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Topic: What math should I learn if computers can do it all? Mathematica,
etc.

Replies: 20   Last Post: Nov 18, 2013 2:11 PM

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Herman Rubin

Posts: 363
Registered: 2/4/10
Re: What math should I learn if computers can do it all? Mathematica, etc.
Posted: Nov 12, 2013 1:06 PM
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On 2013-11-12, Hetware <hattons@speakyeasy.net> wrote:
> I'm working through a 1953 edition of Thomas's _Calculus And Analytic
> Geometry_. When I work problems, I use Mathematica to type my
> transformations, and to check my results. I use it for far more, as
> well; graphing, numerical solutions, etc.


> Many years ago I found computers to be a nuisance when it came to math,
> and more importantly physics. I was contented to have a piece of chalk
> or a pencil and an eraser, than to have all the computing power in (the)
> Universe. Time was the only resource I found in short supply.


> Now that I have used them for years, I realize that computers can do a
> whole lot. They can find integrals for equations which I cannot
> integrate by hand. They can produce graphics which a human could never
> produce, etc.


> I've used a pocket calculator since the 1970's. But, I feel as if I
> should have learned to work the same problems on my own. I feel
> somewhat crippled by using it as a crutch.


> I'm in a conundrum twixt the use of computers to do my thinking for me,
> and learning to think for myself. Should a child learn his times
> tables, or learn to use a computer to do it for him?



Computers can do things which they have beeen programmed to do
and nothing more. I have found that it can be somewhat unwise
to trust computer programs too much. I have found errors in them,
most recently yesterday. Also, mathermaticians keep finding
integrals which the current computer programs have not been
able to find. One can produce a computer progrram to find
the integral of any function integrable in terms of elementary
functions, but this can take a looooong time, so short cuts have
been devised, but they can give up.

As for your last paragraph, there are advantages to being able
to do some things yourself. It takes time to use the computer.
Also, there are things you can find out which you would not
expect doing it yourself. Getting the result yoorself often
leads to more understanding, but not always.

As for what should be learned, memorization is useually a poor
way to learn anything, and might leave out alternatives. I would
expect a child to learn how to construct addition from counting,
and multiplication from addition, and to produce the tables for
himself or herself. This would also provide a quick means of
filling in a forgotten value.


--
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@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558


Date Subject Author
11/11/13
Read What math should I learn if computers can do it all? Mathematica,
etc.
Hetware
11/12/13
Read Re: What math should I learn?
William Elliot
11/12/13
Read Re: What math should I learn?
Matthew Lybanon
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
jimp@specsol.spam.sux.com
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
Lord Androcles
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
Hetware
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
Lord Androcles
11/17/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
Hetware
11/17/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
Lord Androcles
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
Herman Rubin
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
fom
11/13/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
Doc O'Leary
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
Sam Wormley
11/12/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
Ken.Pledger@vuw.ac.nz
11/12/13
Read Re: What math should I learn if computers can do it all?
Mathematica, etc.
Brian Q. Hutchings
11/13/13
Read Re: What math should I learn if computers can do it all? Mathematica, etc.
JohnF
11/13/13
Read Re: What math should I learn if computers can do it all?
Mathematica, etc.
Timsn274
11/12/13
Read Re: What math should I learn if computers can do it all?
Mathematica, etc.
Rock Brentwood
11/13/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
Peter Percival
11/13/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
fom
11/18/13
Read Re: What math should I learn if computers can do it all? Mathematica,
etc.
Peter Percival

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