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"The 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. Eisenkölbl, Monatshefte für Mathematik, Vol. There are a lot of exercises … which makes it perfectly suitable for self-study." (T. The level is always introductory which makes it possible to give a taste of a wide range of topics …. The language is very informal and easy to read. Consequently, the authors … take a lot of time to explain proof techniques and to motivate definitions and style. "The goal of this book is to use the introduction to discrete mathematics …. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. In addition, there are numerous examples, figures and exercises spread throughout the book. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. 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. 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. Represent this situation with a graph.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. It turns out that Al and Cam are friends, as are Bob and Dan. The site allows members to be “friends” with each other. Īl, Bob, Cam, Dan, and Euler are all members of the social networking website Facebook. But first, here are a few other situations you can represent with graphs: Example 4.0.1. We will return to the question of finding paths through graphs later. All that matters is which land masses are connected to which other land masses, and how many times.
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It does not matter how big the islands are, what the bridges are made out of, if the river contains alligators, etc. We have distilled the “important” parts of the bridge picture for the purposes of the problem. The nice thing about looking at graphs instead of pictures of rivers, islands and bridges is that we now have a mathematical object to study. When two vertices are connected by an edge, we say they are adjacent. Graphs are made up of a collection of dots called vertices and lines connecting those dots called edges.
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Pictures like the dot and line drawing are called graphs. Any path in the dot and line drawing corresponds exactly to a path over the bridges of Königsberg. There is an obvious connection between these two problems.