Author(s): Stanat, Donald F.; McAllister, David F.
Publisher: Prentice-Hall International Editions
Year: 1977
Language: English
Pages: 401
City: London
Tags: Mathematics, Electronic data processing, Data processing, Information Technology
CONTENTS
PREFACE
Notation
0: MATHEMATICAL MODELS
0.0: Introduction
0.1: Principles and Models
0.2: Mathematical Models
0.3: Purposes of Models
1: MATHEMATICAL REASONING
1.0: Introduction
1.1: Propositions
1.2: Predicates and Quantifiers
1.3: Quantifiers and Logical Operators
1.4: Logical Inference
1.5: Methods of Proof
1.6: Program Correctness
Axioms of Assignment
2: SETS
2.0: Introduction
2.1: The Primitives of Set Theory
2.2: The Paradoxes of Set Theory
2.3: Relations Between Sets
2.4: Operations on Sets
2.5: Induction
Inductive Definition of Sets
Recursive Procedures
Inductive Proofs
2.6: The Natural Numbers
2.7: Set Operations on ∑
3: BINARY RELATIONS
3.0: Introduction
3.1: Binary Relations and Digraphs
3.2: Trees
Search Trees
Tree Traversal Algorithms
3.3: Special Properties of Relations
3.4: Composition of Relations
3.5: Closure Operations on Relations
3.6: Order Relations
Some Additional Concepts for Posets
3.7: Equivalence Relations and Partitions
Sums and Products of Partitions
4: FUNCTIONS
4.0: Introduction
4.1: Basic Properties of Functions
Inductively Defined Functions
Partial Functions
4.2: Special Classes of Functions
Inverse Functions
One-Sided Inverse Functions
5: COUNTING AND ALGORITHM ANALYSIS
5.0: Introduction
5.1: Basic Counting Techniques
Permutations and Combinations
Decision Trees
5.2: Asymptotic Behavior of Functions
Some Important Classes of Asymptotic Behavior
5.3: Recurrence Systems
Divide and Conquer Algorithms
5.4: Analysis of Algorithms
Searching Algorithms
Sorting Algorithms
6: INFINITE SETS
6.0: Introduction
6.1: Finite and Infinite Sets
6.2: Countable and Uncountable Sets
6.3: Comparison of Cardinal Numbers
6.4: Cardinal Arithmetic
7: ALGEBRAS
7.0: Introduction
7.1: The Structure of Algebras
7.2: Some Varieties of Algebras
Semigroups
Monoids
Groups
Boolean Algebras
7.3: Homomorphisms
7.4: Congruence Relations
7.5: New Algebraic Systems from Old
Quotient Algebras
Product Algebras
APPENDIX: THE PROGRAMMING LANGUAGE
ANSWERS TO SELECTED EXERCISES
BIBLIOGRAPHY
INDEX
