Discrete mathematics / Richard Johnsonbaugh.
By: Johnsonbaugh, Richard
.
Material type: 
BookPublisher: New York : Macmillan, c1993Edition: 3rd ed.Description: xiv, 800 p. : ill. (some col.) ; 27 cm. + hbk.ISBN: 0023607211.Subject(s): Mathematics | Computer science -- MathematicsDDC classification: 510 | Item type | Current library | Call number | Copy number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|---|
| General Lending | MTU Bishopstown Library Lending | 510 (Browse shelf(Opens below)) | 1 | Available | 00151831 | ||
| General Lending | MTU Bishopstown Library Lending | 510 (Browse shelf(Opens below)) | 1 | Available | 00018368 |
Enhanced descriptions from Syndetics:
This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; Algorithms; Counting Methods and the Pigeonhole Principle; Recurrence Relations; Graph Theory; Trees; Network Models; Boolean Algebra and Combinatorial Circuits; Automata, Grammars, and Languages; Computational Geometry. For individuals interested in mastering introductory discrete mathematics.
Includes bibliographical references (pages 659-663) and index.
Logic and proofs -- The language of mathematics -- Algorithms -- Counting methods and the pigeonhole principle -- Recurrence relations -- Graph theory -- Trees -- Network models and petri nets -- Boolean algebras and combinatorial circuits -- Automata, grammars, and languages -- Computational geometry.
Table of contents provided by Syndetics
- Preface
- 1 Logic and Proofs
- Propositions
- Conditional Propositions and Logical Equivalence
- Quantifiers
- Proofs
- Resolution Proofs
- Mathematical Induction
- Strong Form of Induction and well ordering Property
- 2 The Language of Mathematics
- Sets
- Functions
- Sequences and Strings
- Relations
- 3 Relations
- Relations
- Equivalence Relations
- Matrices of Relations
- Relational Databases
- 4 Algorithms
- Introduction
- Correctness of Algorithms
- Analysis of Algorithms
- Recursive Algorithms
- 5 Introduction to Number Theory
- Divisors
- Representation of Integers and Integer Algorithims
- The Euclidean Algorithm
- The RSA Public-Key Cryptosystem
- 6 Counting Methods and the Pigeonhole Principle
- Basic Principles
- Permutations and Combinations
- Algorithms for Generating Permutations and Combinations
- Introduction to Discrete Probability
- Discrete Probability Theory
- Generalized Permutations and Combinations
- Binomial Coefficients and Combinatorial Identities
- The Pigeonhole Principle
- 7 Recurrence Relations
- Introduction
- Solving Recurrence Relations
- Applications to the Analysis of Algorithms
- 8 Graph Theory
- Introduction
- Paths and Cycles
- Hamiltonian Cycles and the Traveling Salesperson Problem
- A Shortest-Path Algorithm
- Representations of Graphs
- Isomorphisms of Graphs
- Planar Graphs
- Instant Insanity
- 9 Trees
- Introduction
- Terminology and Characterizations of Trees
- Spanning Trees
- Minimal Spanning Trees
- Binary Trees
- Tree Traversals
- Decision Trees and the Minimum Time for Sorting
- Isomorphisms of Trees
- Game Trees
- 10 Network Models
- Introduction
- A Maximal Flow Algorithm
- The Max Flow, Min Cut Theorem
- Matching
- 11 Boolean Algebras and Combinatorial Circuits
- Combinatorial Circuits
- Properties of Combinatorial Circuits
- Boolean Algebras
- Boolean Functions and Synthesis of Circuits
- Applications
- 12 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
- 13 Computational Geometry
- The Closest-Pair Problem
- An Algorithm to Compute the Convex Hull
- Appendices
- Matrices
- Algebra Review
- References
- Hints and Solutions to Selected Exercises
- Index