# Discrete mathematics and its applications /

Rosen, Kenneth H.

Discrete mathematics and its applications / Kenneth H. Rosen. - 5th ed. - Boston ; New Delhi : Tata McGraw-Hill, c2003. - xxi, (various pagings) : ill. ; 26 cm.

Includes bibliographic references 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. TOC

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.

0072424346 (acidfree paper) 9780072424348 0071198814

2002070890

Mathematics.

Computer science--Mathematics.

QA39.3 / .R67 2003

511 / ROD 2003

Discrete mathematics and its applications / Kenneth H. Rosen. - 5th ed. - Boston ; New Delhi : Tata McGraw-Hill, c2003. - xxi, (various pagings) : ill. ; 26 cm.

Includes bibliographic references 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. TOC

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.

0072424346 (acidfree paper) 9780072424348 0071198814

2002070890

Mathematics.

Computer science--Mathematics.

QA39.3 / .R67 2003

511 / ROD 2003