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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
|The MathZone Companion Website To the Student|
|The Foundations: Logic and Proofs|
|Predicates and Quantifiers|
|Rules of Inference|
|Introduction to Proofs|
|Proof Methods and Strategy End-of-Chapter Material|
|Basic Structures: Sets, Functions, Sequences and Sums|
|Sequences and Summations End-of-Chapter Material|
|The Fundamentals: Algorithms, the Integers, and Matrices|
|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|
|Strong Induction and Well-Ordering|
|Recursive Definitions and Structural Induction|
|Program Correctness End-of-Chapter Material|
|The Basics of Counting|
|The Pigeonhole Principle|
|Permutations and Combinations|
|Generalized Permutations and Combinations|
|Generating Permutations and Combinations End-of-Chapter Material|
|An Introduction to Discrete Probability|
|Expected Value and Variance End-of-Chapter Material|
|Advanced Counting Techniques|
|Solving Linear Recurrence Relations|
|Divide-and-Conquer Algorithms and Recurrence elations|
|Applications of Inclusion-Exclusion End-of-Chapter Material|
|Relations and Their Properties|
|n-ary Relations and Their Applications|
|Closures of Relations|
|Partial Orderings End-of-Chapter Material|
|Graphs and Graph Models|
|Graph Terminology and Special Types of Graphs|
|Representing Graphs and Graph Isomorphism|
|Euler and Hamilton Paths|
|Graph Coloring End-of-Chapter Material|
|Introduction to Trees|
|Applications of Trees|
|Minimum Spanning Trees End-of-Chapter Material|
|Representing Boolean Functions|
|Minimization of Circuits End-of-Chapter Material|
|Languages and Grammars|
|Finite-State Machines with Output|
|Finite-State Machines with No Output|
|Turing Machines End-of-Chapter Material|
|Axioms for the Real Numbers and the Positive Integers|
|Exponential and Logarithmic Functions|
|Pseudocode Suggested Readings|
|Answers to Odd-Numbered Exercises|
|Index of Biographies|
|Table of Contents provided by Publisher. All Rights Reserved.|