Discrete Mathematics

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  • Edition: 7th
  • Format: Hardcover
  • Copyright: 2007-12-29
  • Publisher: Pearson
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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 textrs"s Web site athttp://condor.depaul.edu/tilde;rjohnson/dm7th.

Author Biography

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.

Table of Contents

Sets and Logic
Conditional Propositions and Logical Equivalence
Arguments and Rules of Inference
Nested QuantifiersProblem-Solving Corner: Quantifiers
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
Equivalence RelationsProblem-Solving Corner: Equivalence Relations
Matrices of Relations
Relational Databases
Examples of Algorithms
Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm
Recursive Algorithms
Introduction to Number Theory
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
Solving Recurrence RelationsProblem-Solving Corner: Recurrence Relations
Applications to the Analysis of Algorithms
Graph Theory
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
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
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
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
Algebra Review
Hints and Solutions to Selected Exercises
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