TY  - BOOK
AU  - Stanat, Donald F.
AU  - McAllister, David F.
TI  - Discrete mathematics in computer science
SN  - 0132161508
U1  - 004.0151 
PY  - 1977///
CY  - New Delhi 
PB  - Prentice Hal of India Pvt. Ltd.
KW  -  
N1  - CONTENTS
PREFACE x 
Notation xiii
0 MATHEMATICAL MODELS 1
0.0	Introduction 1
0.1	Principles and Models 1
0.2	Mathematical Models 2
0.3	Purposes of Models 6
1 MATHEMATICAL REASONING 8
0	Introduction 8
1	Propositions 9
2	Predicates and Quantifiers 20
3	Quantifiers and Logical Operators 29
4	Logical Inference 39
5	Methods of Proof 47
6	Program Correctness 57
Axioms of Assignment 69
2 SETS 75
0	Introduction 75
1	The Primitives of Set Theory 75 
2	The Paradoxes of Set Theory 79
3   Relations Between Sets 82 
4 Operations on Sets 85 
5 Induction 95
Inductive Definition of Sets 95 
Recursive Procedures 98 
Inductive Proofs 100 
6  The Natural Numbers 108 
7  Set Operations on I* 111
3 BINARY RELATIONS 120
0	Introduction 120
1	Binary Relations and Digraphs 120
2	Trees 131
Search Trees 136
Tree Traversal Algorithms 140
3	Special Properties of Relations 145
4	Composition of Relations 149
5	Closure Operations on Relations 155
6	Order Relations 164
{Some Additional Concepts for Posets 173
7	Equivalence Relations and Partitions 178
{Sums and Products of Partitions 187
4 FUNCTIONS 193
0	Introduction 193
1	Basic Properties of Functions 193
Inductively Defined Functions 199 
Partial Functions 201 
2	Special Classes of Functions 204
Inverse Functions 209 
One-Sided Inverse Functions 213
5 COUNTING AND ALGORITHM ANALYSIS 218
0	Introduction 218
1	Basic Counting Techniques 218
Permutations and Combinations 222 Decision Trees 225
2	Asymptotic Behavior of Functions 232
Some Important Classes of Asymptotic Behavior
3	Recurrence Systems 243
Divide and Conquer Algorithms 248
4	Analysis of Algorithms 258
Searching Algorithms 262 Sorting Algorithms 265
6 INFINITE SETS 275
0	Introduction 275
1	Finite and Infinite Sets 275
2	Countable and Uncountable Sets 279
Comparison of Cardinal Numbers 288
4	Cardinal Arithmetic 295
7 ALGEBRAS 300
0	Introduction 300
1	The Structure of Algebras 301
2	Some Varieties of Algebras 309
Semigroups 309 Monoids 310 Groups 311 Boolean Algebras 312
3	Homomorphisms 315
4	Congruence Relations 322
5	New Algebraic Systems from Old 327
Quotient Algebras 327 Product Algebras 329
APPENDIX: THE PROGRAMMING LANGUAGE 332
ANSWERS TO SFI FP.TFD FXFROISFS 339
BIBLIOGRAPHY 391
INDEX 393


ER  -