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E-book: From Boolean Logic to Switching Circuits and Automata: Towards Modern Information Technology

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Logic networks and automata are facets of digital systems. The change of  the design of logic networks from skills and art into a scientific discipline was possible by the development of the  underlying mathematical theory called the Switching Theory. The fundamentals of this theory come from the attempts towards an algebraic description of laws of thoughts presented  in the works by George J. Boole and  the works on logic by Augustus De Morgan.

 

As often the case in engineering, when the importance of a problem and the need for solving it reach certain limits, the solutions are searched by many scholars in different parts of the word, simultaneously or at about the same time, however, quite independently and often unaware of  the work by other scholars. The formulation and rise of Switching Theory is such an example.

 

This book  presents a brief account of the developments of Switching Theory and highlights some less known facts in the history of it.  The readers will find the book a fresh look into the development of the field revealing how difficult it has been to arrive at many of the concepts that we now consider obvious . Researchers in the history or philosophy of computing will find this book a valuable source of information that complements the standard presentations of the topic.

 

 



This volume offers an extensive analysis of the development of switching theory as mathematical foundations for modern design. The text serves as a pictorial history book of applications of Boolean logic in engineering.

Reviews

From the reviews:

This is a book on the history of switching theory and Boolean algebras. The text presents historical remarks on its early development and details on the different authors who made significant contributions to these areas . this is a text for those who are interested in the history of mathematics. (H. Mitsch, Monatshefte für Mathematik, Vol. 164 (4), December, 2011)

Part I Mathematical Foundations
1 From Logic to Mathematical Logic
3(32)
1.1 Revival of Study of Logic in Britain
4(2)
1.2 Elements of Logic by Whately
6(8)
1.3 Ten Rules of Philosophizing by Herschel
14(4)
1.4 Inductive Science by Whewell
18(7)
1.5 Mill and a System of Logic
25(10)
2 Boolean Logic
35(52)
2.1 Formal Logic by De Morgan
38(8)
2.2 Work on Logic by Boole
46(1)
2.3 Mathematical Analysis of Logic
47(4)
2.4 The Calculus of Logic
51(2)
2.5 The Laws of Thought
53(11)
2.6 Boolean Algebra
64(2)
2.7 Work on Logic by Jevons
66(5)
2.8 Jevons and Boole
71(1)
2.9 Mechanization of Boolean Logic
72(12)
2.10 Contributions of P.S. Poreckij
84(3)
3 Algebra of Logic
87(24)
3.1 Algebra of Logic by Schroder
91(15)
3.2 Contributions by Ch. S. Peirce
106(4)
3.3 Venn Diagrams
110(1)
4 Boolean Algebra - A Mathematical Subject
111(10)
4.1 Axiomatization by Huntington
114(3)
4.2 Boolean Algebra - A Strong Mathematical Subject
117(4)
Part II Switching Theory
5 Application of Algebra of Logic in Engineering
121(8)
5.1 Remarks and Ideas by P. Ehrnfest
124(5)
6 Switching Theory - From Art and Skills to Scientific Methods
129(12)
6.1 Switching Theory from Boolean Algebra
132(5)
6.2 Review of the Work by Shannon
137(2)
6.3 Review by Baylis
139(2)
7 Switching Theory in USSR
141(12)
7.1 Pioneering Work by Shestakov
144(5)
7.2 Contributions by Other Researchers
149(4)
8 Switching Theory in Japan
153(14)
8.1 Akira Nakashima
156(7)
8.2 Nakashima and Hanzawa
163(3)
8.3 Continuation of Research
166(1)
9 Switching Theory in Europe
167(16)
9.1 Johanna Piesch
170(4)
9.2 Vienna School in Switching
174(9)
10 Postscript
183(12)
10.1 Switching Theory
183(2)
10.1.1 Boolean Algebra
184(1)
10.2 Algebra of Logic
185(3)
10.2.1 Work
185(2)
G.J. Boole
10.2.2 Work
187(1)
Platon S. Poreckij
10.3 Applications of Boolean Algebra
188(7)
10.3.1 First Applications of Algebra of Logic in Circuit Design
188(1)
10.3.2 Work
188(1)
V.I. Sestakov
10.3.3 Work
189(2)
C.E. Shannon
10.3.4 Work
191(2)
A. Nakashima
10.3.5 Work
193(2)
J. Piesch
References in the Postscript 195(12)
List of Illustrations 207