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"Michael S. Lorrey" says:

...

*> > As it happens, this particular topic has been rather well researched. Mike
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*> > is exaggerating a bit, but it is certainly true that in the first half of
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*> > the 20th century American high schools taught many subjects that are now
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*> > considered advanced college fare. My favorite example is the fact that the
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....

*> few well worn phrases. I just received a message from a girl on a
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*> newsgroup who
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*> is a senior in college and is so happy she came out in the top of
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*> her class in
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*> linear algebra...
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...

And your point is?

Linear algebra is not simple algebra. It's typically taught after

calculus, around the same time as the study of ordinary differential

equations, but before more advanced topics such as modern algebra,

real and complex analysis, number theory, partial differential

equations, topology, and so on. Glancing back at the Springer-Verlag

volume "Linear Algebra", by Klaus Janich, from their "Undergraduate

Texts in Mathematics", I see that they describe the study of linear

algebra as concerning sets, maps, groups, vector spaces, including

complex and Euclidean spaces, bases, matrices and their

classification, eigenvalues and eigenvectors, endomorphism and the

characteristic polynomial. This is not the stuff one typically covers

in high school algebra, but rather an advanced application of the type

of tools that such courses provide to topics that extend beyond the

purview of a basic algebra class. While a very well prepared student

-- say, someone with a perfect calculus advanced placement score --

studying math for a BA at a reasonable college in the U.S. would

typically encounter linear algebra in the first or second year of

study, as I did back in 1987, a person who had only had a good high

school mathematics education and who wished to study math as a

supplementary topic might well wait another year or two for ODE or

Linear Algebra. This is in no way a sign of a deficiency in high

school or higher education standards.

...

*> The year I graduated from high school, 1986, NH had the highest average SAT
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*> scores in the nation, while it had spent the least per capita on education fo
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r

*> many years, and is still one of the five lowest funding states... Our state
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*> Supreme Court is, at the moment, being dismembered by the Governor, the AG, a
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nd

*> the legislature (ostensibly for other reasons, but we all know the real reaso
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n)

*> all because the good 'ol boys couldn't seem to make the connection that money
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*> doesn't equal quality education, despite our history.
*

The United States Senator from New York Daniel Patrick Moynihan

famously observed some years back that he had learned from the Federal

government's own statistics people upon comissioning a review that the

distance from a state capital to Canada had several times the

statistical correlation with results on standardized tests in that

state than did the amount of money spent per pupil. (Specifically,

the closer to Canada, the better the scores.) He joked that the thing

to do was move the state capitals to the northern border of each

state.

Clearly many other factors are at work.

All the best!

James Wetterau

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