Part of their project is to implement a numerical simulation of their forest fire.  I couldn’t let them have all the fun, so below is an example of my version of the simulation in MATLAB.  I have to hold off on posting the code until after they have handed in their project.

In the graphical representation of my simulation, green represents an unburnt tree, black is burnt and red is currently on fire.  The fire lasts for exactly one time step.  I also implemented a 3-D version, where a height of 1 is unburnt, 2 is on fire, and 0 is burnt.  I’ll confess to having way too much fun with this.

I have used a 200×200 lattice with p = 0.5.

Here is a sampling of what is tickling my fancy this morning (Did I actually just say that?)

A student clicked a link on their homework labeled, “Ask My Instructor a question”.  I am sent a link to their problem and they have a chance to type a message to me regarding the problem.

This problem was sent to me,

with the message:

“Help having trouble with this one I don’t understand how to simplify”

So I walk them through the problem in the following way:

We begin by inverting the second fraction and changing the division to multiplication (using the rule that to divide fractions we “invert and multiply”):

Now, we factor each numerator and denominator. We begin by pulling out all the GCFs (greatest common factors):

I can factor the trinomial in the first denominator further,

We now cancel all the common factors:

Multiplying straight across, this leaves

Let me know if this makes sense.

I have say to that I am really enjoying the new equation editor in Word 2007 because it allows me to do just about everything from the keyboard.  For example, I can insert the multiplication “dot” by simply typing the LaTEX form “\cdot” and Word 2007 immediately replaces my text.

The other surprising feature I discovered today was the ability to use standard font formatting such as highlighting and striking out.

Now, off to class…

Feel free to sing along to the tune of “Pop Goes the Weasel” as you read the quadratic formula below:

Speaking of which, I introduced my algebra students to the fact that there exist some rather lengthy formulas for solving cubic and quartic equations. In fact, the four roots of the quartic equation,

can be found in four individual equations over at Planet Math. I dare you to make your algebra students memorize those for the next exam.

In the current project, three teams are developing a formula to calculate the number of hours of daylight that a given point (of latitude) receives for each day of the year.  I’ve introduced the problem and laid out some notation and assumptions to guide them along.  Here are some snapshots from the board on Monday.  The students asked that I document these notes since their copies did not do justice the concepts they were supposed to represent.

Situation: Working along in a spreadsheet and you have the format all set just they way you like it, columns and rows merged, widths perfectly adjusted and you want to insert a table of information.  What you could do is just re-align everything that you just spent hours, if not days, getting just so.  You could make new columns, new rows, adjusting everything.

New Solution: Create the table somewhere out of the way, either on another sheet in the workbook or somewhere way off to the side.  Then copy the region and paste it as a “Picture Link”. 

In Microsoft Excel 2007, after copying the desired region, on the Home tab of the ribbon, click the down arrow just below Paste and select As Picture > Paste Picture Link.

In Microsoft Excel 2003, copy as usual, then while holding shift, select Edit .. Paste Picture Link. 

Now you have an image that you can move around on the spreadsheet anywhere.  By using the Picture Link  you can also update the “out-of-the-way” table and it will update in this picture, as well.

By the way, there is a “Camera” tool in Excel that will also allow you to do the same thing.  Here’s a demo video of the Paste Picture Link tool.

HT: Joel (Father-in-law)

She realized there was a problem when the only sound the phone would make was when it rang.  It would not make any noises and she could not talk to anyone over the phone.  Luckily, she could still communicate with the world through text messaging, so I knew that she wasn’t laying in a ditch somewhere unable to speak when she called me.

We diagnosed the problem when she got home:

How to removed a broken headphone plug from the headphone jack?

Solution:  Cut a piece of a straw about 1 1/2 inches long, then cut it length wise in half.  It is important to note that the phone jack is not a standard headphone plug, but smaller so if you are attempting to use this technique to extract a plug in your mp3 player or other phone, you may need to use more of the straw than just half.  Also, if you use this technique, I take no responsibility for the outcome.  It worked for us, but try it at your own risk.

Now, roll up the straw and insert into the jack to protect the internal parts from the super glue.  Take a tooth pick and douse it in super glue and insert into the jack.  I actually tried this whole technique a couple of times and didn’t get it to work until I used a significant amount of super glue.  Once inserted, I allowed it to set and yanked it out.  Ouila!!

EXTRACTED!!  Woohoo!  It now works like a charm.

On this blog, I have a LaTEX rendered which allows me to enter equations, even though it’s been a while since I’ve bothered to post anything much less something involving typesetting mathematics. So, in essence, besides pointing out the fact that the blogging capability exists in Word 2007, this post is to test image and equation posting from Word 2007.

