A compelling journey through history, mathematics, and philosophy, charting humanity’s struggle against randomness. Our lives are played out in the arena of chance. However little we recognize it in our day-to-day existence, we are always riding the odds, seeking out certainty but settling—reluctantly—for likelihood, building our beliefs on the shadowy props of probability. Chances Are is the story of man’s millennia-long search for the tools to manage the recurrent but unpredictable—to help us prevent, or at least mitigate, the seemingly random blows of disaster, disease, and injustice. In these pages, we meet the brilliant individuals who developed the first abstract formulations of probability, as well as the intrepid visionaries who recognized their practical applications—from gamblers to military strategists to meteorologists to medical researchers, from blackjack to our own mortality.
This is not an easy-reading text on algebra for beginners. Neither is it a manual. It is a book for free reading. It is designed for a reader with some knowledge of algebra, even though half mastered and perhaps half forgotten. The present text hopes to help the reader recall such haphazard knowledge and polish it up, the aim being to fix certain facts in his mind. It is meant to develop in the reader a taste for algebra and problem-solving, and also excite him to dip into algebra textbooks and fill in the blanks in his knowledge.
To make the subject more attractive I have made use of a variety of tools: problems with intriguing plots to excite the reader's curiosity, amusing excursions into the history of mathematics, unexpected uses that algebra is put to in everyday affairs, and more.
Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis.
From the Author's Preface to the Third Edition
