離散数学（第７版） Discrete Mathematics （7TH）

離散数学（第７版）<br>Discrete Mathematics （7TH）

離散数学（第７版）
Discrete Mathematics （7TH）

Johnsonbaugh, Richard

Pearson College Div（2007/12発売）

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製本 Hardcover:ハードカバー版／ページ数 766 p.
言語 ENG
商品コード 9780131593183
DDC分類 519

Full Description

For a one- or two-term introductory course in discrete mathematics.Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

1 Sets and Logic1.1 Sets1.2 Propositions1.3 Conditional Propositions and Logical Equivalence1.4 Arguments and Rules of Inference1.5 Quantifiers1.6 Nested QuantifiersProblem-Solving Corner: Quantifiers2 Proofs2.1 Mathematical Systems, Direct Proofs, and Counterexamples2.2 More Methods of ProofProblem-Solving Corner: Proving Some Properties of Real Numbers2.3 Resolution Proofs2.4 Mathematical InductionProblem-Solving Corner: Mathematical Induction2.5 Strong Form of Induction and the Well-Ordering Property Notes Chapter Review Chapter Self-Test Computer Exercises3 Functions, Sequences, and Relations3.1 FunctionsProblem-Solving Corner: Functions3.2 Sequences and Strings3.3 Relations3.4 Equivalence RelationsProblem-Solving Corner: Equivalence Relations3.5 Matrices of Relations3.6 Relational Databases4 Algorithms4.1 Introduction4.2 Examples of Algorithms4.3 Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm4.4 Recursive Algorithms5 Introduction to Number Theory5.1 Divisors5.2 Representations of Integers and Integer Algorithms5.3 The Euclidean AlgorithmProblem-Solving Corner: Making Postage5.4 The RSA Public-Key Cryptosystem6 Counting Methods and the Pigeonhole Principle6.1 Basic PrinciplesProblem-Solving Corner: Counting6.2 Permutations and CombinationsProblem-Solving Corner: Combinations6.3 Generalized Permutations and Combinations6.4 Algorithms for Generating Permutations and Combinations6.5 Introduction to Discrete Probability6.6 Discrete Probability Theory6.7 Binomial Coefficients and Combinatorial Identities6.8 The Pigeonhole Principle7 Recurrence Relations7.1 Introduction7.2 Solving Recurrence RelationsProblem-Solving Corner: Recurrence Relations7.3 Applications to the Analysis of Algorithms 8 Graph Theory8.1 Introduction8.2 Paths and CyclesProblem-Solving Corner: Graphs8.3 Hamiltonian Cycles and the Traveling Salesperson Problem8.4 A Shortest-Path Algorithm8.5 Representations of Graphs8.6 Isomorphisms of Graphs8.7 Planar Graphs8.8 Instant Insanity9 Trees9.1 Introduction9.2 Terminology and Characterizations of TreesProblem-Solving Corner: Trees9.3 Spanning Trees9.4 Minimal Spanning Trees9.5 Binary Trees9.6 Tree Traversals9.7 Decision Trees and the Minimum Time for Sorting9.8 Isomorphisms of Trees9.9 Game Trees10 Network Models10.1 Introduction10.2 A Maximal Flow Algorithm10.3 The Max Flow, Min Cut Theorem10.4 MatchingProblem-Solving Corner: Matching11 Boolean Algebras and Combinatorial Circuits11.1 Combinatorial Circuits11.2 Properties of Combinatorial Circuits11.3 Boolean AlgebrasProblem-Solving Corner: Boolean Algebras11.4 Boolean Functions and Synthesis of Circuits11.5 Applications12 Automata, Grammars, and Languages12.1 Sequential Circuits and Finite-State Machines12.2 Finite-State Automata12.3 Languages and Grammars12.4 Nondeterministic Finite-State Automata12.5 Relationships Between Languages and Automata13 Computational Geometry13.1 The Closest-Pair Problem13.2 An Algorithm to Compute the Convex HullAppendixA MatricesB Algebra ReviewC PseudocodeReferencesHints and Solutions to Selected Exercises Index