Why Stock Markets Crash - Critical Events in Complex Financial Systems

Praise for the Third Edition

"It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006)

A complete and comprehensive classic in probability and measure theory

Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style. In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students.

This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book. The Anniversary Edition contains features including:

• An improved treatment of Brownian motion
• Replacement of queuing theory with ergodic theory
• Theory and applications used to illustrate real-life situations
• Over 300 problems with corresponding, intensive notes and solutions
• Updated bibliography
• An extensive supplement of additional notes on the problems and chapter commentaries

Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011. Billingsley earned his Bachelor's Degree in Engineering from the U.S. Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R. Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics.

This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.

In Reinventing Discovery, Michael Nielsen argues that we are living at the dawn of the most dramatic change in science in more than 300 years. This change is being driven by powerful new cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business or the workplace or government. But this is the first book about something much more fundamental: how the internet is transforming the nature of our collective intelligence and how we understand the world.

Reinventing Discovery tells the exciting story of an unprecedented new era of networked science. We learn, for example, how mathematicians in the Polymath Project are spontaneously coming together to collaborate online, tackling and rapidly demolishing previously unsolved problems. We learn how 250,000 amateur astronomers are working together in a project called Galaxy Zoo to understand the large-scale structure of the Universe, and how they are making astonishing discoveries, including an entirely new kind of galaxy. These efforts are just a small part of the larger story told in this book--the story of how scientists are using the internet to dramatically expand our problem-solving ability and increase our combined brainpower.

This is a book for anyone who wants to understand how the online world is revolutionizing scientific discovery today--and why the revolution is just beginning.

Throughout history, rich and poor countries alike have been lending, borrowing, crashing--and recovering--their way through an extraordinary range of financial crises. Each time, the experts have chimed, "this time is different"--claiming that the old rules of valuation no longer apply and that the new situation bears little similarity to past disasters. With this breakthrough study, leading economists Carmen Reinhart and Kenneth Rogoff definitively prove them wrong. Covering sixty-six countries across five continents, This Time Is Different presents a comprehensive look at the varieties of financial crises, and guides us through eight astonishing centuries of government defaults, banking panics, and inflationary spikes--from medieval currency debasements to today's subprime catastrophe. Carmen Reinhart and Kenneth Rogoff, leading economists whose work has been influential in the policy debate concerning the current financial crisis, provocatively argue that financial combustions are universal rites of passage for emerging and established market nations. The authors draw important lessons from history to show us how much--or how little--we have learned.

Using clear, sharp analysis and comprehensive data, Reinhart and Rogoff document that financial fallouts occur in clusters and strike with surprisingly consistent frequency, duration, and ferocity. They examine the patterns of currency crashes, high and hyperinflation, and government defaults on international and domestic debts--as well as the cycles in housing and equity prices, capital flows, unemployment, and government revenues around these crises. While countries do weather their financial storms, Reinhart and Rogoff prove that short memories make it all too easy for crises to recur.

An important book that will affect policy discussions for a long time to come, This Time Is Different exposes centuries of financial missteps.