| adapter\'s forword preface to the student list of symbols chapter 1 the foundations: logic and proofs 1.1 propositional logic 1.2 propositional equivalences 1.3 predicates and quantifiers 1.4 nested quantifiers 1.5 rules of inference 1.6 introduction to proofs 1.7 proof methods and strategy end-of-chapter material chapter 2 basic structures: sets, functions, sequences, and sums 2.1 sets 2.2 set operations 2.3 functions 2.4 sequences and summations end-of-chapter material chapter3 counting .3.1 the basics of counting 3.2 the pigeonhole principle 3.3 permutations and combinations 3.4 binomial coefficients 3.5 generalized permutations and combinations 3.6 generating permutations and combinations end-of-chapter material chapter 4 advanced counting techniques 4.1 recurrence relations 4.2 solving linear recurrence relations 4.3 divide-and-conquer algorithms and recurrence relations 4.4 generating functions 4.5 inclusion-exclusion 4.6 applications of inclusion-exclusion end-of-chapter material chapter 5 relations 5.1 relations and their properties 5.2 n-ary relations and their applications 5.3 representing relations 5.4 closures of relations 5.5 equivalence relations 5.6 partial orderings end-of-chapter material chapter 6 graphs 6.1 graphs and graph models 6.2 graph terminology and special types of graphs 6.3 representing graphs and graph isomorphism 6.4 connectivity 6.5 euler and hamilton paths 6.6 shortest-path problems 6.7 planar graphs 6.8 graph coloring end-of-chapter material chapter 7 trees 7.1 introduction to trees 7.2 applications of trees 7.3 tree traversal 7.4 spanning trees 7.5 minimum spanning trees end-of-chapter material answers to exercises |
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