Discrete mathematics and its applications / Kenneth H. Rosen.

By: Rosen, Kenneth H [author]
Language: English Publisher: Boston : McGraw-Hill, c2003Edition: Fifth editionDescription: xxi, 787, 9, 8, 83, 1, 18 pages : illustrations (some color.) ; 26 cmContent type: text Media type: unmediated Carrier type: volume ISBN: 0072424346 (acidfree paper); 9780072424348; 9780071237307Subject(s): Mathematics | Computer science -- MathematicsDDC classification: 511 LOC classification: QA39.3 | .R67 2003Online resources: Table of contents | Publisher description
Contents:
The foundations: logic and proof, sets, and functions : Logic ; Propositional equivalences ; Predicates and quantifiers ; Nested quantifiers ; Methods of proof ; Sets ; Set operations ; Functions -- The fundamentals: algorithms, the integers, and matrices : Algorithms ; The growth of functions ; Complexity of algorithms ; The integers and division ; Applications of number theory ; Matrices -- Mathematical reasoning, induction, and recursion : Proof strategy ; Sequences and summations ; Mathematical induction ; Recursive definitions and structural induction ; Recursive algorithms ; Program correctness -- Counting : The basics of counting ; The pigeonhole principle ; Permutations and combinations ; Binomial coefficients ; Generalized permutations and combinations ; Generating permutations and combinations -- Discrete probability : An introduction to discrete probability ; Probability theory ; Expected value and variance -- Advanced counting techniques : Recurrence relations ; Solving recurrence relations ; Divide-and-conquer algorithms and recurrence relations ; Generating functions ; Inclusion-exclusion ; Applications of inclusion-exclusion -- Relations : Relations and their properties ; n-ary relations and their applications ; Representing relations ; Closures of relations ; Equivalence relations ; Partial orderings -- Graphs : Introduction to graphs ; Graph terminology ; Representing graphs and graph isomorphism ; Connectivity ; Euler and Hamilton paths ; Shortest-path problems ; Planar graphs ; Graph coloring -- Trees : introduction to trees ; Applications of trees ; Tree traversal ; Spanning trees ; Minimum spanning trees -- Boolean algebra : Boolean functions ; Representing Boolean functions ; Logic gates ; Minimization of circuits -- Modeling computation : Languages and grammars ; Finite-state machines with output ; Finite-state machines with no output ; Language recognition ; Turing machines -- Appendixes : A.1. Exponential and logarithmic functions ; A.2. Pseudocode.
Summary: [This text] is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.-Pref.
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Includes bibliographic references (p. 1-8, 4th set) and indexes.

The foundations: logic and proof, sets, and functions : Logic ; Propositional equivalences ; Predicates and quantifiers ; Nested quantifiers ; Methods of proof ; Sets ; Set operations ; Functions --
The fundamentals: algorithms, the integers, and matrices : Algorithms ; The growth of functions ; Complexity of algorithms ; The integers and division ; Applications of number theory ; Matrices --
Mathematical reasoning, induction, and recursion : Proof strategy ; Sequences and summations ; Mathematical induction ; Recursive definitions and structural induction ; Recursive algorithms ; Program correctness --
Counting : The basics of counting ; The pigeonhole principle ; Permutations and combinations ; Binomial coefficients ; Generalized permutations and combinations ; Generating permutations and combinations --
Discrete probability : An introduction to discrete probability ; Probability theory ; Expected value and variance --
Advanced counting techniques : Recurrence relations ; Solving recurrence relations ; Divide-and-conquer algorithms and recurrence relations ; Generating functions ; Inclusion-exclusion ; Applications of inclusion-exclusion --
Relations : Relations and their properties ; n-ary relations and their applications ; Representing relations ; Closures of relations ; Equivalence relations ; Partial orderings --
Graphs : Introduction to graphs ; Graph terminology ; Representing graphs and graph isomorphism ; Connectivity ; Euler and Hamilton paths ; Shortest-path problems ; Planar graphs ; Graph coloring --
Trees : introduction to trees ; Applications of trees ; Tree traversal ; Spanning trees ; Minimum spanning trees --
Boolean algebra : Boolean functions ; Representing Boolean functions ; Logic gates ; Minimization of circuits --
Modeling computation : Languages and grammars ; Finite-state machines with output ; Finite-state machines with no output ; Language recognition ; Turing machines --
Appendixes : A.1. Exponential and logarithmic functions ; A.2. Pseudocode.

[This text] is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.-Pref.

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