"Lecture" for Week 12
Linear algebra
Several years ago I wrote a textbook for our applied-analysis-oriented
linear algebra course (Math. 311). I realized that textbooks on linear
algebra
usually contain very little history, unlike books on calculus,
differential equations, Fourier analysis, abstract algebra, topology,
number theory.
In fact, I realized that I knew very little history of linear algebra.
So, I read up on the topic and wrote a short history chapter for the book.
Prof. Allen has very little on linear algebra either, so in the 2003
course I inserted a rewrite of my chapter on
the history of linear algebra
into the syllabus. I think it
is still valuable, although less necessary than before because Katz does
have some material that overlaps it. This seems to be the best week for
it, although it relates to topics in Katz's Chapters 16, 17, 19, 20, and
even 5.
George Green
Green has a somewhat unusual biography. He was a self-taught young man
from a small town in England who wrote an essay of about 100 pages in
which he introduced all the things that bear his name and are so important
in partial differential equations and the physics of fields (such as
electromagnetism): Green's theorem, Green's integral identities, Green
functions. (The essay is available on the Web, but the notation is so
archaic that it is difficult to read.)
The value of his work was recognized and he was invited to Cambridge to
become an undergraduate (at a rather late age) and eventually a college
Fellow. Unfortunately, he fell ill and died soon thereafter.
No photographs or portraits of him are extant.
This information comes from a nice, short article,
L. Challis and F. Sheard,
The Green of Green Functions, Physics Today 56 No. 12 (Dec. 2003)
41-46.
(As usual, you can get this on line through TAMU Evans Library, but it is
not legal or practical for me to link to it.)