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| Authored by: Anonymous on Friday, August 31 2012 @ 11:02 AM EDT |
Have you had a chance to review the following:
http://groklawstatic.ibiblio.org/article.php%3fstory=20110426051819346
http://groklawstatic.ibiblio.org/article.php%3fstory=20110908075658894
I think it provides very good arguments and evidences on this topic and more
importantly numerous references are given.
[ Reply to This | Parent | # ]
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| Authored by: PolR on Friday, August 31 2012 @ 11:51 AM EDT |
| Computation
theory is a branch of mathematics, actually a sub-branch of mathematical logic.
You are asking for a justification of the most basic concepts of this
field.
Expositions of my views complete with links and references to
literature is found in these groklaw articles. This is where you will find what
I mean by "published in literature".
A Simpler
Explanation of Why Software is Mathematics
This particular article
contains a detailed discussion of what an algorithm is and how it relates to
computers.
1+1 (pat.
pending) — Mathematics, Software and Free Speech
In this article the
definition of algorithm is discussed specifically in appendix A. I quote there a
well known definition of Stephen Kleene and also some work from Turing and
Knuth.
Since access to a library is problematic for you, I suggest
you gain access to this book and read the chapters on Alan Turing and the
invention of the modern computers. It is inexpensive, easy to read and still in
print. You may order it from an on-line bookstore.
Davis, Martin,
Engines of Logic, Mathematicians and the Origin of the Computer, W.W. Norton and
Company, 2000. This book was originally published under the title The Universal
Computer: The Road from Leibnitz to Turing.
An on-line resource
you may find interesting is the Stanford Encyclopedia of Philosophy. Jack
Copeland who also happens to be a
well known historian of Alan Turing has posted there articles on the Church-Turing thesis
and the
modern history of computing which summarize some of the relevant
information. See also Neil Immerman's aritcle on computability and
complexity. But these on-line references don't contain the full story. [ Reply to This | Parent | # ]
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| Authored by: bprice on Sunday, September 02 2012 @ 08:19 AM EDT |
Can you give an example of a paper that supports your definition,
preferably a paper that's available online. I'm unable to get to a library for
the foreseeable future.
My personal favourite is the EWD collection, at the University of
Texas, of many of the works of E. W. Dijkstra. Their home page also links to
"Discipline in Thought which is a website
dedicated to disciplined thinking, calculational mathematics, and mathematical
methodology".
My bookcase is puny in comparison to the bookcase of anyone
who's competent to teach CompSci, so I'll just list my favourites on the topic.
You, as an instructor of CompSci, would have them right to hand:
Dahl,
Dijkstra, and Hoare, Structured Programming, 1972.
Dijkstra, A
Discipline of Programing, 1976.
Wirth, Algorithms + Data Structures
= Programs, 1976.
Yes, they're old, but so is the recognition that
programming is a branch of mathematics. Since the CompSci is, and has always
been, a branch of mathematics, the fact is not belaboured, but is (largely)
assumed. The references I give support that definition by that assumption;
these references (and most others) make little sense unless one accepts the
mathematical nature of programming.
---
--Bill. NAL: question the
answers, especially mine. [ Reply to This | Parent | # ]
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