From Boolean Logic to Switching Circuits and Automata

Towards Modern Information Technology

Author: Radomir S. Stankovic

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 212

View: 371

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.

Algebraic Extensions of Fields

Author: Paul J. McCarthy

Publisher: Courier Corporation


Category: Mathematics

Page: 192

View: 548

Graduate-level coverage of Galois theory, especially development of infinite Galois theory; theory of valuations, prolongation of rank-one valuations, more. Over 200 exercises. Bibliography. "...clear, unsophisticated and direct..." — Math.

Introduction to Modern Algebra and Matrix Theory

Author: Otto Schreier



Category: Algebra

Page: 378

View: 341

Affine space; linear equations; Euclidean space; theory of determinants; Field theory; the fundamental theorem of algebra; Elements of group theory; Linear transformations and matrices.

Modern Algebra and the Rise of Mathematical Structures

Author: Leo Corry

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 452

View: 889

This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.