Introduction to Random Graphs 1st Edition by Alan Frieze (PDF)

Description

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

User’s Reviews

Editorial Reviews: Review “This is a well-planned book that is true to its title in that it is indeed accessible for anyone with just an undergraduate student’s knowledge of enumerative combinatorics and probability.” Miklós Bóna, MAA Reviews Book Description The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading. About the Author Alan Frieze is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University, Pennsylvania. He has authored more than 300 publications in top journals and was invited to be a plenary speaker at the Seoul ICM 2014. In 1991 he received the Fulkerson prize in discrete mathematics.Michał Karoński is a founder of the Discrete Mathematics Research group at Adam Mickiewicz University in Poznan, Poland. He has authored over 50 publications and currently serves as co-Editor-in-Chief of Random Structures and Algorithms. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is terrible and inscrutable. The first few pages alone provide plenty of examples(1) The authors prove, in simplified notation, that f(x) <= sqrt( 2 * pi * m) g(x), where m is some constant. But for some unstated reason, they state the result as f(x) <= sqrt(100 * m) g(x)Clearly 2*pi < 100 so what they stated is not incorrect given the proof. By why in the name would you state a bounding result with a dramatically larger bound than the one you can achieve? Why would you prove x > y and then state THEOREM: x + 100 > y ???????(2) A few pages later, as part of some proof, they basically re-prove the DeMoivre-Laplace Limit theorem (ie you can approximate a binomial distribution with a normal distribution). However, while some authors devote 5 pages to the subject, they basically do it in half a page and leave the incredibly difficult details to the reader. Either they should have provided a clear proof of this theorem, or just stated it as a known result!!!!!If you’re gonna give a half-assed proof, why give it at all? Just state the result!These two examples can be found in the first 8 pages, and I WONT be reading more.

⭐A comprehensive introduction to the subject and more.The book starts off with a well paced introduction to the main topic areas, so that anyone new to probabilistic arguments can easily follow along.The later parts of the book take the reader up to the frontiers of thesubject, and give fascinating insights into the topic.There is a wealth of useful information on random graphs, and anextensive bibliography for further research into specific topics.

⭐Magnífica presentacion

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