Discrete Mathematics and Its Applications

"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 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.

ISBN 0073229725   Part volume WITH MathZone ISBN13 9780073229720 (What's this?)   Volumes 1 Publisher McGraw-Hill Education - Europe   Weight (grammes) 2141 Imprint McGraw Hill Higher Education   Published in London Format Hardback   Previous ISBN 9780072880083 Publication date 26 Jul 2006   Height (mm) 266 Library of Congress 2006012468   Width (mm) 223 DEWEY 510   Spine width (mm) 40 DEWEY edition DC22   Academic level General Pages 1008

Preface The MathZone Companion Website To the Student 1 The Foundations: Logic and Proofs 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy End-of-Chapter Material 2 Basic Structures: Sets, Functions, Sequences and Sums 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations End-of-Chapter Material 3 The Fundamentals: Algorithms, the Integers, and Matrices 3.1 Algorithms 3.2 The Growth of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.7 Applications of Number Theory 3.8 Matrices End-of-Chapter Material 4 Induction and Recursion 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness End-of-Chapter Material 5 Counting 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 Binomial Coefficients 5.5 Generalized Permutations and Combinations 5.6 Generating Permutations and Combinations End-of-Chapter Material 6 Discrete Probability 6.1 An Introduction to Discrete Probability 6.2 Probability Theory 6.3 Bayes' Theorem 6.4 Expected Value and Variance End-of-Chapter Material 7 Advanced Counting Techniques 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence elations 7.4 Generating Functions 7.5 Inclusion-Exclusion 7.6 Applications of Inclusion-Exclusion End-of-Chapter Material 8 Relations 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.4 Closures of Relations 8.5 Equivalence Relations 8.6 Partial Orderings End-of-Chapter Material 9 Graphs 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Paths 9.6 Shortest-Path Problems 9.7 Planar Graphs 9.8 Graph Coloring End-of-Chapter Material 10 Trees 10.1 Introduction to Trees 10.2 Applications of Trees 10.3 Tree Traversal 10.4 Spanning Trees 10.5 Minimum Spanning Trees End-of-Chapter Material 11 Boolean Algebra 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits End-of-Chapter Material 12 Modeling Computation 12.1 Languages and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines End-of-Chapter Material Appendixes A.1 Axioms for the Real Numbers and the Positive Integers A.2 Exponential and Logarithmic Functions A.3 Pseudocode Suggested Readings Answers to Odd-Numbered Exercises Photo Credits Index of Biographies Index

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