Download e-book for iPad: Discrete Mathematics: Elementary and Beyond (Undergraduate by László Lovász, József Pelikán, Katalin L. Vesztergombi

By László Lovász, József Pelikán, Katalin L. Vesztergombi

ISBN-10: 0387955844

ISBN-13: 9780387955841

Discrete arithmetic is instantly turning into some of the most very important parts of mathematical examine, with functions to cryptography, linear programming, coding concept and the idea of computing. This ebook is geared toward undergraduate arithmetic and laptop technological know-how scholars drawn to constructing a sense for what arithmetic is all approximately, the place arithmetic may be useful, and what types of questions mathematicians paintings on. The authors speak about a couple of chosen effects and strategies of discrete arithmetic, normally from the parts of combinatorics and graph idea, with a bit quantity concept, likelihood, and combinatorial geometry. at any place attainable, the authors use proofs and challenge fixing to assist scholars comprehend the strategies to difficulties. furthermore, there are many examples, figures and routines unfold in the course of the ebook.

Show description

Read Online or Download Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics) PDF

Similar graph theory books

Introduction to Graph and Hypergraph Theory - download pdf or read online

This ebook is for math and computing device technology majors, for college students and representatives of many different disciplines (like bioinformatics, for instance) taking classes in graph thought, discrete arithmetic, information constructions, algorithms. it's also for somebody who desires to comprehend the fundamentals of graph idea, or simply is curious.

Download PDF by Junming Xu: Topological Structure and Analysis of Interconnection

This booklet presents the main uncomplicated difficulties, thoughts, and well-established effects from the topological constitution and research of interconnection networks within the graph-theoretic language. It covers the elemental ideas and techniques of community layout, numerous famous networks comparable to hypercubes, de Bruijn digraphs, Kautz digraphs, double loop, and different networks, and the latest parameters to degree functionality of fault-tolerant networks comparable to Menger quantity, Rabin quantity, fault-tolerant diameter, wide-diameter, constrained connectivity, and (l,w)-dominating quantity.

Download e-book for iPad: The Mathematical Coloring Book: Mathematics of Coloring and by Alexander Soifer

I have not encountered a e-book of this type. the simplest description of it i will provide is that it's a secret novel… i discovered it demanding to forestall analyzing sooner than i stopped (in days) the entire textual content. Soifer engages the reader's awareness not just mathematically, yet emotionally and esthetically. could you benefit from the booklet up to I did!

Download e-book for kindle: Evolutionary Equations with Applications in Natural Sciences by Jacek Banasiak, Mustapha Mokhtar-Kharroubi

With the unifying subject of summary evolutionary equations, either linear and nonlinear, in a posh setting, the ebook provides a multidisciplinary combination of themes, spanning the fields of theoretical and utilized practical research, partial differential equations, chance idea and numerical research utilized to numerous versions coming from theoretical physics, biology, engineering and complexity idea.

Additional resources for Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics)

Sample text

The number of k-subsets of an n-set is such an important quantity that there is a special notation for it: nk (read “n choose k”). Thus n k = n! (n − k)! 6) The number of different lottery tickets is 90 5 , the number of handshakes 7 at the start of Alice’s birthday party is 2 , etc. 1 we will see why). The value of nn is 1, since an n-element set has exactly one n-element subset, namely itself. It may look a bit more tricky to find that n0 = 1, but it is just as easy to explain: Every set has a single 0-element subset, namely the empty set.

Nn−1 , since (ignoring the factor 1 again) n! is the product of n − 1 factors, each of which is at most n. 3) 2n−1 ≤ n! ≤ nn−1 . These bounds are very far apart; for n = 10, the lower bound is 29 = 512, while the upper bound is 109 (one billion). 3). Which is larger, n! or 2n ? In other words, does a set with n elements have more permutations or more subsets? For small values of n, subsets are winning: 21 = 2 > 1! = 1, 22 = 4 > 2! = 2, 23 = 8 > 3! = 6. But then the picture changes: 24 = 16 < 4!

If you can’t find the answer, read the following section and return to this exercise afterwards. 48 3. 2. How to distribute n pennies to k children? 4 Distributing Money Instead of distributing presents, let’s distribute money. Let us formulate the question in general: We have n pennies that we want to distribute among k kids. Each child must get at least one penny (and, of course, an integer number of pennies). How many ways can we distribute the money? Before answering this question, we must clarify the difference between distributing money and distributing presents.

Download PDF sample

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


by Donald
4.3

Rated 4.29 of 5 – based on 9 votes