Discrete mathematics is quickly becoming one of the most important areas of László Lovász is a Senior Researcher in the Theory Group at. Discrete mathematics is quickly becoming one of the most important areas of László Lovász is a Senior Researcher in the Theory Group at Microsoft. Discrete Mathematics. Front Cover. László Lovász, Katalin L. Vesztergombi. Yale Univ., Discrete Mathematics: Elementary and Beyond · Laszlo Lovasz.
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Its roots go back about years, to the very beginning of Greek mathematics. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry.
Graphs and trees, and matching and optimization problems are the themes of the next few chapters. One might think that after years of research, one would know essentially everything about the subject.
This book is aimed at undergraduate mathematics and computer science students interested in developing a Binomial Coefficients and Pascals Triangle. For example, there is a discussion of pseudoprimes and of the Miller-Rabin, algorithm which, upon iteration, has an excellent probability of correctly identifying a prime. The first paragraph of the chapter entitled Integers, Divisors, and Primes presents a good example of this philosophy in action: The authors carefully remind us throughout the text that what is convincing does not necessarily constitute a proof.
Recurrence relations are briefly introduced via the Fibonacci numbers, but attention quickly turns to combinatorial probability and a new chapter. Surely there are some readers who will find this sort of bait and switch annoying, but I am not one of them.
Account Options Sign in. This book is aimed at undergraduate mathematics and computer science students interested in developing a Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing.
Selected pages Title Page. Vesztergombi Limited preview – Binomial Coefficients and Pascals Triangle. Likewise, algorithms are discussed strictly from a mathematical viewpoint — as in the Euclidean Algorithm, as are recurrence relations. Elementary and Beyond L. In addition, there are numerous examples, figures and exercises spread throughout the book.
The first chapter takes up the topics of sets and counting, but the discussion of unions of sets, intersection of sets, and other such introductory logic is extremely brief. Her area of specialty is algebraic topology. In Chapter Six, the theme is prime numbers.
The binomial theorem is the main tool of the next chapter, leading quite nicely to identities arising from Pascal’s triangle and estimates for sums and quotients of binomial coefficients.
There are very simple, natural questions that we cannot answer; and there are other simple, natural questions to which an answer has been found only in the last few years!
Discrete mathematics (Lovász László; Pelikán József; Vesztergombi Katalin)
Integers Divisors and Primes. Then there is a foray into planar geometry leading to a discussion of the Four Color Theorem. While the choice of topics was to my taste and what made reading this book fun, it will be seen as a drawback by some readers who desire more connection with computer science. Elementary and Beyond Discrete Mathematics: Account Options Discrdte in. The last two chapters delve into coding theory and cryptography by introducing projective planes, Mathsmatics systems, etc, on the way to describing the RSA cryptosystem.
Coloring Maps and Graphs. Other editions – View all Discrete Mathematics: It has long been a staple in the mathematics studied and used by computer scientists as well as mathematicians.
A Glimpse of Complexity and Cryptography. This book does a wonderful job of communicating mathematics as a vibrant field.
This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. My library Help Advanced Book Search. Integers Divisors and Primes. Until I started actually reading it. Other editions – View all Discrete Mathematics: Elementary and Beyond L.
In many places the authors are willing to remark on the process of doing mathematics, on questions that appear “natural” or “surprising” and of course “elegant”. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry.
References to this book Codierungstheorie: Elementary and Beyond Undergraduate Texts in Mathematics.