Montag, 18. November 2013
Harvard Professor Oliver Knill
November 6, 2013 — Wolfram Blog Team
1433 1184 208
Last month, students in the midterm review
session of Harvard’s Math 21a class received a lesson
in Mathematica they would not soon forget. Professor
Oliver Knill coded a 3D-animated Miley Cyrus
swinging on a wrecking ball to the beat of her song
(by the same name). Knill used the same principles
of mathematics that his class was reviewing for the midterm—
and now he just may be the coolest professor ever.
We snagged Professor Knill as soon as we found out,
and we were lucky enough to have him agree to answer
a few questions for us! Here, he gives us a little insight
into how he uses Mathematica for both code and
creativity—and generates memorable lessons for
his students in the process.
Q: Hello, Oliver, thank you so much for taking
this opportunity to talk with us about your
experience using Mathematica as a teaching tool.
Why don’t you start off by telling us
a little bit about yourself and how you
came to use Mathematica in the classroom?
A: In my undergraduate years at ETH Zürich,
I was a course assistant for a course using the
computer algebra systems Macsyma, REDUCE,
and Cayley (now Magma). My mentor was
Roman Maeder, then a professor at ETH and
also one of the early Mathematica developers
and author of several books on Mathematica.
As graduate students, we had access to early v
ersions of Mathematica, and I have been using
it since for teaching and research.
Using it in the classroom was not easy at first.
In 1993, at my first teaching position at Caltech,
I had to carry around a heavy portable laptop and
use a special device on the overhead projector
to display the screen. Now, every classroom
is equipped with projectors, and using
technology for illustration has become routine.
Mathematica is a good choice because it is easy to learn.
Students with no programming background can
pick it up quickly.
Q: We were very impressed by
your recent (and rather edgy) use of Mathematica!
What inspired you to come up with the idea, and
how did you go about coding it?
A: In a language like Mathematica, one can produce
illustrations quickly. For a midterm review, I wanted
to demonstrate how quadrics can be used to build up
objects. It’s possible to do an animation in 3–4 hours
from scratch because of the way programs are built up.
At every moment one has a working project.
One of the benefits of a high-level programming
language like Mathematica is fast developing time.
This applies in particular to animations done for
educational settings. So, in order to illustrate
quadrics for my multivariable calculus course,
I animated part of a Miley Cyrus video with a
couple of surfaces.
That “Wrecking Ball” video had received an
astounding 12.3 million views in 24 hours,
and of course, most of the students had seen it.
By the way, the initial artistic close-up shot
in the video was clearly inspired by other
music videos, like Sinead O’Connor.
Back to the animation. Of course, a ray tracer l
ike POV-Ray would have produced more r
ealistic pictures, but it also would have taken
more programming time. Development in
Mathematica is fast because one can build
up complex structures using simple
building blocks that are easy to animate.
The code below was written in a couple
rule I always follow, whether using
Mathematica for scientific experiments
or illustrations or animations, is to always
keep a running prototype. This allows me
tf hours and is pretty self-explanatory.
Oneo finish a product, even if time is up.
Having had no time for tears and ears initially,
they are added now as hyperbolic
paraboloids or ellipsoids.
streamline code. While this costs time, it can
in the long-term save time. You see for example
that ArcTan[Tan[t]] implements a sawtooth
function. It could have been done more elegantly
with the built-in function SawtoothWave[x].
One can also see how to access graphics
objects like surfaces given by ParametricPlot3D.
An example is “Ear“. To access the graphics part,
like for scaling, translating, or coloring, work
with Ear[], then at the end put everything
together with Graphics3D.
Setting global options also helps to simplify
code. I did not want to use any mesh features
throughout the clip, so this was defaulted to
Q: You seem to really know how to connect
with your students. Do you have any advice
for other professors and educators looking
to incorporate Mathematica into their teaching plans?
A: We have a long tradition at Harvard of using
Mathematica. It had been used before I came
here 13 years ago. Having a culture is important,
dents and teachers can use the software. But it
is also important not to overuse any technology.
Every tool has its sweet spot, and finding this
can be personal and depend on the setup.
With respect to the course I’m teaching,
Mathematica projects have always been
light and on the creative side, so that projects
can be completed with moderate effort in the
order of magnitude of a few hours. Still, one
has to be able to dedicate time to help the class.
Last year, we had our students build Mathematica
objects for 3D printing. Thanks to a grant from
the Elson Family Arts Initiative, we were
able to print some of them.
Download this post as a Computable Document Format (CDF) file.
Notiert von marcus knill um 07:32
Im Netz gefunden:
tu-dresden.de/die_tu_dresden/...und.../Knill-Arg.technikenl.pdfArgumentationstechniken. (M. Knill: "Natürlich, zuhörerorientiert, inhaltzentriert reden". SVSF Verlag 1991, Hoelstein). Plausibilität. Argument ist plausibel,.
Notiert von marcus knill um 07:32