A Basis for Theoretical Computer Science (Monographs in Computer Science) by M.A. Arbib (PDF)

Description

Computer science seeks to provide a scientific basis for the study of inform a­ tion processing, the solution of problems by algorithms, and the design and programming of computers. The last forty years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the development of mathematical techniques to allow the rigorous specification of program, process, and machine. The present volume is one of a series, The AKM Series in Theoretical Computer Science, designed to make key mathe­ matical developments in computer science readily accessible to under­ graduate and beginning graduate students. Specifically, this volume takes readers with little or no mathematical background beyond high school algebra, and gives them a taste of a number of topics in theoretical computer science while laying the mathematical foundation for the later, more detailed, study of such topics as formal language theory, computability theory, programming language semantics, and the study of program verification and correctness. Chapter 1 introduces the basic concepts of set theory, with special emphasis on functions and relations, using a simple algorithm to provide motivation. Chapter 2 presents the notion of inductive proof and gives the reader a good grasp on one of the most important notions of computer science: the recursive definition of functions and data structures.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is translated to Japanese at 1984.It is refered on Switching Theory for Logic Synthesis by Tsutomu Sasao.In Japan, it is classic textbook on computer science.

⭐After over 20 years and on a shelf with dozens of more complete texts on any of the subjects covered by Arbib et al, this little text remains my first choice of reference. Why? Because it concisely covers the key definitions and thorems providing a formal basis for computation that are essential for graduate study.

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