Discrete Mathematical Structures for Computer Science, Volume 2This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow. |
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a₁ a₂ algorithm b₁ b₂ binary operation Boolean algebra Boolean expression Boolean polynomials called code words compute congruence relation Consider construct corresponding coset cycle decoding denoted determine digit digraph edges encoding function equivalence relation EXERCISE SET Figure finite set finite-state machine function f group code group G Hasse diagram homomorphism input isomorphic labeled language lattice Let f Let G lower bound mathematical induction matrix monoid Moore machine multiplication table normal subgroup number of 1's offspring P₁ partial order path permutation poset positive integer Proof Prove pseudocode quotient r₁ real numbers recursive regular expression result s₁ Section semigroup sentence sequence shown in Fig Solution statement Step string subgroup of G subroutine subset subtree Suppose symbol symmetric relation syntax diagram Theorem topological sorting transitive true truth table undirected upper bound vertex vertices w₁ w₂