Re: Gifted math student

In article <1144865964.619956.38690@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Timothy Clemans <clemacetc@xxxxxxx> wrote:
Arithmetic is very important. If one studies abstract algebra, they
will use number theory to introduce algebraic structures.

This is not the place to talk about a social life. If a person only
goes to college for mathematics than I think there is a problem. Every
student needs to know arithmetic, elementary algebra(algebra 1 & 2),
geometry and begin analysis.

Why does one have to know how to do arithmetic? One
needs to know what integers are, and their properties,
and what the operations mean, but NOT how to carry
them out in a particular base.

Nor should number theory be used to introduce algebraic
structures. The integers are the simplest infinite
integral domain, but no theorems of number theory are
needed to understands this.

Elementary algebra can be learned in a short time if
one has previously the linguistic concept of variable;
the exercises might last a month. A proof-oriented
geometry course can be useful, but if proofs are
otherwise learned, not absolutely necessary. REal
analysis, not calculus, can be done with this, and
should precede any calculus course, which will now
go very quickly.




--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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