Sets, relations, and induction

Author(s)

• Fejer, Peter A.
• Simovici, Dan A.

Bibliographic Information

Sets, relations, and induction

Peter A. Fejer, Dan A. Simovici

（Texts and monographs in computer science, . Mathematical foundations of computer science ; v. 1）

Springer-Verlag, c1991

• : New York
• : Berlin

Note

Includes bibliographical references and index

Description and Table of Contents

Volume

: New York ISBN 9780387974507

Description

Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science. This volume treats basic topics, mostly of a set-theoretical nature (sets, functions and relations, partially ordered sets, induction, enumerability, and diagonalization) and illustrates the usefulness of mathematical ideas by presenting applications to computer science. Readers will find useful applications in algorithms, databases, semantics of programming languages, formal languages, theory of computation, and program verification. The material is treated in a straightforward, systematic, and rigorous manner. The volume is organized by mathematical area, making the material easily accessible to the upper-undergraduate students in mathematics as well as in computer science and each chapter contains a large number of exercises. The volume can be used as a textbook, but it will also be useful to researchers and professionals who want a thorough presentation of the mathematical tools they need in a single source. In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata, and logic programming.

Table of Contents

1 Elementary Set Theory.- 1.1 Introduction.- 1.2 Sets, Members, Subsets.- 1.3 Building New Sets.- 1.4 Exercises and Supplements.- 1.5 Bibliographical Comments.- 2 Relations and Functions.- 2.1 Introduction.- 2.2 Relations.- 2.3 Functions.- 2.4 Sequences, Words, and Matrices.- 2.5 Images of Sets Under Relations.- 2.6 Relations and Directed Graphs.- 2.7 Special Classes of Relations.- 2.8 Equivalences and Partitions.- 2.9 General Cartesian Products.- 2.10 Operations.- 2.11 Representations of Relations and Graphs.- 2.12 Relations and Databases.- 2.13 Exercises and Supplements.- 2.14 Bibliographical Comments.- 3 Partially Ordered Sets.- 3.1 Introduction.- 3.2 Partial Orders and Hasse Diagrams.- 3.3 Special Elements of Partially Ordered Sets.- 3.4 Chains.- 3.5 Duality.- 3.6 Constructing New Posets.- 3.7 Functions and Posets.- 3.8 Complete Partial Orders.- 3.9 The Axiom of Choice and Zorn's Lemma.- 3.10 Exercises and Supplements.- 3.11 Bibliographical Comments.- 4 Induction.- 4.1 Introduction.- 4.2 Induction on the Natural Numbers.- 4.3 Inductively Defined Sets.- 4.4 Proof by Structural Induction.- 4.5 Recursive Definitions of Functions.- 4.6 Constructors.- 4.7 Simultaneous Inductive Definitions.- 4.8 Propositional Logic.- 4.9 Primitive Recursive and Partial Recursive Functions.- 4.10 Grammars.- 4.11 Peano's Axioms.- 4.12 Well-Founded Sets and Induction.- 4.13 Fixed Points and Fixed Point Induction.- 4.14 Exercises and Supplements.- 4.15 Bibliographical Comments.- 5 Enumerability and Diagonalization.- 5.1 Introduction.- 5.2 Equinumerous Sets.- 5.3 Countable and Uncountable Sets.- 5.4 Enumerating Programs.- 5.5 Abstract Families of Functions.- 5.6 Exercises and Supplements.- 5.7 Bibliographical Comments.- References.

Volume

: Berlin ISBN 9783540974505

Description

This is the first of a two-volume work presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science. This volume treats basic topics, mostly of a set-theoretical nature (sets, functions and relations, partially ordered sets, induction, enumerability and diagonalization) and illustrates the usefulness of mathematical ideas by presenting applications to computer science. Readers will find useful applications in algorithms, databases, semantics of programming languages, formal languages, theory of computation and program verification. The volume is organized by mathematical area, making the material easily accessible to the upper-undergraduate student in mathematics or computer science and each chapter contains a large number of exercises. The volume can be used as a textbook, but it will also be useful to researchers and professionals who want a thorough presentation of the mathematical tools they need in a single source. In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata and logic programming.

by "Nielsen BookData"

Details

• NCID: BA11595887
• ISBN:
  • 0387974504
  • 3540974504
• LCCN: 90049595
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York ; Tokyo
• Pages/Volumes: x, 425 p.
• Size: 25 cm
• Classification:
  • LCC : QA76.9.M35
  • DC20 : 004/.01/51
• Subject Headings:
  • LCSH : Computer science -- Mathematics
• Parent Bibliography ID:
  • BA00039349