By László Lovász, József Pelikán, Katalin L. Vesztergombi

ISBN-10: 0387955844

ISBN-13: 9780387955841

Discrete arithmetic is instantly changing into the most very important components of mathematical study, with functions to cryptography, linear programming, coding thought and the speculation of computing. This e-book is aimed toward undergraduate arithmetic and desktop technology scholars drawn to constructing a sense for what arithmetic is all approximately, the place arithmetic might be useful, and what forms of questions mathematicians paintings on. The authors speak about a couple of chosen effects and techniques of discrete arithmetic, quite often from the parts of combinatorics and graph thought, with a bit quantity conception, likelihood, and combinatorial geometry. anyplace attainable, the authors use proofs and challenge fixing to aid scholars comprehend the options to difficulties. furthermore, there are lots of examples, figures and workouts unfold during the booklet.

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Extra info for Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics)

Sample text

2 Distributing Presents Suppose we have n different presents, which we want to distribute to k children, where for some reason, we are told how many presents each child should get. So Adam should get nAdam presents, Barbara, nBarbara presents, etc. In a mathematically convenient (though not very friendly) way, we call the children 1, 2, . . , k; thus we are given the numbers (nonnegative integers) n1 , n2 , . . , nk . We assume that n1 + n2 + · · · + nk = n, else there is no way to distribute all the presents and give each child the right number of them.

Possible ways, etc. So the number of ways the presents can be laid out (given the distribution of the presents to the children) is a product of factorials: n1 ! · n2 ! · · · nk ! Thus the number of ways of distributing the presents is n! n2 ! · · · nk ! 1 We can describe the procedure of distributing the presents as follows. First, we select n1 presents and give them to the first child. This can be done in n ways. Then we select n2 presents from the remaining n − n1 and give them n1 to the second child, etc.

We compute the total sum of entries in this table in two different ways. First, what are the row sums? We get 1 for Al and 0 for everybody else. This is not a coincidence. If we consider a student like Al, who does not have any picture, then this student contributes to the bonus column, but nowhere else, which means that the sum in the row of this student is 1. Next, consider Ed, who has all 3 pictures. He has a 1 in the bonus column; in the next 3 columns he has 3 terms that are −1. In each of the next 3 columns he has a 1, one for each pair of pictures; it is better to think of this 3 as 32 .

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Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics) by László Lovász, József Pelikán, Katalin L. Vesztergombi


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