TY - BOOK AU - Rosen,Kenneth H. TI - Discrete mathematics and its applications SN - 0072424346 (acidfree paper) AV - QA39.3 .R67 2003 U1 - 511 21 PY - 2003/// CY - Boston PB - McGraw-Hill KW - Mathematics KW - Computer science N1 - 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 N2 - [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 UR - http://www.loc.gov/catdir/toc/mh031/2002070890.html UR - http://www.loc.gov/catdir/description/mh024/2002070890.html ER -