In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.
INSTANT NEW YORK TIMES BESTSELLER “Most appealing... technical accuracy and lightness of tone... Impeccable.”—Wall Street Journal “A porthole into another world.”—Scientific American “Brings science dissemination to a new level.”—Science The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality. Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables. No one else could so smoothly guide readers toward grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.
Any literate person should be familiar with the central ideas of modern science. In his sparkling new book, Peter Atkins introduces his choice of the ten great ideas of science. With wit, charm, patience, and astonishing insights, he leads the reader through the emergence of the concepts, and then presents them in a strikingly effective manner. At the same time, he works into his engaging narrative an illustration of the scientific method and shows how simple ideas can have enormous consequences. His choice of the ten great ideas are: * Evolution occurs by natural selection, in which the early attempts at explaining the origin of species is followed by an account of the modern approach and some of its unsolved problems. * Inheritance is encoded in DNA, in which the story of the emergence of an understanding of inheritance is followed through to the mapping of the human genome. * Energy is conserved, in which we see how the central concept of energy gradually dawned on scientists as they mastered the motion of particles and the concept of heat. * All change is the consequence of the purposeless collapse of energy and matter into disorder, in which the extraordinarily simple concept of entropy is used to account for events in the world. * Matter is atomic, in which we see how the concept of atoms emerged and how the different personalities of the elements arise from the structures of their atoms. * Symmetry limits, guides, and drives, in which we see how concepts related to beauty can be extended to understand the nature of fundamental particles and the forces that act between them. * Waves behave like particles and particles behave like waves, in which we see how old familiar ideas gave way to the extraordinary insights of quantum theory and transformed our perception of matter. * The universe is expanding, in which we see how a combination of astronomy and a knowledge of elementary particles accounts for the origin of the universe and its long term future. * Spacetime is curved by matter, in which we see the emergence of the theories of special and general relativity and come to understand the nature of space and time. * If arithmetic is consistent, then it is incomplete, in which we learn the origin of numbers and arithmetic, see how the philosophy of mathematics lets us understand the nature of this most cerebral of subjects, and are brought to the limits of its power. C. P. Snow once said 'not knowing the second law of thermodynamics is like never having read a work by Shakespeare'. This is an extraordinary, exciting book that not only will make you literate in science but give you deep enjoyment on the way.
Perhaps the most widely read thinker of all time, Confucius transformed Chinese philosophy with his belief that the greatest goal in life was pursuit of 'The Way': a search for virtue not as a means to rewards in this world or the next, but as the pinnacle of human existence.
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Now available in a fully revised and updated second edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving.
"Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem. Diaconis and Graham are mathematicians as well as skilled performers with decades of professional experience between them. In this book they share a wealth of conjuring lore, including some closely guarded secrets of legendary magicians. Magical Mathematics covers the mathematics of juggling and shows how the I Ching connects to the history of probability and magic tricks both old and new. It tells the stories--and reveals the best tricks--of the eccentric and brilliant inventors of mathematical magic. Magical Mathematics exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card monte, traces the history of mathematical magic back to the thirteenth century and the oldest mathematical trick--and much more"-
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
