Table of contents
|
| Table of contents
|
| Beautiful crypto | A graduation requirement | Harsh reality | Math sacrificed & intertwined | Plotting to meet the students | What's happenin'? | Some honesty |
Beautiful and omnipresent crypto
I had been exposed much earlier in my life to the intricacies and
romance of cryptography (crypto). Within the last five years, everyone
who used e-mail or electronic commerce became a user of crypto, and
become at least somewhat involved with the legal, social, and
political controversies surrounding the applications of crypto. And
everyone used ATM's and played CD's, so that population also was a
candidate for joining my crypto crowd.
A graduation requirement
Rutgers is one of many U.S. institutions of higher education which
have graduation requirements involving "quantitative reasoning". The
ability to think about such things and to have a certification that
such is possible (a passing grade) is surely a part of being a good
citizen. Certainly calculus or precalculus courses fulfill that
requirement: so, good, the majority of our undergraduates are now
covered, for the great bulk of undergraduate majors must take
one of those courses. The realities of the learning communities
fostered by many of these courses will be ignored here.
Harsh and perhaps exaggerated realities
At many schools the courses which cater to the quantitative reasoning
graduation requirement are frequently not nice. Neither the
instructors nor the students see them as pleasant experiences. The
students emphatically view these courses as an evil and irrelevant
hindrance to their academic journey. The instructors see the courses
as less pleasant duties, involving esoteric and possibly uninteresting
topics taught to an unwilling clientele.
Math: sacrificed & intertwined
When I heard many accomplished speakers discuss aspects of crypto
during a DIMACS summer meeting in ways that were accessible to those
without a deep mathematical background and were also intellectually
challenging and honest, I resolved to try to concoct a course on
crypto for "liberal arts students". The background I'd ask for would
be "good knowledge of Algebra 2, and some knowledge of analytic
geometry." I assumed that most of my students would not be in love
with mathematics and that some would have severe allergic reactions to
standard mathematical instruction. I further assumed that I would need
to demonstrate the relevance of every topic I wanted to cover. If
necessary, I was willing to cater to the 10 minute attention span of a
(so-called) MTV generation. I was also willing to sacrifice the stark
beauty and intellectual rigor of a pursuit of mathematical truth
only in an effort to show how crypto is intertwined with many
concerns of social and political policy. Here's a verification of my
resolve: exactly one result was proved in the course I wound up
teaching.
Plotting to meet the students
To address the students I wanted to reach, I decided to teach about
history and law and society, and I tried to use methods such as essays
and group discussion that students in the humanities and social
sciences would find customary. I frequently felt awkward and
constantly had to guard against giving lectures to the blackboard. I
always needed to remember to embed the exciting math in a context. I
also resolved to make the students "active learners". I also didn't
want to teach things that the students couldn't try themselves,
limiting as that might seem (Maple made it not so limiting, in
fact). To some extent, little of this is new. Most instructors of such
courses attempt such strategies. I was lucky enough to have a coherent
and engaging object of study: crypto and its historical and
contemporary uses.
What's happenin'?
I very much catered to now: I made few references to the use of
crypto by governments and the military before World War II. That was
sad, since the people and the ideas were very interesting. But I
wanted to capture the attention of those who now would send love notes
by e-mail, would trade MP3's, and would buy almost anything on the
web. I did allude to history as far back as 3,000 years ago (the
hashing lecture). I certainly discussed the serious economic and
social implications of the loss of privacy, and the important
questions of intellectual property and its protections. I constantly
urged students to try to think of the world in 10 or 20 or 30 years. I
hope that by example I was able to show them the relevance and
importance of mathematics to their lives.
Some honesty
I was willing to teach if they were willing to learn: to attend, to
participate, to think, to work. I constructed the course assuming this
about the students.
| Table of contents
|