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Discrete Mathematics and Its Applications

by: Rosen, Kenneth H.

Discrete Mathematics and Its Applications

by: Rosen, Kenneth H.

ISBN 13:
9780072899054
ISBN 10:
0072899050
Edition: 4th
Format: Hardcover
Copyright: 12/01/1998
Publisher: McGraw-Hill College

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Summary

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.

Amazon no longer offers textbook rentals. We do!

Discrete Mathematics and Its Applications

Discrete Mathematics and Its Applications

9780072899054

0072899050

Summary

Table of Contents

To the Student

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

Appendixes A