September 13, 2011, 7:30 am
To all the new readers: Ready for some math? We love math here at Casting Out Nines, and I’ll be taking at least one day a week to talk about a math topic specifically. If you have a math post you’d like to see, email me (robert [dot] talbert [at] gmail [dot] com) or leave a comment.
The Fundamental Theorem of Calculus is central to an understanding of how differential and integral calculus connect. It says that if f is a continuous function on a closed interval [a,b] and x is in the interval, then the function
is an antiderivative for f. That is, F’(x) = f(x). The FTC (technically, this is just one part of that theorem) shows you how to construct antiderivatives for any continuous function. Possibly more importantly, it connects two concepts about change — the rate of change and the amount of accumulated change in a function. It’s a big deal.
I use a lot of technology in my…
March 1, 2009, 4:40 pm
I’ve started reading through Stewart and Tall’s book on algebraic number theory, partly to give myself some fodder for learning Sage and partly because it’s an area of math I’d like to explore. I’m discovering a lot about algebra in the process that I should have known already. For example, I didn’t know until reading this book that the Gaussian integers were invented to study quadratic reciprocity. For me, the Gaussian integers were always just this abstract construction that Gauss invented evidently for his own amusement (which maybe isn’t too far off from the truth) and which exists primarily so that I would have something to do in abstract algebra class. Here are the Gaussian integers! Now, go and find which ones are units, whether this is a principal ideal domain, and so on. Isn’t this fun?
Well, yes, actually it is fun for me, but that’s because I like a…
February 5, 2008, 10:18 am
The ICTCM is coming up fast, and I’ll be there, mostly to give a talk on using wikis in upper-level math courses (like this one from my topics course in Cryptology) and take a minicourse on Camtasia. But I’ll also be checking out the latest and greatest (?) ideas and products in educational technology. One general category I am quite interested in is making all this technology that we use — especially computer algebra systems — portable and accessible from all different locations, in particular so that commuter students aren’t left out of the loop.
The fact that commuter students are left out is a growing concern for me, at least. We have Derive and Maple installed on my campus, but it’s a network install — and you have to be on campus to use it. Some campuses have a network installation that works from off campus, but we (and other places like us) also have a network that cannot be …
January 9, 2008, 4:01 pm
I just had a visit from one of our IT people to help me upgrade from Maple 10 to Maple 11. (Hoping that this would clear up the Maple/Leopard incompatibility issue.) We have a multiple-seat license for Maple that involves having some of the licenses on our campus network. Only a certain number of copies of Maple can be open at any given time.
But the install disc never made it out of the paper sleeve. The IT guy told me that, with Maple 11, you must be connected to the campus server in order to use it, due to the nature of the network license. And he said this was a new “feature” of Maple 11. With Maple 10, I installed the software along with a license file, and then I could use it wherever I wanted, network connection or no. But apparently Maple 11 can only be used on campus and when I am connected to the campus network. (I can’t connect from off-campus.)
I handed the disc back to the…
January 8, 2008, 7:58 pm
Lots of activity on the software front lately.
OmniFocus, the GTD app which I wrote about here, was released in version 1.0 today. I’ve been very satisfied with OmniFocus since settling on it for my GTD needs, especially since I managed to combine discounts to get it for under $20. I don’t know how many of those discounts are still available, but definitely the educational pricing is still there (though you have to look around for it at the Omni web site).
Bento, called the “missing database from iWork”, was released out of beta today as well. I’ve been demoing Bento for the last few days as a tracking system for students, and it’s very nice and visual. But I found the $49 price tag to be a little pricey, especially when the entire iWork ’08 suite is $79.
Sage, an open-source computer algebra system comparable to Matlab, has been gathering lots of buzz. With all my issues with Maple 1…