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Discrete mathematics and its applications / Kenneth H. Rosen.

By: Material type: TextSeries: McGraw-Hill international editions., Mathematics seriesPublication details: Boston : WCB/McGraw-Hill, c1999.Edition: 4th edDescription: xxii, 678 p. : ill. ; 27 cmISBN:
  • 0072899050 (acidfree paper)
  • 9780072899054
Subject(s): LOC classification:
  • QA39.2 .R654
Contents:
1. The Foundations: Logic, Sets, and Functions -- 1.1. Logic -- 1.2. Propositional Equivalences -- 1.3. Predicates and Quantifiers -- 1.4. Sets -- 1.5. Set Operations -- 1.6. Functions -- 1.7. Sequences and Summations -- 1.8. The Growth Functions -- 2. The Fundamentals: Algorithms, the Integers, and Matrices -- 2.1. Algorithms -- 2.2. Complexity of Algorithms -- 2.3. The Integers and Division -- 2.4. Integers and Algorithms -- 2.5. Applications of Number Theory -- 2.6. Matrice -- 3. Mathematical Reasoning -- 3.1. Methods of Proof -- 3.2. Mathematical Induction -- 3.3. Recursive Definitions -- 3.4. Recursive Algorithms -- 3.5. Program Correctness -- 4. Counting -- 4.1. The Basics of Counting -- 4.2. The Pigeonhole Principle -- 4.3. Permutations and Combinations -- 4.4. Discrete Probability -- 4.5. Probability Theory -- 4.6. Generalized Permutations and Combinations -- 4.7. Generating Permutations and Combinations -- 5. Advanced Counting Techniques -- 5.1. Recurrence Relations -- 5.2. Solving Recurrence Relations -- 5.3. Divide-and-Conquer Relations -- 5.4. Generating Functions -- 5.5. Inclusion-Exclusion -- 5.6. Applications of Inclusion-Exclusion -- 6. Relations -- 6.1. Relations and Their Properties -- 6.2. n-ary Relations and Their Applications -- 6.3. Representing Relations -- 6.4. Closures of Relations -- 6.5. Equivalence Relations -- 6.6. Partial Orderings -- 7. Graphs -- 7.1. Introduction to Graphs -- 7.2. Graph Terminology -- 7.3. Representing Graphs and Graph Isomorphism -- 7.4. Connectivity -- 7.5. Euler and Hamilton Paths -- 7.6. Shortest Path Problems -- 7.7. Planar Graphs -- 7.8. Graph Coloring -- 8. Trees -- 8.1. Introduction to Trees -- 8.2. Applications of Trees -- 8.3. Tree Traversal -- 8.4. Trees and Sorting -- 8.5. Spanning Trees -- 8.6. Minimum Spanning Trees -- 9. Boolean Algebra -- 9.1. Boolean Functions -- 9.2. Representing Boolean Functions -- 9.3. Logic Gates -- 9.4. Minimization of Circuits -- 10. Modeling Computation -- 10.1. Languages and Grammar -- 10.2. Finite-State Machines with Output -- 10.3. Finite-State Machines with no Output -- 10.4. Language Recognition -- 10.5. Turing Machines.
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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
Books Methodist University Library Main General Stacks QA39.2 .R654 (Browse shelf(Opens below)) Available 29035
Books Methodist University Library Main General Stacks QA39.2 .R654 (Browse shelf(Opens below)) Available 29046
Books Methodist University Library Main General Stacks Reference QA39.2 .R654 (Browse shelf(Opens below)) Available 14548
Books Methodist University Library Main General Stacks QA39.2 .R654 (Browse shelf(Opens below)) Available 29049
Books Methodist University Library Main General Stacks QA39.2 .R654 (Browse shelf(Opens below)) Available 29055

Includes index

1. The Foundations: Logic, Sets, and Functions --
1.1. Logic --
1.2. Propositional Equivalences --
1.3. Predicates and Quantifiers --
1.4. Sets --
1.5. Set Operations --
1.6. Functions --
1.7. Sequences and Summations --
1.8. The Growth Functions --
2. The Fundamentals: Algorithms, the Integers, and Matrices --
2.1. Algorithms --
2.2. Complexity of Algorithms --
2.3. The Integers and Division --
2.4. Integers and Algorithms --
2.5. Applications of Number Theory --
2.6. Matrice --
3. Mathematical Reasoning --
3.1. Methods of Proof --
3.2. Mathematical Induction --
3.3. Recursive Definitions --
3.4. Recursive Algorithms --
3.5. Program Correctness --
4. Counting --
4.1. The Basics of Counting --
4.2. The Pigeonhole Principle --
4.3. Permutations and Combinations --
4.4. Discrete Probability --
4.5. Probability Theory --
4.6. Generalized Permutations and Combinations --
4.7. Generating Permutations and Combinations --
5. Advanced Counting Techniques --
5.1. Recurrence Relations --
5.2. Solving Recurrence Relations --
5.3. Divide-and-Conquer Relations --
5.4. Generating Functions --
5.5. Inclusion-Exclusion --
5.6. Applications of Inclusion-Exclusion --
6. Relations --
6.1. Relations and Their Properties --
6.2. n-ary Relations and Their Applications --
6.3. Representing Relations --
6.4. Closures of Relations --
6.5. Equivalence Relations --
6.6. Partial Orderings --
7. Graphs --
7.1. Introduction to Graphs --
7.2. Graph Terminology --
7.3. Representing Graphs and Graph Isomorphism --
7.4. Connectivity --
7.5. Euler and Hamilton Paths --
7.6. Shortest Path Problems --
7.7. Planar Graphs --
7.8. Graph Coloring --
8. Trees --
8.1. Introduction to Trees --
8.2. Applications of Trees --
8.3. Tree Traversal --
8.4. Trees and Sorting --
8.5. Spanning Trees --
8.6. Minimum Spanning Trees --
9. Boolean Algebra --
9.1. Boolean Functions --
9.2. Representing Boolean Functions --
9.3. Logic Gates --
9.4. Minimization of Circuits --
10. Modeling Computation --
10.1. Languages and Grammar --
10.2. Finite-State Machines with Output --
10.3. Finite-State Machines with no Output --
10.4. Language Recognition --
10.5. Turing Machines.

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