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Discrete mathematics and its applications

Author: Kenneth H Rosen
Publisher: Boston : WCB/McGraw-Hill, ©1999.
Series: McGraw-Hill international editions., Mathematics series.
Edition/Format:   Print book : English : 4th edView all editions and formats
Summary:

Balancing theory and relevant applications in its approach, this text covers nonhomogeneous linear recurrence relations with constant coefficients and probability theory.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Kenneth H Rosen
ISBN: 0072899050 9780072899054 0071167560 9780071167567
OCLC Number: 39905655
Description: xxii, 678 pages : illustrations ; 27 cm
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.
Series Title: McGraw-Hill international editions., Mathematics series.
Responsibility: Kenneth H. Rosen.
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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. 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