“If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations.”
- Keith Devlin, Stanford University, National Public Radio’s “Math Guy” and author of The Math Gene and The Unfinished Game
From probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives, Second Edition investigates the often surprising effects of risk and chance in our lives. Featuring a timely update, the Second Edition continues to be the go-to guidebook for an entertaining presentation on the mathematics of chance and uncertainty.
The new edition develops the fundamental mathematics of probability in a unique, clear, and informal way so readers with various levels of experience with probability can understand the little numbers found in everyday life. Illustrating the concepts of probability through relevant and engaging real-world applications, the Second Edition features numerous examples on weather forecasts, DNA evidence, games and gambling, and medical testing. The revised edition also includes:
The application of probability in finance, such as option pricing The introduction of branching processes and the extinction of family names An extended discussion on opinion polls and Nate Silver’s election predictions
Probabilities: The Little Numbers That Rule Our Lives, Second Edition is an ideal reference for anyone who would like to obtain a better understanding of the mathematics of chance, as well as a useful supplementary textbook for students in any course dealing with probability.
Guided by stalwart detective Hemlock Soames and his sidekick, Dr. John Watsup, readers will delve into almost two hundred mathematical problems, puzzles, and facts. Tackling subjects from mathematical dates (such as Pi Day), what we don't know about primes, and why the Earth is round, this clever, mind-expanding book demonstrates the power and fun inherent in mathematics.
Every number in this book is identified by its "field marks," "similar species," "personality," and "associations." For example, one field mark of the number 6 is that it is the first perfect number-- the sum of its divisors (1, 2, and 3) is equal to the number itself. Thus 28, the next perfect number, is a similar species. And the fact that 6 can easily be broken into 2 and 3 is part of its personality, a trait that is helpful when large numbers are being either multiplied or divided by 6. Associations with 6 include its relationship to the radius of a circle. In addition to such classifications, special attention is paid to dozens of other fascinating numbers, including zero, pi, 10 to the 76th power (the number of particles in the universe), transfinite and other exceptionally larger numbers, and the concept of infinity.
Ideal for beginners but organized to appeal to the mathematically literate, The Kingdom of Infinite Number will not only add to readers' enjoyment of mathematics, but to their problem-solving abilities as well.
Geometry advanced into the widening territories of projective geometry, non-Euclidean geometries, the geometry of n-dimensions, and topology or "rubber sheet" geometry. More than 80 drawings, integrated with the text, assist in cultivating a grasp of the abstract foundations of modern mathematics, the search for truly consistent assumptions, the recognition that absolute consistency is unattainable, and the realization that some problems can never be solved.
The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.
Special features include:
* an exploration ofthe logical relationship between problem posing and problem solving
* a special chapter devoted to teaching problem posing as a separate course
* sketches, drawings, diagrams, and cartoons that illustrate the schemes proposed
* a special section on writing in mathematics
In this controversial book, Steven Goldberg provides a compelling look at the intersection of two of America's most powerful communities—law and science—to explain this apparent contradiction. Rarely considered in tandem, law and science highlight a fundamental paradox in the American character, the struggle between progress and process. Science, with its ethic of endless progress, has long fit beautifully with America's self image. Law, in accordance with the American ideal of giving everyone a fair say, stresses process above all else, seeking an acceptable, rather than a scientifically correct, result. This characteristic has been especially influential in light of the explosive growth of the legal community in recent years.
Exposing how the legal system both supports and restricts American science and technology, Goldberg considers the role and future of three projects—artificial intelligence, nuclear fusion, and the human genome initiative—to argue for a scientific vision that infuses research with social goals beyond the pure search for truth. Certain to provoke debate within a wide range of academic and professional communities, Culture Clash reveals one of the most important and defining conflicts in contemporary American life.