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Discrete Mathematics and Its Applications

ISBN-10: 0072930330
ISBN-13: 9780072930337
Edition: 5th 2003 (Revised)
Authors: Kenneth H. Rosen
List price: $136.88 Buy it from $10.77
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Description: Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include  More...

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Book details

List price: $136.88
Edition: 5th
Copyright year: 2003
Publisher: Glencoe/McGraw-Hill
Publication date: 4/22/2003
Binding: Hardcover
Pages: 896
Size: 8.00" wide x 9.75" long x 1.25" tall
Weight: 4.092
Language: English

Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject.True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed.The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

Discrete Mathematics and Its Applications, Fifth Edition
The Foundations: Logic and Proof, Sets, and Functions
Logic
Propositional Equivalences
Predicates and Quantifiers
Nested Quantifiers
Methods of Proof
Sets
Set Operations
Functions
The Fundamentals: Algorithms, the Integers, and Matrices
Algorithms
The Growth of Functions
Complexity of Algorithms
The Integers and Division
Applications of Number Theory
Matrices
Mathematical Reasoning, Induction, and Recursion
Proof Strategy
Sequences and Summations
Mathematical Induction
Recursive Definitions and Structural Induction
Recursive Algorithms
Program Correctness
Counting
The Basics of Counting
The Pigeonhole Principle
Permutations and Combinations
Binomial Coefficients
Generalized Permutations and Combinations
Generating Permutations and Combinations
Discrete Probability
An Introduction to Discrete Probability
Probability Theory
Expected Value and Variance
Advanced Counting Techniques
Recurrence Relations
Solving Recurrence Relations
Divide-and-Conquer Algorithms and Recurrence Relations
Generating Functions
Inclusion-Exclusion
Applications of Inclusion-Exclusion
Relations
Relations and Their Properties
n-ary Relations and Their Applications
Representing Relations
Closures of Relations
Equivalence Relations
Partial Orderings
Graphs
Introduction to Graphs
Graph Terminology
Representing Graphs and Graph Isomorphism
Connectivity
Euler and Hamilton Paths
Shortest-Path Problems
Planar Graphs
Graph Coloring
Trees
Introduction to Trees
Applications of Trees
Tree Traversal
Spanning Trees
Minimum Spanning Trees
Boolean Algebra
Boolean Functions
Representing Boolean Functions
Logic Gates
Minimization of Circuits
Modeling Computation
Languages and Grammars
Finite-State Machines with Output
Finite-State Machines with No Output
Language Recognition
Turing Machines
Appendixes
Exponential and Logarithmic Functions
Pseudocode
Table of Contents provided by Publisher. All Rights Reserved.

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