--- An associative algebra approach to logic, arithmetic and automata"
is available, for 19.50 euro + postage. For more details see my homepage
http://home.claranet.nl/users/benschop
--- Order via my email, given there.
PS: After re-acquiring the copyright from Springer in 2010, the
booktitle
was changed as above, and Ch.9 (elementary proof Goldbach) improved.
It was printed by abc.nl (American Book Center, Amsterdam, Febr.2011).
Two reviews are included (ACM Computing Reviews, and Zentralblatt.Math)
of which the first follows:
=======
ACM Computing Review CR137206: "Associative Digital Network Theory",
--- An associative algebra approach to logic, arithmetic and state
machines.
(prof. Harvey Cohn, CUNY, Aug.2009)
As a historical fact, mathematics developed from applications
-- in rational mechanics and number theory -- for which
commutative algebra was most natural. If the basic applications
were from network theory (Turing machines ) the associative
algebra/(ab)c = a(bc) /would have been more natural, with Boolean
algebra /aa = a ,/ and commutative algebra /ab = ba,/ as special cases.
Benschop develops this thesis in an idiosyncratic fashion,
reinforced by a long career of practical experience. This book
may well be an important historical document, also useful for
seminars, even if it is not presented primarily for class usage.
There are profuse illustrations in classic number theory, as well
as claims that the outlook sheds new light on classic problems
such as those of Fermat and Goldbach, interpreted as machines.
As unlikely as it is that this may be practical, it makes for an
interesting book.
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