofile&u=16


Regards,

A. Jorge Garcia

calcpage@aol.com

New to the Blog-O-Sphere?

It seems that some of my readers find this format a bit confusing and hard to follow. Actually nothing could be farther from the truth! Just keep in mind 2 things:

(1) The most current posts are always at the top of the blog. So as to keep the web-blog current, the postings are listed in reverse chronological order. That way, if you check the blog often, you only need to see the top 1 or 2 posts to keep up to date without having to wade thru a ton of stuff you already read! If you are new to the blog, you really need to start reading from the bottom and work your way up.

(2) Also, there are usually several threads in a web-blog. In my blog, there’s this “General” thread of course. However, there are currently three major threads in addition to “General:” LinuxClusters, ScientificComputing and SmartBoards. There may be more topics in the future, but right now there’s just the three! As stated previously, these topics basically cover all the activities I’m involved with relating to teaching and learning with technology. Now, if you want to follow only one of these threads at a time, simply click on the topic you want to the left of your screen. That way, you can read all the posts, again from the bottom up, related to one thread at a time so you don’t get confused with all the threads seemingly all intertwined!

Hope that helps,

A. Jorge Garcia, calcpage@aol.com

A Few Clarifications

I’ve gotten some feedback that people are confused about what exactly ShadowFax and CIS(Theta) are. I don’t blame you since CIS(Theta) has referred to a cluster for several years and now it doesn’t!

Everything I talk about in this weblog now comes under the aegis of CIS(Theta) the “Computing & Information Sciences Thinktank.” In other words, everything I do in room 429 at Baldwin Senior High School relating to teaching with technology and learning with technology as well as setting up and using a Linux cluster is part of CIS(Theta) and is described in this blog.

So, the new Linux cluster could not be called CIS(Theta) any longer. We had a “rechristening” ceremony and renamed our cluster ShadowFax. However, technically speaking, this was not a rechristening as this cluster is comprised of all brand new hardware. Now, you may ask, where does the name Shadowfax come from? It’s a name taken from JRR Tolkein’s Lord of the Rings trilogy. ShadowFax is the Lord Of All Horses and Gandolf’s swift steed! Since, our new cluster is SO fast, what better name could we choose?

Hope that helps,

A. Jorge Garcia, calcpage@aol.com

Poor Man's Cluster - Step 1

Poor Man's Cluster - Step 1
Topic: LinuxClusters

Now, the next step is to choose your favorite Linux Distribution to install on the cluster.

There are several live CD distributions that came out in the early years of clustering to set up a Linux cluster by simply booting the CD!  Some of these include

http://clusterknoppix.sw.be/

http://dirk.eddelbuettel.com/quantian.html or http://www.quantian.net

http://bccd.cs.uni.edu/

http://idea.uab.es/mcreel/ParallelKnoppix/ (recently renamed Pelican HPC)

The cluster we setup last year was based on the QUANTIAN DVD and used the openMOSIX Linux kernel for load balancing jobs.  In fact, we installed this DVD to a Linux partition on every node.  In this way, the classroom could be used by teachers that needed Windows and those that needed Linux as each PC was setup to dual boot.  A nice bonus to using this distribution is that it included Octave and R.

We were unable to use the PVM or MPI libraries as we set up a second Linux network (each PC has 2 ethernet cards) that’s supposed to be isolated from the rest of the school.  However, to date, the tech dept has not been able to adequately isolate my room from conflicting DHCP servers.  Not the mention that we had several PXE server conflicts when we tried Parallel Knoppix.  The idea with Parallel Knoppix is to boot one CD on the master node, then all the workers PXE boot from there.

We used openMOSIX to good effect for several years.  For example, last year we made several plots of Mandelbrot fractals using code inspired by http://nullprogram.com/blog/2007/10 (see BCCD) and  http://nullprogram.com/blog/2007/10 (see Mandelbrot Set).

This year we had a problem.  First, the openMOSIX project closed.  Second, we suddenly found ourselves with new 64 bit CPUs!  So, we had to start from scratch!  More on that next time.

