This title will be printed on demand on the EBM in either store.
Description This book is intended for researchers at industrial laboratories, teachers and students at technical universities, in electrical engineering, computer science and applied math departments, interested in new developments of modeling and designing digital networks (state machines, combinational and sequential logic) in general, as combined math/engineering discipline. As background an undergraduate level of ”Modern appied algebra” (Birkhoff-Bartee -1970), and “Algebraic Structure of Sequential Machines” (Hartmanis-Stearns” -1970) will suffice.
"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 This book may well be an important historical document, also useful for seminars, even if it is not presented primarily for class usage.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."
PS: After re-acquiring the copyright from Springer in 2010, the booktitle is now: "The Associative Structure of State Machines - An associative algebra approach to logic, arithmetic and automata", printed by abc.nl (American Book Center, Amsterdam, Febr.2011) with an extended Ch.9 (elementary proof Goldbach). This review refers to the paperback edition