preface xvii a word to students xxi 1 fundamentals 1.1 sets and subsets 1.2 operations on sets 1.3 sequences 131.4 properties of integers 1.5 matrices 1.6 mathematical structures 2 logic 2.1 propositions and logical operations 2.2 conditional statements 2.3 methods of proof 2.4 mathematical induction 2.5 mathematical statements 2.6 logic and problem solving 3 counting 3.1 permutations 3.2 combinations 3.3 pigeonhole principle 3.4 elements of probability 3.5 recurrence relations4 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 data structures for relations and digraphs 4.7 operations on relations 4.8 transitive closure 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 design 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 9.6 other mathematical structures 10 languages and finite-state machines 10.1 languages 10.2 representations of special grammars and languages 10.3 finite-state machines 10.4 monoids, machines, and languages 10.5 machines and regular languages 10.6 simplification of machines 11 groups and coding 11.1 coding of binary information and error detection 11.2 decoding and error correction 11.3 public key cryptology appendix a: algorithms and pseudocode 455 appendix b: additional experiments in discrete mathematics appendix c: coding exercises answers to odd-numbered exercises answers to chapter self-tests glossary index photo credits