Good Luck,

A. Jorge Garcia, calcpage@aol.com, http://calcpage.tripod.com, http://www.zazzle.com/cistheta2008, http://cistheta2007.deviantart.com, http://www.youtube.com/cistheta2007

Cool Final Projects!

Now that we have the go ahead for next year’s Calculus Research Lab, I decided to have my AP Calculus students try out a little Scientific Computing this year as a final project.  I introduced Octave, a Linux FOSS version of MATLAB released under the GNU Public License. 

Our final project is going very well even as we speak!  What’s really cool about Octave is that the primary data structure is a matrix.  You can work with a matrix of integers or reals of any dimension.  You can have a rectangular matrix: 2x3, 4x2, etc.  You can work with square matrices: 2x2, 3x3, etc.  You can even represent a row vector as a matrix: 1x4, 1x5, etc.  You can easily represent column vectors too: 3x1, 5x1.  And of course, you can represent a single number: 1x1.  We can add, subtract, multiply and transpose any of these matrices.  We can find the determinant of a matrix and its inverse.

First we talked about vector arithmetic (vector sums and differences, dilations, scalar dot products, vector cross products, triple scalar products, angles, areas and volumes in R^2 and R^3).  Then we kicked it up a notch with Matrix Algebra (systems of equations, linear programming and encryption).  Now we are doing Symbolic Calculus using the symbols library from Octave Forge!  We even threw in some plotting and programming our own user-defined functions! 

In fact, we used Octave as a scripted language by writing text files such as vector.m that we made executable (chmod 755 vector.m).  As long as the first uncommented line of the file read #!/usr/bin/octave –q, the octave interpreter would be invoked automagically!  We also used diary files such as vector.txt to print out the output of a given script.

My AP Computer Science students learned OOPs programming with Java this year.  So, their final project is learning OOPs in C++ (GNU GCC g++)!

Good Luck,

A. Jorge Garcia 

calcpage@aol.com

Died and Gone to Heaven!

I’m taking the show on the road this summer!  At Nassau Community College, the Math Dept is in Cluster B.  Cluster B is a three story building, more of a tower really, with offices and classrooms. In the center of the tower is a large lecture hall taking up space on both the second and third floors.  I’ve taught my summer courses in there before and it was very nice as lecture halls went.  We could seat 125 students, there were comfortable chairs, tables and balconies!  The instructor would teach at the front of the room which was a pit on the second floor with overhead projectors and plenty of chalk boards and marker boards (and A/C).  The only problem with this room was that it was getting a bit old (several chairs and tables were in disrepair) and there was no technology to speak of except for my trusty TI-84 overhead!

This room, B218, has undergone a huge renovation for this summer.  This room has become a multimedia center.  All the tables, chairs and carpeting have been replaced.  All four walls have 50” HD LCD monitors.  The front of the room has a huge marker board (10’ high x 20’ wide) with a large pull-down PC projection screen and two PC Projectors.  The teacher’s desk has a PC with BlueRay DVD player, audio system and control system that lets you integrate all of this into your lessons!

I installed Smart Notebook 10 on my laptop as well as VTI and BlueTooth so I could use the Smart AirLiner Slate.  I hooked up my laptop to the media control system and now I am in Nirvana!  My AirLiner lessons can now be projected on the PC projector and all 4 HD monitors.  I can play videos, I can record my classes and I can see what I write!  From the teacher’s desk, I cannot see the HD monitors on the 4 walls ahead of me (oriented toward students facing me).  Neither can I see the PC projection behind me.  However, I have my laptop and AirLiner in front of me, so I can see what I write on the laptop screen – almost like having a tablet PC! 

At Baldwin, I did not have this kind of feedback.  To see what I wrote I’d have to look up at the PC projection at the front of the room as I wrote from the back of the room.  I got used to this, but it took a lot of practice!

Hoping you got some food for thought,

A. Jorge Garcia, 

calcpage@aol.com