I have been impressed with the new equation editor in Word 2007. It doesn’t reach the ease of use level (at least for me) of simply typing the LaTEX syntax, but it is quicker than in older versions of Word. It’s quicker because I use the keyboard for almost everything and I can just access “most” of the features I need straight from the keyboard quickly and easily, without having to remember a ton of keyboard shortcuts.

Just for kicks, here are a few samples:

UPDATE: Apparently these equations did not get posted either as images or anything else…. (10/13/08)

And here is a random picture that is on my hard drive and I have no idea why. A little formatting was added in Word 2007. It seems that this is not as useful as the picture insert tool in Windows Live Writer, since I am unable to simply link to a source picture and insert thumbnail. I only appear to be able to insert the picture as a whole.

UPDATE: Formatting carried through as expected. That’s a good thing.

Sciencedebate2008.com:

The Story

In November, 2007, a small group of six citizens - two screenwriters, a physicist, a marine biologist, a philosopher and a science journalist - began working to restore science and innovation to America’s political dialogue.  They called themselves Science Debate 2008, and they called for a presidential debate on science.  The call tapped a wellspring of concern over the state of American science. 

Within weeks, more than 38,000 scientists, engineers, and other concerned Americans signed on, including nearly every major American science organization, dozens of Nobel laureates, elected officials and business leaders, and the presidents of over 100 major American universities.  See who here.  Among other things, these signers submitted over 3,400 questions they want the candidates for President to answer about science and the future of America. 

Take a look and tell me what you think.

Algebra, says Devlin, is a language, a very precise language written in symbols, and it’s everywhere: in nearly all electronic devices, every statistic and each Internet search engine - and, indeed, in every train leaving Boston.

"You can store information using it. You can communicate information using it," Devlin said. "Google has made billions capitalizing on algebra."

Yet our schools don’t always do a very good job teaching it, Devlin said. Instead of showing students the possibilities and beauty algebra offers, they ultimately steer frustrated and bored students away from math and the 21st century careers that use it - the opposite of the intended result.

…

Algebra, by the dictionary’s definition, is essentially abstract arithmetic, letters and symbols representing relationships between groups, sets, matrices or fields. It’s a way to find a piece to a puzzle using the pieces you already have in place.

It comes in very handy for engineers, financial analysts and sociologists, not to mention World of Warcraft video game players, some of whom use algebraic formulas to decide which weapon is more effective under certain circumstances - perhaps another hook to lure unsuspecting teens into seeing the useful side of algebra.

…

Laptop computer. The computer is just an implementation in electrical circuits of a special form of algebra (called Boolean algebra) invented in the 19th century. Ordinary algebra is used to design and manufacture computers, and is at the heart of how to program them.

Cell phone. A cell phone is a particular kind of computer. An important feature of cell phones is that your phone receives all the signals sent to every cell phone in the region, but only responds to signals sent to your phone. This is achieved by using signal coding systems built on algebra.

Parking cop. Today’s parking enforcement officers may carry equipment connecting them directly to a central vehicle database that registers your parking fine before you get back to the car and see the ticket on the windshield. Without algebra, such a system could not exist.

Hybrid car. Modern cars often come equipped with GPS, a highly sophisticated system that is designed using enormous amounts of mathematics that builds on algebra.

Delivery truck. Large retail chains use mathematical methods to determine the routing and scheduling of their delivery trucks; algebra is fundamental to those methods.

Stoplight. These days, stoplights are centrally controlled by computers, so there is even algebra involved in turning the light from red to green.

IPod. This is a math device in your hand. The iPod stores music using sophisticated mathematics built on algebra. And the iPod shuffle mechanism uses regular school algebra to order your songs randomly.

…

Even though it is a very pro-algebra article, my favorite quote was by an unknown source:

"Algebra … the intensive study of the last three letters of the alphabet."

The first problem I faced was installing a network printer so that it would be available to all users on that machine.  This is probably a minor problem for seasoned IT pros, but since I am not one, it took some investigating.  I learned that local printers are installed automatically for all users, while network printers are associated with user profiles.  This means that when you install a network printer it is only available to the user profile that you used when installing.

The solution is to install the network printer as a local printer.  In other words, go to Control Panel .. Printers.  Click "Add a printer".  Select that you want to install a local printer.  At this point you will create a new port, using a Standard TCP/IP port.  You’ll need to have the IP address of the printer to do this and you’ll also want to have the drivers handy.

Since it is installed as a local printer it will now be available to all users when they log in.  The bug I still haven’t worked out, though some of you may have an idea, is that even though I have selected it to be the default printer in my profile, it is not necessarily the default printer for other users.  If is the first printer installed, no problem, but otherwise it is not the default for other users.