Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
fom

Posts: 1,968
Registered: 12/4/12
Re: What math should I learn if computers can do it all? Mathematica,
etc.

Posted: Nov 12, 2013 5:20 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 11/12/2013 12:06 PM, Herman Rubin wrote:
> 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.


Along these same lines...

There have been two articles within, say, the last three
years talking about mathematics in relation to the sciences
upon which we depend. Both appeared in prominent science
magazines directed to the general public.

One of them, appearing in Science News, had been directed
at the unsound use of statistics in general scientific
study. The other, appearing in Scientific American, considered
the consequences of using highly accurate computerized
calculations. The premise of its underlying question had
been how the elimination of "fudge factors" previously introduced
at intermediate points in calculations might impact the reliability
of the physical systems built by engineers.

Since it has been some time, I have certainly oversimplified
the articles with these statements. But in both articles,
the primary issue questioned the use of computationally simplified
numerical methods without judgement based on the underlying
mathematical principles. One can introduce covert error where
the computer programs themselves have no errors.

In fact, this has been the defense of numerous financial
analysts who developed the programs leading to the debacle
of securitized mortgages. Complex computer programs rely
on numerous rigid assumptions. On their account, the changing
laws surrounding housing markets invalidated assumptions
upon which those mathematical models had been constructed.
Of course, this is a "he said"-"she said" thing. But, if true,
those people who relied on those programs and who would not purposely
choose to engage in fraud did not recognize that their programs
were no longer faithfully calculating risks.

A similar analysis had been applied to accounting methods
prior to the recession associated with the "dot com" collapse.
In the past, accounting records had been relatively stable
because of costs involved with maintaining records. With
the advent of spreadsheet programs, it became a simple matter
to compare the analyses of different bookkeeping policies.
With exception for the bare minimums of GAAP governed by
legal policies associated with taxation, companies could
undermine assumptions involved with annual reports by
adjusting bookkeeping and business practice at a moment's
notice.

One could argue that there is *more* reason to learn
the mathematics with the power computational tools
bring to the table.




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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.