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 The Probabilistic Method
| מחבר: Author: Автор: مؤلف: | by Noga Alon and Joel H. Spencer |
| הוצאה לאור: Published by: Издательство: دار نشر: | Wiley-Interscience |
This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics.
The book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Sections labeled "The Probabilistic Lens" offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations.
The Third Edition also features:
A new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques
An elementary approach using probabilistic techniques to the powerful Szemeredi Regularity Lemma and its applications
New sections devoted to percolation and liar games
A new chapter that provides a modern treatment of the Erdos-Renyi phase transition in the Random Graph Process
Written by two leading authorities in the field, The Probabilistic Method, Third Edition is an ideal reference for researchers in combinatorics and algorithm design who would like to better understand the use of probabilistic methods. The book's numerous exercises and examples also make it an excellent textbook for graduate-level courses in mathematics and computer science
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| ISBN: | 0470170204 |
| הערות: Notes: Примечания: ملاحظات: | NOGA ALON, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University, Israel. A member of the Israel National Academy of Sciences, Dr. Alon has written over 400 published papers, mostly in the areas of combinatorics and theoretical computer science. He is the recipient of numerous honors in the field, including the Erdös Prize (1989), the Pólya Prize (2000), the Landau Prize (2005), and the Gödel Prize (2005).
JOEL H. SPENCER, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of Mathematical Sciences at New York University and is the cofounder and coeditor of the journal Random Structures and Algorithms. Dr. Spencer has written over 150 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley. |
 Modern Graph Theory
| מחבר: Author: Автор: مؤلف: | Bela Bollobas |
| הוצאה לאור: Published by: Издательство: دار نشر: | Springer |
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.
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| ISBN: | 0387984887 |
Graph Theory
| מחבר: Author: Автор: مؤلف: | Reinhard Diestel |
| הוצאה לאור: Published by: Издательство: دار نشر: | Springer |
| ISBN: | 3540261834 |
Geometric Algorithms and Combinatorial Optimization
| מחבר: Author: Автор: مؤلف: | Martin Grötsche, Laszlo Lovasz, Alexander Schrijver |
| הוצאה לאור: Published by: Издательство: دار نشر: | Springer |
| ISBN: | 3540567402 |
Computational Complexity
| מחבר: Author: Автор: مؤلف: | Christos H. Papadimitriou |
| הוצאה לאור: Published by: Издательство: دار نشر: | Addison Wesley |
| ISBN: | 0201530821 |
Theory of Linear and Integer Programming
| מחבר: Author: Автор: مؤلف: | Alexander Schrijver |
| הוצאה לאור: Published by: Издательство: دار نشر: | Wiley |
Introduction to the Theory of Computation
| מחבר: Author: Автор: مؤلف: | Michael Sipser |
| הוצאה לאור: Published by: Издательство: دار نشر: | Course Technology |
| ISBN: | 0534950973 |
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