> Too Much Calculus

Not for me! Heck, I never took freshman
calculus or pre-calculus and, instead
read a book and started on sophomore
calculus then continued with, right,
ordinary differential equations, advanced
calculus for applications, and advanced
calculus, topology, modern analysis,
measure theory, functional analysis,
exterior algebra, etc. Not enough calculus
for me!

Strang, of course, is emphasizing linear
algebra. Great! It's terrific stuff.
I had an abstract algebra course that
started on vector spaces and matrix theory.
Then I got famous book from Princeton on
multi-variable calculus and read the
first chapters on linear algebra,
e.g., learned Gram-Schmidt. Then
I got a linear algebra book and read a
few chapters and applied them to some
problems in classical mechanics. Then
I wrote my math honors paper in group
representation theory, right, more linear
algebra. The out of school, I wanted to
know linear algebra better and read a
good book cover to cover, carefully.
Then I got Halmos, Finite Dimensional
Vector Spaces and read it cover to cover.
Wrote Halmos about his proof of the Hamelton-Cayley
theorem and got back a nice answwer!

Then I got another famous text on multi-variable
calculus and read it cover to cover,
including the parts on exterior algebra.
Then I did that again from Spivak's
Calculus on Manifolds -- right, a lot of
both calculus and linear algebra. Then
I got Forsythe and Moler, Computer
Solution of Linear Algebraic Systems,
read it cover to cover, directed a project
in interval arithmetic for linear algebra,
took a course in numerical analysis with
a lot of linear algebra for solution of
partial differential equations, e.g.,
iterative solutions (Gauss-Seidel) and
wrote corresponding code.

I also used linear algebra in work with
the fast Fourier transform, multi-variate
statistics, and more.

For more on linear algebra, I read
the first part, linear algebra, of
von Neumann, Quantum Mechanics.

From a world class guy in linear algebra,
I took an advanced course in linear
algebra -- by then the course was beneath
me and I led the class by a wide margin.
Favorite theorem -- the polar decomposition.

Read Coddington's book on differential
equations -- gorgeous book.

The combination of linear algebra and
calculus, with other math, continued.

At one time
a little calculus did a lot:
The initial value problem for
the little first order, linear
ordinary differential equation

y'(t) = k y(t) ( b - y(t) )

saved FedEx, that is, kept it from
going out of business. So, useful
calculus!

So, sure, I like linear algebra
and like the combination!

I definitely do not see that I
had too much calculus!

Here's what I saw, and still fume
about: All I could get in chemistry
was one too simple course in high school
and one too simple course in college.
All I could get in physics was one
too simple course. I college, by the
time I got to Maxwell's equations, I
didn't know enough calculus to do really
well. In college I never got math enough
to do well with quantum mechanics.

But in grades 9-12 and then in the first
two years of college, I was force fed
like a goose with six years of English
literature, with each year yet another
play by Shakespeare. I agree that there
was a good writer in England in the
1600s -- Newton! So it was also Chaucer,
Milton, Wordsworth, ..., Dickens, the
great natural order (all corresponding
theorems and proofs omitted!), etc. With
good information about people? Nope.

Then there was history: It never got to the
20th century. It never touched on technology,
economics, or any other causes. There
was plenty of time in history courses; it's
just that the courses didn't have much
content.

If my startup works, then I'll get back to
more in calculus, functional analysis,
stochastic processes, and mathematical
physics. "More calculus, Ma!".