Discrete mathematics with combinatorics (Q2746979)

There are 22 chapters covering set theory; number theory; logic; algebraic structures such as groups, rings, fields and lattices; graphs, trees and networks; algorithms and recursion; coding theory and combinatorics.NEWLINENEWLINENEWLINESearch and sort algorithms, the Euclidean algorithm, Huffman's algorithm, Prim's algorithms, Warshall's algorithm, the Ford-Fulkerson algorithm, the Floyd-Warshall algorithm and Dijkstra's algorithms are discussed.NEWLINENEWLINENEWLINEBurnside's counting lemma, Euler's theorem on integers, Euler's formula for planar graphs, Pólya's counting theorem, Lagrange's theorem on groups, Kuratowski's theorem on planar graphs, fundamental theorem of arithmetics, Chinese remainder theorem, prime factorization theorem and Vandermonde's theorem on combinations are some of the results established in this book.NEWLINENEWLINENEWLINEThere are plenty of examples and exercises, figures and tables. The following exercises typify the level of the course: (1) Prove, using mathematical induction, that \(n^2> 2n+1\) for \(n\geq 3\). (2) Give an example of a binary operation \(*\) on the set of all real numbers such that this set does not form a semigroup. (3) Find a two-element subgroup of the octic group. (4) Prove that any graph with four vertices is planar. (5) What is the chromatic number of a hypercube? (6) Find the language generated by the grammar \(\Gamma= (N,T,S,P)\) defined by \(N= \{S,A,B\}\), \(T= \{a,b\}\) and the set of productions \(P\) given by \(S\to AB\), \(A\to aA\), \(A\to\lambda\), \(B\to Bb\), \(B\to\lambda\).NEWLINENEWLINENEWLINEThis book can be used as a text on discrete mathematics. Printing and the get-up are attractive.