Discrete mathematical structures = 离散数学结构. 4th ed. /

contents

preface xi

1 fundamentals

1．1 sets and subsets

1．2 operations on sets

1．3 sequences

1．4 divison in the integers

1．5 matrices
1．6 matematical structures

2 logic 46

2．1 propositions and logical operations

2．2 conditional statements

2．3 methods of proof
2．4 mathematical induction

3 counting
3．1 permutations

3．2 combinations

3. 3 pigeonhole principle
3．4 elements of probability

3．5 recurrence relations

.4 relations and digraphs

4．1 product sets and partitions

4．2 relations and digraphs

4．3 paths in relations and digraphs

4．4 properties of relations
4．5 equivalence relations

4．6 computer rrpresentation of relations and digraphs

4．7 operations on relations

4．8 transitive and warshall's algorithm
5 functions

5. 1 functions

5．2 functions for computer science

5．3 growth of functions

5．4 permutation functions

6 order relations and structures
6. 1 partially ordered sets

6．2 extremal elements of partially ordered sets
6. 3 lattices

6. 4 finite boolean algebras

6．5 functions on boolean algebras
6．6 circuit designs
7 trees
7．1 trees
7. 2 labeled trees

7．3 tree searching
7. 4 undirected trees

7. 5 minimal spanning trees
8 topics in graph theory
8．1 graphs
8．2 euler paths and circuits
8．3 hamiltonian paths and circuits
8．4 transport networks
8. 5 matching problems

8. 6 coloring graphs

9 semigroups and groups

9．1 binary operations revisited
9．2 semigroups
9．3 products and quotients of semigroups

9．4 groups

9．5 products and quotients of groups
10 languages and finite-state machines
10．1 languages
10．2 rrpresentations of special grammars and languages
10．3 finite-state machines
10．4 semigroups，machines，and languages

10．5 machines and regulat languages
10．6 sunplification of machines
11 groups and coding

11．1 coding of binary information and error detection

11．2 decoding and error correction

appendix a:algorithms and pseudocode
appendix b:experiments in discrete mathematics

answers to odd－numbered exercises
answers to chapter self-tests
index