Re: Learning quantum mechanics at age 14

From: Ralph Hartley (hartley_at_aic.nrl.navy.mil)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 19:44:38 +0000 (UTC)

Arnold Neumaier wrote:
> Sci~Girl wrote:
>>In order to truly understand quantum mechanics I'd need to understand
>>calculus.
>
> You can understand some part of quantum mechanics already
> without calculus, namely everything involving entanglement,
> quantum cryptography, and the like. This only needs linear
> algebra, which may be easier. (On the other hand, calculus
> is not really difficult either, once one gets used to it.)
> Linear algebra (i.e., vectors and matrices) is more fundamental
> to quantum mechanics than calculus.

This is one of my biggest problems with how mathematics is taught (at
least in the US, is it the same elsewhere?).

Calculus (even multi variable) is taught first, often in high school
nowadays, and *then* linear algebra. This results in many people
learning calculus, but no linear algebra.

I think this is backwards, because linear algebra is both easier and
more useful than calculus.

Quantum mechanics is not the only field in which calculus is used but
linear algebra is fundamental.

In an ideal world, one would learn both, but seriously, what percentage
of college graduates *ever* use calculus again? Many of those, I
suspect, would have a use for linear algebra, if they had ever learned
any. How many of those would *actually* apply math to a problem that
needs it? I don't know. You can lead a horse to water ...

I should confess that I have spoken about this to a woman who succeeded
in learning calculus, but failed to learn linear algebra, so your
mileage may vary.

If you are going to read math "outside" class (we know you are actually
  inside class when you do it, no one is fooled, we remember), read
linear algebra.

Easy, useful, your competitors aren't learning it.

Ralph Hartley

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