Re: Gifted math student
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 10 Apr 2006 21:18:21 -0400
In article <1144537782.605732.141940@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Timothy Clemans <clemacetc@xxxxxxx> wrote:
The book Mathematics for the Nonmathematician and Mathematics: It's
content, methods, and meaning should greatly help him. I would expect
that he should read a section many times.
It is important to note that logic is important and I think can be
formally studied at age 10 or after.
It can be studied at age 6 or earlier by a gifted
student. My son used some preliminary materials
plus Suppes, _Introduction to Logic_, a college text.
My late wife's college text can be used by literate
children of any age, but some of the applications may
use material which would not be known, and can be
omitted without loss.
What I would do is get a book like Arithmetic Refresher, run him
through it, and make sure he has it all.
Then use a book on the SAT test.
Thrid use a book such as How to Prove It.
Forget about arithmetic; it is irrelevant to understanding
mathematics at any level. It also detracts from any
attempt to understand the integers, as it deals only with
a particular representation, with no intrinsic properties.
A number is a number whether it is in base 10, in base 2,
in base 60, in "scientific" notation in any of these bases,
if it is represented as a number of tick marks, or in any
other manner.
It also important to note that arithmetic and mathematics is not the
same. Mathematics is two parts: slove equations, and prove theorems.
There are other more important parts. Understanding the
concepts, which is almost completely eliminated now, and
was mostly vague in the past. Peano's Postulates and
their development are an excellent introduction to the
ordinal concept of the integers, but the cardinal one
has to be put into it. I consider trying to do it all
with the cardinal concept in the new math to have been a
mistake, as there is no way to define "finite" without at
some point using ordinals.
The second part is to understand the structure of proofs.
Proving theorems is what a mathematician does, but first
one must know what it means, and this applies to those
who are not mathematicians as well. And for applying
mathematics to anything, one needs to understand the
concepts to formulate the problem. Non-mathematicians
do not have to know how to solve problems, but how to
formulate them. Even mathematicians often have to use
computer packages to solve problems.
Have you considered homeschooling him?
--
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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