Author : Michael Krivelevich
Publisher : Cambridge University Press
Page : 129 pages
File Size : 34,33 MB
Release : 2016-04-25
Category : Mathematics
ISBN : 1107136571
A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
Author : Michael Krivelevich
Publisher : Cambridge University Press
Page : 129 pages
File Size : 19,41 MB
Release : 2016-04-25
Category : Mathematics
ISBN : 1316552942
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
Author : Zvi Lotker
Publisher : Springer
Page : 424 pages
File Size : 18,23 MB
Release : 2018-10-30
Category : Computers
ISBN : 3030013251
This book constitutes the refereed post-conference proceedings of the 25th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2018, held in Ma'ale HaHamisha, Israel, in June 2018. The 23 full papers and 8 short papers presented were carefully reviewed and selected from 47 submissions. They are devoted to the study of the interplay between structural knowledge, communications, and computing in decentralized systems of multiple communicating entities and cover a large range of topics.
Author : Alan Frieze
Publisher : Cambridge University Press
Page : 483 pages
File Size : 38,50 MB
Release : 2016
Category : Mathematics
ISBN : 1107118506
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author : Allan Lo
Publisher : Cambridge University Press
Page : 274 pages
File Size : 18,26 MB
Release : 2019-06-27
Category : Mathematics
ISBN : 1108740723
Eight articles provide a valuable survey of the present state of knowledge in combinatorics.
Author : M. J. D. Hamilton
Publisher : Cambridge University Press
Page : 200 pages
File Size : 44,79 MB
Release : 2023-12-21
Category : Mathematics
ISBN : 1108905617
This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.
Author : Rick Durrett
Publisher : Cambridge University Press
Page : 203 pages
File Size : 42,24 MB
Release : 2010-05-31
Category : Mathematics
ISBN : 1139460889
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 341 pages
File Size : 36,18 MB
Release : 2017
Category : Computers
ISBN : 110717287X
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author : Derek F. Holt
Publisher : Cambridge University Press
Page : 307 pages
File Size : 37,88 MB
Release : 2017-02-23
Category : Mathematics
ISBN : 1108211046
Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.
Author : Renzo Cavalieri
Publisher : Cambridge University Press
Page : 197 pages
File Size : 31,13 MB
Release : 2016-09-26
Category : Mathematics
ISBN : 1316798933
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
