Discrete Mathematics and Its Applications
by Rosen, KennethEdition: 6th
Format: Hardcover
Pub. Date: 2006-07-26
Publisher(s): McGraw-Hill Education
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Summary
Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.
Table of Contents
| Preface | |
| The MathZone Companion Website To the Student | |
| The Foundations: Logic and Proofs | |
| Propositional Logic | |
| Propositional Equivalences | |
| Predicates and Quantifiers | |
| Nested Quantifiers | |
| Rules of Inference | |
| Introduction to Proofs | |
| Proof Methods and Strategy End-of-Chapter Material | |
| Basic Structures: Sets, Functions, Sequences and Sums | |
| Sets | |
| Set Operations | |
| Functions | |
| Sequences and Summations End-of-Chapter Material | |
| The Fundamentals: Algorithms, the Integers, and Matrices | |
| Algorithms | |
| The Growth of Functions | |
| Complexity of Algorithms | |
| The Integers and Division | |
| Primes and Greatest Common Divisors | |
| Integers and Algorithms | |
| Applications of Number Theory | |
| Matrices End-of-Chapter Material | |
| Induction and Recursion | |
| Mathematical Induction | |
| Strong Induction and Well-Ordering | |
| Recursive Definitions and Structural Induction | |
| Recursive Algorithms | |
| Program Correctness End-of-Chapter Material | |
| Counting | |
| The Basics of Counting | |
| The Pigeonhole Principle | |
| Permutations and Combinations | |
| Binomial Coefficients | |
| Generalized Permutations and Combinations | |
| Generating Permutations and Combinations End-of-Chapter Material | |
| Discrete Probability | |
| An Introduction to Discrete Probability | |
| Probability Theory | |
| Bayes’ Theorem | |
| Expected Value and Variance End-of-Chapter Material | |
| Advanced Counting Techniques | |
| Recurrence Relations | |
| Solving Linear Recurrence Relations | |
| Divide-and-Conquer Algorithms and Recurrence elations | |
| Generating Functions | |
| Inclusion-Exclusion | |
| Applications of Inclusion-Exclusion End-of-Chapter Material | |
| Relations | |
| Relations and Their Properties | |
| n-ary Relations and Their Applications | |
| Representing Relations | |
| Closures of Relations | |
| Equivalence Relations | |
| Partial Orderings End-of-Chapter Material | |
| Graphs | |
| Graphs and Graph Models | |
| Graph Terminology and Special Types of Graphs | |
| Representing Graphs and Graph Isomorphism | |
| Connectivity | |
| Euler and Hamilton Paths | |
| Shortest-Path Problems | |
| Planar Graphs | |
| Graph Coloring End-of-Chapter Material | |
| Trees | |
| Introduction to Trees | |
| Applications of Trees | |
| Tree Traversal | |
| Spanning Trees | |
| Minimum Spanning Trees End-of-Chapter Material | |
| Boolean Algebra | |
| Boolean Functions | |
| Representing Boolean Functions | |
| Logic Gates | |
| Minimization of Circuits End-of-Chapter Material | |
| Modeling Computation | |
| Languages and Grammars | |
| Finite-State Machines with Output | |
| Finite-State Machines with No Output | |
| Language Recognition | |
| Turing Machines End-of-Chapter Material | |
| Appendixes | |
| Axioms for the Real Numbers and the Positive Integers | |
| Exponential and Logarithmic Functions | |
| Pseudocode Suggested Readings | |
| Answers to Odd-Numbered Exercises | |
| Photo Credits | |
| Index of Biographies | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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