Jason, all,

If I had bothered to search on "computational mathematics" I would have found 
that the potential ambiguity that worried me is already actual, as you clearly 
show.  Do you think that the phrase "computative mathematics" is too close to 
the phrase "computational mathematics" for comfort?  I hope not, but please say 
so if it is.

Problem is, the "applied" in "applied mathematics" is used in various ways 
that, as Dieudonné of the Bourbaki group pointed out in his Britannica article 
(15th edition I think), jumbles trivial and nontrivial areas of math together, 
and has all too many, umm, applications. One area of pure math X may be 
_applied_ in another area of math Y, whih is to say that Y is the guiding 
research interest. If on the other hand Y is applied in X, then that's to say 
that X is the guiding research interest. And both X and Y remain areas of 
'pure' math. Then there are areas of so-called 'applied' but often nontrivial 
math like probability theory. Then there are applications in statistics and in 
the special sciences. Then there applications in practical/productive 
sciences/arts. And of course, sometimes theoretical or 'pure' math is developed 
specifically for a particular application. (All in all, we won't be able to get 
rid of the term "applied," but in some cases we may be find an alternate term 
with the same denotation in the given context).

Best, Ben

----- Original Message ----- 
From: Khadimir 
To: Benjamin Udell 
Cc: PEIRCE-L@listserv.iupui.edu 
Sent: Monday, March 12, 2012 2:14 PM
Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce 

This latest post caught my attention.

Since my first degree was a B.S. in "computational mathematics," I thought that 
I would weigh-in.  

One can make the distinctions as follows, beginning with pure vs. applied 
mathematics.  I will give a negative definition, since I am not so skilled with 
the Peircean terminology used so far; applied mathematics is the use of 
mathematics as a formal, ideal system to specific problems of existence.  For 
instance, consider the use of statistical confidence intervals to solve 
problems in manufactoring relating to the rate of production of defective vs. 
non-defective goods.  Pure mathematics is not bound by existent conditions, but 
"pure" becomes "applied" when used in that context.  Hence, I am treated 
applied mathematics as an informal, existential constraint that alters the 
purpose and use of pure mathematics.

Computational mathematics is for the most part a subset of applied mathematics, 
which focuses on how to adapt computational formulas so that they may be run or 
run more efficiently on a given computation system, e.g., a binary computer.  
Computational mathematics, then, is primarily focused on formulas and 
computation of said formulas, which is to be more specific about the limits 
that make it an applied mathematic.

I offer this as a different viewpoint, one coming from where the distinction 
has practical effects.

Jason H.

On Mon, Mar 12, 2012 at 12:47 PM, Benjamin Udell <bud...@nyc.rr.com> wrote:

  Malgosia, Irving, Gary, list,

  I should add that this whole line of discussion began because I put the cart 
in front of the horse. The adjectives bothered me. "Theoretical math" vs. 
"computational math" - the latter sounds like of math about computation. And 
"creative math" vs. what - "consumptive math"? "consumptorial math"?  Then I 
thought of theorematic vs. corollarial, thought it was an interesting idea and 
gave it a try. The comparison is interesting and there is some likeness between 
the distinctions.  However I now think that trying to align it to Irving's and 
Pratt's distinctions just stretches it too far.  And it's occurred to me that 
I'd be happy with the adjective "computative" - hence, theoretical math versus 
computative math.

  However, I don't think that we've thoroughly replaced the terms "pure" and 
"applied" as affirmed of math areas until we find some way to justly 
distinguish between so-called 'pure' maths as opposed to so-called 'applied' 
yet often (if not absolutely always) mathematically nontrivial areas such as 
maths of optimization (linear and nonlinear programming), probability theory, 
the maths of information (with laws of information corresponding to 
group-theoretical principles), etc.

  Best, Ben

  ----- Original Message ----- 
  From: Benjamin Udell 

  Sent: Monday, March 12, 2012 1:14 PM 
  Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's 
Peirce edition

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