Schaum's Outline of Discrete Mathematics
The first edition of this book sold more than 100,000 copies—and this new edition will show you why! Schaum’s Outline of Discrete Mathematics shows you step by step how to solve the kind of problems you’re going to find on your exams. And this new edition features all the latest applications of discrete mathematics to computer science! This guide can be used as a supplement, to reinforce and strengthen the work you do with your class text. (It works well with virtually any discrete mathematics textbook.) But it is so comprehensive that it can even be used alone as a text in discrete mathematics or as independent study tool!
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Binary Trees 10 4 Representing Binary Trees in Memory 10 5 Traver
Chapter PROPERTIES OF THE INTEGERS
LANGUAGES GRAMMARS MACHINES
ORDERED SETS AND LATTICES
Appendix A RECURRENCE RELATIONS
6 Warshalls Algorithm Shortest Paths 9 7 Linked Repre
Accordingly adjacency list adjacency matrix algorithm belong binary tree Boolean algebra Boolean expression called complement complete sum-of-products congruence equation connected Consider consists contains corresponding defined deleted denote directed graph divides divisors edges equivalence relation EXAMPLE exists F F F F T F Find the number Find the probability finite function fundamental product G in Fig graph G hence homomorphism identity element input integers integral domain inverse isomorphic ITEM Karnaugh map lattice linear linearly ordered maximal element minimal modulo multiplication node nonzero obtain one-to-one operation ordered pairs ordered set output partial order partition polynomial positive integers prime implicants proposition Prove Theorem real numbers recurrence relation sample space semigroup sequence Show simple path Step subgroup subset subtree sum-of-products sum-of-products form Suppose symbol symmetric traversal true truth table Turing machine unique solution variables Venn diagram vertex vertices words x'yz xy'z zero
Page 126 - The number of permutations of n objects taken r at a time is denoted by P(n,r), „Pr,Pn.r, P"r, or (n), We shall use P(n,r).
Page 330 - Then there exists integers q and r such that a = bq + r and 0 < r < \b\ Also, the integers q and r are unique.
Page 186 - G is defined to be the sum of the weights of the edges in the path.
Page 40 - One of the most important concepts in mathematics is that of a function.
Page 94 - A matrix with m rows and n columns is called an m by n matrix, written mx n.
Page 26 - ... the congruence relationship, an important branch of number theory. Computer engineers find these concepts and notations particularly useful in describing operations performed upon numbers in the digital computer. Two integers a and b are said to be "'congruent modulo m ' if a - b is exactly divisible by m , where m , which is called the "modulus
Page 40 - ... x is called the independent variable, and y is called the dependent variable. The symbol /(*), which is read "/of x," is often used instead of y to represent the range value of the function.
Page 146 - B in a probability space 5 are said to be independent if the occurrence of one of them does not influence the occurrence of the other. More specifically, B is independent of A if P(B) is the same as P(B\A). Now substituting P(B) for P(B\A) in the Multiplication Theorem P(A f}B) = P(A)P(B | A) yields P(AHB) = P(A)P(B).
Page 97 - AB is defined if and only if the number of columns of A is equal to the number of rows of B...
Page 98 - A matrix that has the same number of rows as columns is called a square matrix. The principal, or main diagonal of a square matrix contains the elements xn, x22, x33, . . . xnn.