"Lecture" for Week 6
Papers 2 and 3
I can't think of any topic for a "position paper" that is more appropriate
than the one I gave in 2003, so here it is
again.
For your long term paper you have a broad scope to choose from, but I
would like to approve the topic. You should certainly be thinking about
a topic by now. October 23 seems like a good deadline for submitting a
topic for approval. On the Allen and Geller web pages you can see some
topics that were either suggested or used in the past.
Next week I will list the titles from my 2003 class. The point, of
course, is not to do the same thing, but to have your creativity jogged to
do something similar.
Logarithms
In Fall '03 the textbook exercises on the late renaissance period did not
inspire me at all, so I substituted
some materials I had written for
calculus students about logarithms. The M. 629 students liked them,
so here they are again (see the assignments),
but marked "optional" since
we have enough to do this week and next.
For you young folks who don't know what a slide rule is: Suppose you took
two ordinary rulers and put the "0" end of one against the point 3.12 on
the other, then read off on the second ruler the number opposite the point
4.29 on the first. You would get the sum 3.12 + 4.29, a rather clumsy way
of adding two numbers. But now suppose that the labels on the rulers are
the exponentials of the distances of the points from the ends, or,
equivalently, each number is plotted at a position equal to its logarithm.
Then, because of the law of exponents
ea+b = ea eb, the
number you read
off is the product of the two numbers you located on the rulers. This is
actually a practical (cost-effective) way of multiplying numbers to
3-place accuracy -- or was, until Hewlett-Packard devastated the slide
rule market around 1970.
Cubic equations
Several years ago I actually needed to understand the exact solutions of a
cubic equation for a research purpose.
Here is what I learned.