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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.
New to This Edition :
Features :
Author Bio
Rosen, Kenneth H. : AT&T Laboratories
Discrete Mathematics and Its Applications, Fifth Edition
Chapter 1: The Foundations: Logic, Sets, and Functions
1.1, Logic
1.2, Propositional Equivalences
1.3, Predicates and Quantifiers
1.4, Nested Quantifiers
1.5, Methods of Proof
1.6, Sets
1.7, Set Operations
1.8, Functions
Chapter 2: The Fundamentals: Algorithms, the Integers, and Matrices
2.1, Algorithms
2.2, The Growth of Functions
2.3, Complexity of Algorithms
2.4, Integers and Algorithms
2.5, Applications of Number Theory
2.6, Matrices
Chapter 3: Mathematical Reasoning, Induction, and Recursion
3.1, Art and Strategy of Proof
3.2, Sequences and Sums
3.3, Mathematical Induction
3.4, Recursive Definitions and Structural Induction
3.5, Recursive Algorithms
3.6, Program Correctness
Chapter 4: Counting
4.1, The Basics of Counting
4.2, The Pigeonhole Principle
4.3, Permutations and Combinations
4.4, Binomial Coefficients
4.5, Generalized Permutations and Combinations
4.6, Generating Permutations and Combinations
Chapter 5: Discrete Probability
5.1, An Introduction to Discrete Probability
5.2, Probability Theory
5.3, Expected Value and Variance
Chapter 6: Advanced Counting Techniques
6.1, Recurrence Relations
6.2, Solving Recurrence Relations
6.3, Divide-and-Conquer Relations
6.4, Generating Functions
6.5, Inclusion-Exclusion
6.6, Applications of Inclusion-Exclusion
Chapter 7: Relations
7.1, Relations and Their Properties
7.2, n-ary Relations and Their Applications
7.3, Representing Relations
7.4, Closures of Relations
7.5, Equivalence Relations
7.6, Partial Orderings
Chapter 8: Graphs
8.1, Introduction to Graphs
8.2, Graph Terminology
8.3, Representing Graphs and Graph Isomorphism
8.4, Connectivity
8.5, Euler and Hamilton Paths
8.6, Shortest Path Problems
8.7, Planar Graphs
8.8, Graph Coloring
Chapter 9: Trees
9.1, Introduction to Trees
9.2, Applications of Trees
9.3, Tree Traversal
9.4, Spanning Trees
9.5, Minimum Spanning Trees
Chapter 10: Boolean Algebra
10.1, Boolean Functions
10.2, Representing Boolean Functions
10.3, Logic Gates
10.4, Minimization of Circuits
Chapter 11: Modeling Computation
11.1, Languages and Grammars
11.2, Finite-State Machines with Output
11.3, Finite-State Machines with No Output
11.4, Language Recognition
11.5, Turing Machines
Appendix.1: Exponential and Logarithmic Functions
Appendix.2: Pseudocode
Other Editions for Discrete Mathematics and Its Application - Text Only
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.
New to This Edition :
Features :
Author Bio
Rosen, Kenneth H. : AT&T Laboratories
Table of Contents
Discrete Mathematics and Its Applications, Fifth Edition
Chapter 1: The Foundations: Logic, Sets, and Functions
1.1, Logic
1.2, Propositional Equivalences
1.3, Predicates and Quantifiers
1.4, Nested Quantifiers
1.5, Methods of Proof
1.6, Sets
1.7, Set Operations
1.8, Functions
Chapter 2: The Fundamentals: Algorithms, the Integers, and Matrices
2.1, Algorithms
2.2, The Growth of Functions
2.3, Complexity of Algorithms
2.4, Integers and Algorithms
2.5, Applications of Number Theory
2.6, Matrices
Chapter 3: Mathematical Reasoning, Induction, and Recursion
3.1, Art and Strategy of Proof
3.2, Sequences and Sums
3.3, Mathematical Induction
3.4, Recursive Definitions and Structural Induction
3.5, Recursive Algorithms
3.6, Program Correctness
Chapter 4: Counting
4.1, The Basics of Counting
4.2, The Pigeonhole Principle
4.3, Permutations and Combinations
4.4, Binomial Coefficients
4.5, Generalized Permutations and Combinations
4.6, Generating Permutations and Combinations
Chapter 5: Discrete Probability
5.1, An Introduction to Discrete Probability
5.2, Probability Theory
5.3, Expected Value and Variance
Chapter 6: Advanced Counting Techniques
6.1, Recurrence Relations
6.2, Solving Recurrence Relations
6.3, Divide-and-Conquer Relations
6.4, Generating Functions
6.5, Inclusion-Exclusion
6.6, Applications of Inclusion-Exclusion
Chapter 7: Relations
7.1, Relations and Their Properties
7.2, n-ary Relations and Their Applications
7.3, Representing Relations
7.4, Closures of Relations
7.5, Equivalence Relations
7.6, Partial Orderings
Chapter 8: Graphs
8.1, Introduction to Graphs
8.2, Graph Terminology
8.3, Representing Graphs and Graph Isomorphism
8.4, Connectivity
8.5, Euler and Hamilton Paths
8.6, Shortest Path Problems
8.7, Planar Graphs
8.8, Graph Coloring
Chapter 9: Trees
9.1, Introduction to Trees
9.2, Applications of Trees
9.3, Tree Traversal
9.4, Spanning Trees
9.5, Minimum Spanning Trees
Chapter 10: Boolean Algebra
10.1, Boolean Functions
10.2, Representing Boolean Functions
10.3, Logic Gates
10.4, Minimization of Circuits
Chapter 11: Modeling Computation
11.1, Languages and Grammars
11.2, Finite-State Machines with Output
11.3, Finite-State Machines with No Output
11.4, Language Recognition
11.5, Turing Machines
Appendix.1: Exponential and Logarithmic Functions
Appendix.2: Pseudocode
Other Editions for Discrete Mathematics and Its Application - Text Only