Category Archives: Computer algebra systems

February 23, 2012, 6:48 am

What Happens if We Just Ask Questions?

Someone asked me recently what was the one thing that’s changed the most about my teaching over the last 10 years. My response was that I’m a lot more likely now than I was in 2002 to organize my classes around asking and answering questions rather than covering material. Here’s one reason why.

The weekly Mathematica labs that we have in my Calculus 3 class are set up so that some background material (usually a combination of math concepts and new Mathematica commands) is presented in the lab handout followed by some situations centered around questions, the answers to which are likely to involve Calculus 3 and Mathematica. I said likely, not inevitably. There is no rule that says students must use Calculus 3 to answer the question. The only rules are: (1) the entire solution has to be done in a Mathematica notebook, and (2) the solutions have to be clear, convincing, and…

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September 28, 2011, 4:00 am

Midweek recap, 09.28.2011

Good stuff from the internet this past week:

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September 21, 2011, 9:00 am

Midweek recap, 9.21.2011

Interesting stuff from elsewhere on the web this week:

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September 14, 2011, 8:00 am

Midweek recap, 9.14.2011

Happy Hump Day! Here are some items of interest from the past week:

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September 13, 2011, 7:30 am

Taking the Fundamental Theorem challenge

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…

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March 15, 2010, 12:27 pm

ICTCM day 2

Euclid, Greek mathematician, 3rd century BC, a...

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[Ed. note: This post was originally written on March 13 while at the ICTCM, but I ran out of time on my $12.95 per day internet access before being able to post it and only now have had the chance to get back online. So it's about 36 hours out of sync.]

Slower day at the ICTCM than yesterday. For one thing, I took some time out in the morning to get the MATLAB course prepped for Monday; and I needed time to finish some grading in the afternoon. But I manage to have a pretty productive day nonetheless.

The main event — one of the primary reasons I came here — was a Geogebra 3.2 minicourse this morning. I’ve been a diehard Geometers Sketchpad user for a long time, but after becoming aware of Geogebra lately, I began to wonder if it might be time for a switch. I have no problem with the usability …

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January 31, 2010, 1:52 pm

MATLAB course details and update

We start classes this week, a bit later than most other folks thanks to our January term. That means the long-awaited MATLAB course will be formally kicking off. I’ve had a few people ask me about what we’re doing in this course, so here’s an update.

This has been a tricky course to plan, because the audience is definitely not the usual one for an introductory MATLAB course. Almost all the introductory textbooks and materials I reviewed for the course, and all the introductory MATLAB courses I looked at from other schools, have a particular student demographic in mind: they are all engineering majors; they are all freshmen or sophomores with either a semester of programming under their belts or at least a very high level of comfort with computers and the “guts” of programming; and they are all attending large universities in which the particular academic makeup of the institution plays …

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January 20, 2010, 10:31 am

Courses and "something extra"

Some of the most valuable courses I took while I was in school were so because, in addition to learning a specific body of content (and having it taught well), I picked up something extra along the way that turned out to be just as cool or valuable as the course material itself. Examples:

  • I was a psychology major at the beginning of my undergraduate years and made it into the senior-level experiment design course as a sophomore. In that course I learned how to use SPSS (on an Apple IIe!). That was an “extra” that I really enjoyed, perhaps moreso than the experiment I designed. (I wish I still knew how to use it.)
  • In my graduate school differential geometry class (I think that was in 1995), we used Mathematica to plot torus knots and study their curvature and torsion. Learning Mathematica and how to use it for mathematical investigations were the “something extra” that I took from the …

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July 15, 2009, 12:39 pm

MATLAB for the masses

matlabThe upcoming academic year will contain a number of new projects for me that are going to be quite exciting. I’ve twittered about one of these projects recently, and each time I do so, I get replies from folks wanting to know more, so I’m now shifting discussion of this to the blog. The project: Designing and teaching a one-hour course on the computer software MATLAB for a general mathematical audience. This course, titled “Computer Tools for Problem Solving”, is going to begin in Spring 2010. It will be a one-hour lab-oriented course to be taken corequisite with Calculus II. Every student who takes Calculus II will be expected also to take the MATLAB course.
Why are we doing this? Three reasons.
To speed up our 3:2 engineering program. Under this program, students go to my college for 3 years to take foundational math and science courses along with liberal arts courses; then transfer to…

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October 15, 2008, 8:54 pm

Technology in proofs?

We interrupt this blogging hiatus to throw out a question that came up while I was grading today. The item being graded was a homework set in the intro-to-proof course that I teach. One paper brought up two instances of the same issue.

  • The student was writing a proof that hinged on arguing that both sin(t) and cos(t) are positive on the interval 0 < t < π/2. The “normal” way to argue this is just to appeal to the unit circle and note that in this interval, you’re remaining in the first quadrant and so both sin(t) and cos(t) are positive. But what the student did was to draw graphs of sin(t) and cos(t) in Maple, using the plot options to restrict the domain; the student then just said something to the effect of “The graph shows that both sin(t) and cos(t) are positive.”
  • Another proof was of a proposition claiming that there cannot exist three consecutive natural numbers such that the …

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