Schaum's Outline of Discrete Mathematics

McGraw Hill Professional, Jun 22, 1997 - Mathematics - 528 pages
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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Contents

 Chapter SET THEORY 1 RELATIONS 27 FUNCTIONS AND ALGORITHMS 50 LOGIC AND PROPOSITIONAL CALCULUS 78 VECTORS AND MATRICES 102 COUNTING 133 PROBABILITY THEORY 152 GRAPH THEORY 188
 BINARY TREES 276 Binary Trees 10 4 Representing Binary Trees in Memory 10 5 Traver 294 Chapter PROPERTIES OF THE INTEGERS 315 ALGEBRAIC SYSTEMS 364 LANGUAGES GRAMMARS MACHINES 405 ORDERED SETS AND LATTICES 442 BOOLEAN ALGEBRA 477 Appendix A RECURRENCE RELATIONS 521

 DIRECTED GRAPHS 233 6 Warshalls Algorithm Shortest Paths 9 7 Linked Repre 253

Popular passages

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.