Incorporating a collection of recent results, Pólya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications. The book first substantiates the realization of distributions with urn arguments and introduces several modern tools, including exchangeability and stochastic processes via urns. It reviews classical probability problems and presents dichromatic Pólya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Pólya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the Pólya process to the discrete urn scheme, and explores extensions and generalizations. He also discusses how functional equations for moment generating functions can be obtained and solved. The final chapters cover applications of urns to computer science and bioscience. Examining how urns can help conceptualize discrete probability principles, this book provides information pertinent to the modeling of dynamically evolving systems where particles come and go according to governing rules.
Examining how urns can help conceptualize discrete probability principles, this book provides information pertinent to the modeling of dynamically evolving systems where particles come and go according to governing rules.
Both a biography of Pólya's life, and a review of his many mathematical achievements by today's experts.
Both a biography of Pólya's life, and a review of his many mathematical achievements by today's experts.
Prepared for units ECT405, ECT705 offered by the Faculty of Education in Deakin University's Open Campus Program.
Prepared for units ECT405, ECT705 offered by the Faculty of Education in Deakin University's Open Campus Program.
This book features articles written by some of the most prominent leading applied mathematicians as well as young and promising ones. The common objective of these articles is to present an important issue which is currently widely discussed in scientific investigation with major human, economic or ecological implications. Each article is as deep as an expert lecture but is also self-contained, so that even isolated scientists with limited resources can profit greatly from it.
This book is a collection of articles written by some of the most prominent leading applied mathematicians, as well as articles from young and promising scientists from Africa, Asia and Europe.
Banyak orang mengatakan bahwa matematika adalah pelajaran yang gampang-gampang susah. Betapa tidak. Banyaksiswa yang mendapatkan nilai matematika yang baik di sekolah tetapi tidak sedikit juga yang mendapatkan nilai kurang baik. Bahkan tanpa teknik belajar yang baik matematika bisa menjadi mata pelajaran yang sangat sulit dan membosankan. Hal ini tidak hanya terjadi pada pelajar di tingkat pendidikan yang lebih tinggi. Bahkan pelajar SD pun mengalami hal yang sama. (Balai Pustaka)
Banyak orang mengatakan bahwa matematika adalah pelajaran yang gampang-gampang susah.
"Geometry Of Conics deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.
Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.
