Discrete Mathematics for Computer Scientists - download pdf or read online

By Cliff L Stein, Robert Drysdale, Kenneth Bogart

ISBN-10: 0132122715

ISBN-13: 9780132122719

Stein/Drysdale/Bogart's Discrete arithmetic for machine Scientists is perfect for machine technological know-how scholars taking the discrete math direction. Written particularly for machine technology scholars, this precise textbook at once addresses their wishes by means of delivering a beginning in discrete math whereas utilizing motivating, correct CS purposes. this article takes an active-learning strategy the place actions are offered as workouts and the fabric is then fleshed out via reasons and extensions of the workouts.

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Extra resources for Discrete Mathematics for Computer Scientists

Example text

Let |S| denote the size of the set S. 1 Using this notation, we can state the sum principle as follows. If S1 , S2 , . . , Sm are disjoint sets, then |S1 ∪ S2 ∪ · · · ∪ Sm | = |S1 | + |S2 | + · · · + |Sm |. 2). ” m m Si = i=1 |Si |. i=1 When we can write a set S as a union of disjoint sets S1 , S2 , . . , Sk , we say that we have partitioned S into the sets S1 , S2 , . . , Sk and that the sets S1 , It may look strange to have |{a, b, a}| = 2, but an element either is or is not in a set. An element cannot be in a set multiple times.

It is straightforward to verify that each of these sets appears six times in L as six different lists. Essentially the same argument gives us the number of k-element subsets of {1, 2, . . , n}. ” Here is the argument: The set of all k-element permutations of {1, 2, . . , n} can be partitioned into nk disjoint blocks,6 with each block comprising all k-element permutations of a k-element subset of {1, 2, . . , n}. 1. 1. 18 Chapter 1: Counting of the product principle, we get n k!. k Division by k!

6, therefore, represents the number of subsets of a particular size chosen from an appropriately sized set. In particular, the three terms are the number of k-element subsets of an n-element set, the number of (k − 1)-element subsets of an (n − 1)-element set, and the number of k-element subsets of an (n − 1)-element set. Thus, we should be able to use the sum principle to explain the relationship among these three quantities. This explanation will provide a proof that is just as valid as an algebraic derivation.

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Discrete Mathematics for Computer Scientists by Cliff L Stein, Robert Drysdale, Kenneth Bogart


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