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Discrete Mathematics and its Applications

Author(s):Kenneth H. Rosen, Wcb, McGraw-Hill
Publisher:McGraw-Hill Science/Engineering/Math; 4th edition
Date     : 1998
Pages    :824
Format   :DJVU
OCR      :No
Quality  :Bad
Language :English
ISBN     :0072899050

This text is designed for the sophomore/junior level introduction to discrete mathematics taken by students preparing for future coursework in areas such as math, computer science and engineering. Rosen has become a bestseller largely due to how effectively it addresses the main portion of the discrete market, which is typically characterized as the mid to upper level in rigor. The strength of Rosen’s approach has been the effective balance of theory with relevant applications, as well as the overall comprehensive nature of the topic coverage.

Table of Contents

Preface
To the Student
The Companion Web Site
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 Matrices
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 Grammars
10.2 Finite-State Machines with Output
10.3 Finite-State Machines with No Output
10.4 Language Recognition
10.5 Turing Machines
Appendixes
A.1 Exponential and Logarithmic Functions
A.2 Pseudocode
Suggested Readings
Solutions to Odd-Numbered Exercises
Index of Biographies
Index

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