Discrete Mathematics

Discrete Mathematics : United States Edition

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Description

For a one- or two-term introductory course in discrete mathematics. This best-selling book provides an accessible introduction to discrete mathematics, using an algorithmic approach that focuses on problem-solving techniques. The new edition weaves techniques of proofs into the text as a running theme. Each chapter has a special section dedicated to showing students how to attack and solve problems.show more

Product details

  • Paperback | 688 pages
  • 213.4 x 279.4 x 27.9mm | 1,655.63g
  • Pearson Education (US)
  • Pearson
  • United States
  • English
  • 6th edition
  • 0131176862
  • 9780131176867

Table of contents

(NOTE: All Chapters end with Notes, Chapter Review, Chapter Self-Test, and Computer Exercises.) 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.show more

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132 ratings
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3 20% (26)
2 10% (13)
1 6% (8)
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