Discrete mathematics and its applications
著者
書誌事項
Discrete mathematics and its applications
McGraw-Hill Higher Education, c2007
6th ed
- : international ed
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注記
Includes bibliographical references (p. B1-B7) and index
内容説明・目次
- 巻冊次
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: international ed ISBN 9780071244749
内容説明
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.
目次
PrefaceThe MathZone Companion WebsiteTo the Student1 The Foundations: Logic and Proofs1.1 Propositional Logic1.2 Propositional Equivalences1.3 Predicates and Quantifiers1.4 Nested Quantifiers1.5 Rules of Inference1.6 Introduction to Proofs1.7 Proof Methods and StrategyEnd-of-Chapter Material2 Basic Structures: Sets, Functions, Sequences and Sums2.1 Sets2.2 Set Operations2.3 Functions2.4 Sequences and SummationsEnd-of-Chapter Material3 The Fundamentals: Algorithms, the Integers, and Matrices3.1 Algorithms3.2 The Growth of Functions3.3 Complexity of Algorithms3.4 The Integers and Division3.5 Primes and Greatest Common Divisors3.6 Integers and Algorithms3.7 Applications of Number Theory3.8 MatricesEnd-of-Chapter Material4 Induction and Recursion4.1 Mathematical Induction4.2 Strong Induction and Well-Ordering4.3 Recursive Definitions and Structural Induction4.4 Recursive Algorithms4.5 Program CorrectnessEnd-of-Chapter Material5 Counting5.1 The Basics of Counting5.2 The Pigeonhole Principle5.3 Permutations and Combinations5.4 Binomial Coefficients5.5 Generalized Permutations and Combinations5.6 Generating Permutations and CombinationsEnd-of-Chapter Material6 Discrete Probability6.1 An Introduction to Discrete Probability6.2 Probability Theory6.3 Bayes' Theorem6.4 Expected Value and VarianceEnd-of-Chapter Material7 Advanced Counting Techniques7.1 Recurrence Relations7.2 Solving Linear Recurrence Relations7.3 Divide-and-Conquer Algorithms and Recurrence elations7.4 Generating Functions7.5 Inclusion-Exclusion7.6 Applications of Inclusion-ExclusionEnd-of-Chapter Material8 Relations8.1 Relations and Their Properties8.2 n-ary Relations and Their Applications8.3 Representing Relations8.4 Closures of Relations8.5 Equivalence Relations8.6 Partial OrderingsEnd-of-Chapter Material9 Graphs9.1 Graphs and Graph Models9.2 Graph Terminology and Special Types of Graphs9.3 Representing Graphs and Graph Isomorphism9.4 Connectivity9.5 Euler and Hamilton Paths9.6 Shortest-Path Problems9.7 Planar Graphs9.8 Graph ColoringEnd-of-Chapter Material10 Trees10.1 Introduction to Trees10.2 Applications of Trees10.3 Tree Traversal10.4 Spanning Trees10.5 Minimum Spanning TreesEnd-of-Chapter Material11 Boolean Algebra11.1 Boolean Functions11.2 Representing Boolean Functions11.3 Logic Gates11.4 Minimization of CircuitsEnd-of-Chapter Material12 Modeling Computation12.1 Languages and Grammars12.2 Finite-State Machines with Output12.3 Finite-State Machines with No Output12.4 Language Recognition12.5 Turing MachinesEnd-of-Chapter MaterialAppendixesA.1 Axioms for the Real Numbers and the Positive IntegersA.2 Exponential and Logarithmic FunctionsA.3 PseudocodeSuggested ReadingsAnswers to Odd-Numbered ExercisesPhoto CreditsIndex of BiographiesIndex
- 巻冊次
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ISBN 9780072880083
内容説明
"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 600 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.
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