Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-29T03:40:44.371Z Has data issue: false hasContentIssue false

Introduction

Published online by Cambridge University Press:  18 March 2010

Get access

Summary

Many branches of mathematics owe a debt to classical combinatorics. This is especially true of probability theory. Plenty of good examples show how combinatorial considerations lead to very deep and difficult probabilistic results. The links between combinatorial and probabilistic problems have played an important role in forming probability theory as a mathematical discipline, and now manifest themselves in elementary courses devoted to this subject. The initial stage of the development of probability theory was characterized by the essential contribution of combinatorial methods in forming the mathematical background of the science. The current situation is quite different: well-developed probabilistic methods find a wide range of applications in solving various combinatorial problems. This is revealed in the search for asymptotic results in combinatorial analysis, where the probabilistic formulations of combinatorial problems provide the possibility to use the working system of notions of probability theory effectively and to take advantage of the powerful techniques of limit theorems in finding asymptotic formulae. It is appropriate to mention here that asymptotic results play an essential role in combinatorial analysis: they simplify calculations in problems oriented to applications and present the whole picture of investigated phenomena in a more transparent form.

For convenience of references some basic notions and facts of probability theory are listed in the first chapter of the book. Although these facts are presented in a systematic and unified form, this part of the monograph is not assumed to be a sub-stitute for a textbook on probability theory, but is directed to those readers who have some basic knowledge of the subject.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×