Monthly Archives: December 2005

Differential Equations

I just have to say that one of the things I have been most looking forward to teaching has been Differential Equations. Actually, I am particularly fond of Numerical Analysis but Wayland Baptist University does not offer that class as part of its regular program, even though I did have the opportunity to teach it as a Special Topics course a few years back. Anyways, diff. eq. has somehow evaded me to this point in terms of being my class. When I first started teaching at Wayland, another professor was teaching it. He retired but was asked to return after we lost one of our faculty, our Statistician. Diff. Eq. was offered to him to give him something besides all freshman level stat courses. Being on a two year course rotation has meant that I’ve had to wait to teach the course for which I am most qualified. I really look forward to this semester for that reason.
I am a bit worried that, since it is my favorite course, I won’t be able to finish as I am so often sidetracked by over explanation. In fact, even now I am torn as I am preparing my lecture notes. Do I cover all the simple analytical techniques for first order systems such as separable equations, exact equations, linear (integrating factors), special integrating factors (to convert to exact), homogeneous equations, linear coefficients, and so on and on? Then, do I include a wealth of numerical methods for solving such as Euler, Improved Euler, Backwards Euler, Runge Kutta, Taylor series methods, and so on and on? How much emphasis is placed on existence and uniqueness of solutions? How much time should I spend on the development of the models themselves? It’s all so good!

Mathematical Blunder #3

Think numbers not dots!

Problem: (from eon)

A simple little puzzle. Suppose you are given two ordinary 6 sided dice. Is it possible to put the numbers 0-9 (with repetition) onto the faces of both dice, such that using both dice you can display all the days of the month i.e. 01 – 31 .

My Response:

Can’t be done.

My reasoning is as follows. Each of the dice must have a 1 and 2, in order to denote 11 and 22. This leave 4 spaces on each die, which in order to denote 01 – 09, we must put a 0 on each of the dice. This leaves 3 space on each die, which if we only but the remaining numbers 4 – 9 (7 total), will not fit in the remaining six places.

Is there a more elegant proof?

I am wrong. It can be done. So can anyone figure out why I am wrong? No cheating by checking out the response by tpc.

Latest Marsenne Prime Found

Distributed computing enjoys prime success – ZDNet UK News

A Central Missouri State University team using more than 700 computers has found the largest prime number so far, a gargantuan 9,152,052-digit numeral

Wow! That’s about 1.3 million more digits than the last one found. There’s $100,000 in it for the first one to come up with a 10 million digit prime. Doesn’t look like that is far off.

NOTE to the non-mathematicians: a prime number is a number that is only by itself and 1. Large primes have become particularly useful in modern cryptography, the science of making and breaking codes. For more information on how you could get in on the action, check out GIMPS

HT: Mathematics Weblog

Resolution Solution

I am becoming a goal oriented person. That’s not been true my entire life but having just finished some major long term goals this year, I am now in a bit of a vacuum when it comes to life goals. I had a few big ones, such as finish my Ph.D., have a family, teach mathematics at a University. Check, check and check. Over the next few days, I am going to be writing the goals of 2006 into a new page on this blog. You’ll find the link to the right under my reading list link (which is also going to be revised and updated). These may be a little cheesy, but sounds like a good guide to me.

Resolution Solution

Joan Esherick, a freelance writer, lives with her family in Pennsylvania.

Need Some Goal-Setting Help? Here are 10 easy tips:

  • Write down your goals.
  • Then cut them in half!
  • Tell someone your goals.
  • Keep track of your progress.
  • Reward yourself with each success.
  • Be optimistic.
  • Be prepared for difficulty and failure.
  • Adjust course as needed.
  • Measure growth by months and years, not days.
  • Treat each day as a brand-new beginning.
  • —J.E.

The Mathematics of Christmas

This may be a tad late for the season, but I found it quite interesting. Check out the full article.

The Mathematics of Christmas by Keith Devlin

I guess it was an early sign that I was heading for a career in mathematics that, when I was a young child, the run-up to Christmas always presented me with a numerical puzzle. How could Santa Claus possibly visit all children at midnight on the same night? I never did get a satisfactory answer from my parents, whose stock response was “No one knows; he just does.”

These days, the adult me can address the question in a mathematically more sophisticated way. Just how big is the task facing Santa on Christmas Eve? [more]

Down Time

I doubt, with the holiday, that anyone noticed but the blog was down for the last few days. We left town to visit family and my wireless router, Linksys WRT54G, decided to spontaneously change my static IP setting. As a result, the dynamic DNS forwarding was going to a non-existent server. Yada yada yada, It’s back up now. Sorry for any inconvenience caused to those of you who have become addicted to the incomprehensible math speak of Natural Blogarithms.

Oh and by the way, Merry Christmas!!!!

More Math Humor

I cannot take credit for this but found it downright hilarious. I hope it is appreciated.

There’ve been a lot of tropical storms/hurricanes this season–so many that they used up the standard names and had to begin using letters of the Greek alphabet as names. We’re up to Epsilon, now. The other day, an airplane went to the eye of that storm to gather data. They fell short of getting good data, but they were within Epsilon.

HA HA HA!! HT: Confessions and Cunctator