# Discrete Mathematics : International Edition

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## 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.show more

## Product details

• Paperback | 792 pages
• 195 x 242 x 30mm | 1,426g
• Pearson
• United States
• English
• 7th edition
• 0131354302
• 9780131354302
• 859,478

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: Quantifiers 2 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 Exercises 3 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 Databases 4 Algorithms4.1 Introduction4.2 Examples of Algorithms4.3 Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm4.4 Recursive Algorithms 5 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 Cryptosystem 6 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 Principle 7 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 Insanity 9 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 Trees 10 Network Models10.1 Introduction10.2 A Maximal Flow Algorithm10.3 The Max Flow, Min Cut Theorem10.4 MatchingProblem-Solving Corner: Matching 11 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 Applications 12 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 Automata 13 Computational Geometry13.1 The Closest-Pair Problem13.2 An Algorithm to Compute the Convex Hull AppendixA MatricesB Algebra ReviewC PseudocodeReferencesHints and Solutions to Selected Exercises Indexshow more

Richard Johnsonbaugh is Professor Emeritus of Computer Science, Telecommunications and Information Systems, DePaul University, Chicago. Prior to his 20-year service at DePaul University, he was a member and sometime chair of the mathematics departments at Morehouse College and Chicago State University. He has a B.A. degree in mathematics from Yale University, M.A. and Ph.D. degrees in mathematics from the University of Oregon, and an M.S. degree in computer science from the University of Illinois, Chicago. His most recent research interests are in pattern recognition, programming languages, algorithms, and discrete mathematics. He is the author or co-author of numerous books and articles in these areas. Several of his books have been translated into various languages. He is a member of the Mathematical Association of America.show more

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