Two days ago, I bought a copy of "Mathematica 5.2 For Students" from the campus bookstore for $150 after tax. This is the same software that sells for around $2000 after tax to non-students. It's a fantastic package, and I'm happy I bought it. However, yesterday, after having already installed a copy on my home's dual G5, I tried to install a copy on my PowerBook. Wolfram's licencing scheme doesn't allow that: I could either buy their $100/year "Premium Support" contract, which would allow me to run other copies on other nodes, or buy another copy. If I'd paid full boat for the original copy, that might have made sense, but at the student discount, it made more sense to actually buy another package entirely. FYI for science and engineering students.
Recently in Mathematics Category
First day of school after summer break; school is on the quarter system. This morning's class was the first day for me of 4th quarter calculus (vector calculus with applications, partial derivatives, and multiple integrals) taught by the reputedly toughest math instructor on campus... which is why I chose him. I found out that not only are all the quizzes given without notice: so are the exams! No kidding. This is going to be fun to watch. I'm taking the guy seriously about the Importance of Being Earnest about our study habits, and am wondering how many of the rest of us will be doing the same.
Computer, compute to the last digit the value of pi.
Spock
TOS, Wolf in the Fold
Anton Sherwood has moved his musings to a blogging system with a commenting facility and much friendlier navigation. No trivial feat, given that he's been blogging (in one place) since February 2002... this meant converting over 1400 postings! Take a look.
This is not to say that I believe all religious people are readily capable of murder. Rather, I claim that once you structure your life around ideas that you are not permitted to test, but which you accept as beyond testing (that is, on "faith"), you've abandoned your most important survival tool, namely reason.
Introduce a bad axiom into a mathematical formal system, you can prove anything. Similarly, if you abandon reason for "faith", you lose your only tool with which to distinguish the truth. This could leave you helpless to escape the idea that "God" demands that you kill, and from there it is a short step to shooting abortion doctors or flying planes into skyscrapers.
I've noticed an interesting phenomenon in my math classes over the last couple of years, which has become more pronounced as the subject matter becomes (to some people) more difficult: the Desperate Calculator Jockey. This is the guy who never studies, is too lazy to do his homework, but somehow manages to struggle his way from one class to the next. He can usually be seen furiously punching formulae into a top-of-the-line TI-89 or its near-equivalent, expecting some magical insight into the problem from the resulting graph. While this approach may actually work in some instances, such as with a simple "differentiate this function" problem, the approach is an utter - and deserved - failure when the student is confronted with the dreaded applications problem (the so-called "word problem.")
Oh, my... this is where thinking skills are really tested, and where numerical prosthesis is nearly worthless. I love these problems: exercises in aircraft fuel vs range optimization, predictions of least-time photon transit through a non-vacuum medium (Snell's Law, an application of the Brachistochrone curve), calculations of marginal cost & maximization of profit, how to make the largest rectangular horse corral with a fixed length of expensive fencing... the good stuff. The Calculator Jockeys rarely know where to start decomposing a problem to its tractable constituents, instead, as usual, attempting to invoke an answer from the aether by keypunch.
I can pretty much tell from looking around a room who's faking it and who's getting it: those who are actually learning the calculus are learning with their pencils, which are constantly moving on paper. The fakers, on the other hand, are constantly pushing buttons. The joke's on the latter group: with the exception of actual symbolic manipulation packages such as Wolfram's Mathematica, hand calculators - to date - depend entirely on methods such as linear approximation. This means that the calculator jockey can actually get the wrong answer for a derivative of a function at a point on a curve, since the curve may not actually be differentiable at that point, but the linear approximation around that point of a secant line connecting points on either side of the original point may exist. Suckers.
If you've ever been exposed to this question, you'll consider it trivial, but I'm wondering which of my readers will get this first:
What is the only function in all of calculus that is its own derivative?
