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    Discrete Mathematics

    ISBN-10: 0131593188
    ISBN-13: 9780131593183
    Author(s): Richard Johnsonbaugh
    Description: Focused on helping readers understand and construct proofs and, generally, expanding their mathematical maturity this best-seller is an accessible introduction to discrete mathematics. Takes an algorithmic approach that emphasizes problem-solving  More...
    List price: $168.00
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    List Price: $168.00
    Edition: 7th
    Publisher: Prentice Hall PTR
    Binding: Hardcover
    Pages: 792
    Size: 8.00" wide x 10.00" long x 1.50" tall
    Weight: 3.630
    Language: English

    Focused on helping readers understand and construct proofs and, generally, expanding their mathematical maturity this best-seller is an accessible introduction to discrete mathematics. Takes an algorithmic approach that emphasizes problem-solving techniques. Expands discussion on how to construct proofs and treatment of problem solving. Increases number of examples and exercises throughout. Updates textrsquo;s Web site athttp://condor.depaul.edu/tilde;rjohnson/dm7th.

    Sets and Logic
    Sets
    Propositions
    Conditional Propositions and Logical Equivalence
    Arguments and Rules of Inference
    Quantifiers
    Nested QuantifiersProblem-Solving Corner: Quantifiers
    Proofs
    Mathematical Systems, Direct Proofs, and Counterexamples
    More Methods of ProofProblem-Solving Corner: Proving Some Properties of Real Numbers
    Resolution Proofs
    Mathematical InductionProblem-Solving Corner: Mathematical Induction
    Strong Form of Induction and the Well-Ordering Property Notes Chapter Review Chapter Self-Test Computer Exercises
    Functions, Sequences, and Relations
    FunctionsProblem-Solving Corner: Functions
    Sequences and Strings
    Relations
    Equivalence RelationsProblem-Solving Corner: Equivalence Relations
    Matrices of Relations
    Relational Databases
    Algorithms
    Introduction
    Examples of Algorithms
    Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm
    Recursive Algorithms
    Introduction to Number Theory
    Divisors
    Representations of Integers and Integer Algorithms
    The Euclidean AlgorithmProblem-Solving Corner: Making Postage
    The RSA Public-Key Cryptosystem
    Counting Methods and the Pigeonhole Principle
    Basic PrinciplesProblem-Solving Corner: Counting
    Permutations and CombinationsProblem-Solving Corner: Combinations
    Generalized Permutations and Combinations
    Algorithms for Generating Permutations and Combinations
    Introduction to Discrete Probability
    Discrete Probability Theory
    Binomial Coefficients and Combinatorial Identities
    The Pigeonhole Principle
    Recurrence Relations
    Introduction
    Solving Recurrence RelationsProblem-Solving Corner: Recurrence Relations
    Applications to the Analysis of Algorithms
    Graph Theory
    Introduction
    Paths and CyclesProblem-Solving Corner: Graphs
    Hamiltonian Cycles and the Traveling Salesperson Problem
    A Shortest-Path Algorithm
    Representations of Graphs
    Isomorphisms of Graphs
    Planar Graphs
    Instant Insanity
    Trees
    Introduction
    Terminology and Characterizations of TreesProblem-Solving Corner: Trees
    Spanning Trees
    Minimal Spanning Trees
    Binary Trees
    Tree Traversals
    Decision Trees and the Minimum Time for Sorting
    Isomorphisms of Trees
    Game Trees
    Network Models
    Introduction
    A Maximal Flow Algorithm
    The Max Flow, Min Cut Theorem
    MatchingProblem-Solving Corner: Matching
    Boolean Algebras and Combinatorial Circuits
    Combinatorial Circuits
    Properties of Combinatorial Circuits
    Boolean AlgebrasProblem-Solving Corner: Boolean Algebras
    Boolean Functions and Synthesis of Circuits
    Applications
    Automata, Grammars, and Languages
    Sequential Circuits and Finite-State Machines
    Finite-State Automata
    Languages and Grammars
    Nondeterministic Finite-State Automata
    Relationships Between Languages and Automata
    Computational Geometry
    The Closest-Pair Problem
    An Algorithm to Compute the Convex Hull
    Appendix
    Matrices
    Algebra Review
    Pseudocode
    References
    Hints and Solutions to Selected Exercises
    Index

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    • Due Date: 12/24/2014

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