Introductory discrete mathematics / V.K. Balakrishnan.
By: Balakrishnan, V. K.Series: Dover books on mathematics. Publisher: New York : Dover Publications, 1996Edition: Dover ed.Description: xiv, 236 p. : ill. ; 24 cm.ISBN: 9780486691152.Subject(s): Mathematics | Computer science -- MathematicsDDC classification: 511
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"An unabridged, corrected republication of the work first published by Prentice Hall, Englewood Cliffs, N.J., 1991"--T.p. verso.
Includes bibliographical references (p. 219-223) and index.
Set theory and logic. Introduction to set theory ; Functions and relations ; Inductive proofs and recursive definitions --
Combinatorics. Two basic counting rules ; Permutations ; Combinations ; More on permutations and combinations ; The pigeonhole principle ; The inclusion-exclusion principle ; Summary of results in combinatorics --
Generating functions. Ordinary generating functions ; Exponential generating functions --
Recurrence relations. Homogeneous recurrence relations ; Inhomogeneous recurrence relations ; Recurrence relations and generating functions ; Analysis of algorithms --
Graphs and digraphs. Adjacency matrices and incidence matrices ; Joining in graphs ; Reaching in digraphs ; Testing connectedness ; Strong orientation of graphs --
More on graphs and digraphs. Eulerian paths and Eulerian circuits ; Coding and de Bruijn digraphs ; Hamiltonian paths and Hamiltonian cycles ; Applications of Hamiltonian cycles ; Vertex coloring and planarity of graphs --
Trees and their applications. Spanning trees ; Binary trees --
Spanning tree problems. More on spanning trees ; Kruskal's greedy algorithm ; Prim's greedy algorithm ; Comparison of the two algorithms --
Shortest path problems. Dijkstra's algorithm ; Floyd-Warshall algorithm ; Comparison of the two algorithms --
What is NP-completeness? Problems and their instances ; The size of an instance ; Algorithm to solve a problem ; The "Big Oh" or the O(·) notation ; Easy problems and difficult problems ; the Class P and the Class NP ; Polynomial transformations and NP-completeness ; Coping with hard problems.