"Lecture" for Week 5
A whirlwind tour through 1000 years ...
China and India
- Here is my personal musical take on the
Chinese remainder theorem
(The current home of
RESIDUE_INT is here.)
- The other most famous contribution of classical China is Gaussian
elimination for solving systems of linear equations,
16 centuries before Gauss. Stillwell will get to that in Sec. 6.2, and I
will in a much later week on the history of linear algebra.
- Katz has a section on Indian contributions to trigonometry.
Indian mathematicians from Bhaskara I to the 14th century worked at
calculating tables of sines, etc., presumably for applications to astronomy
and navigation. To this end they developed various approximation
and interpolation formulas that are understandable today but must
have been nonobvious and ingenious at the time.
The Islamic period
This week's reading, especially the Islamic part, is full of unfamiliar
and complicated names. It's good we don't have a final exam, right?
I feel I ought to be providing some guidance as to which are the most
important figures from the Islamic culture. My list is
I have to admit that the main criterion for
getting on this list is that I had heard of the person before doing
the reading the first time.
Perhaps the most striking or inspiring thing about these
periods is that some individuals did do significant mathematics
in such isolation, in societies that were not conducive to it.
- Omar Khayyam
- Avicennna and Averroes, who
weren't primarily mathematicians (mentioned in long footnotes in the
The medieval period
Continuing the list of famous figures:
I made an attempt to find out why Leonardo of Pisa is called
Both Katz and Allen say that the name was not applied to him until the
19th century; Katz obviously dislikes the name and brings it up as seldom
But Carl Boyer's history-of-math book says that it just means "son of
Bonaccio" -- Leonardo being himself one of those rich merchants' sons that
he and his successors made a living teaching, according to Katz p. 214.
- Oresme (Katz tells us to pronounce it "o-REM").
Betraying my physics
background (and my years as a calculus teacher), I
find him to be the most interesting figure of
this period. Apparently he was the first to draw
graphs of functions representing quantities other than positions,
and had some understanding of the relations between position, velocity,
Time for a State of the Course address
- Broken links
- Remember that you have a book review
due soon, and a major term paper that you should have started working on
Note to self: Remember that you have to tell them what to do for
the short "position paper" due in April.
- I'm delighted that you are making good use of the eCampus discussion
forum. Those of you who have not got into the habit of checking it
frequently should do so. (Note to self: Do that yourself!)
Between the help you give each other and Ngoc's hard work on the
homework, I have needed to do very little handholding.
I have carefully avoided commenting on the "how much should we help
each other" issue, waiting to see how it would play out, and I think
you have all arrived at a sensible and mature middle ground.