These noteworthy accounts of the lives of David Hilbert and Richard Courant are closely related: Courant's story is, in many ways, seen as the sequel to the story of Hilbert. Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Contance Reid.

    Whether they bind computers, economies, or terrorist organizations, networks are everywhere in the real world, yet only recently have scientists attempted to explain their mysterious workings.From epidemics of disease to outbreaks of market madness, from people searching for information to firms surviving crisis and change, from the structure of personal relationships to the technological and social choices of entire societies, Watts weaves together a network of discoveries across an array of disciplines to tell the story of an explosive new field of knowledge, the people who are building it, and his own peculiar path in forging this new science.

    Some say it has gone. In The Future of Ideas, Lawrence Lessig explains how the revolution has produced a counterrevolution of potentially devastating power and effect. Creativity once flourished because the Net protected a commons on which widest range of innovators could experiment. But now, manipulating the law for their own purposes, corporations have established themselves as virtual gatekeepers of the Net while Congress, in the pockets of media magnates, has rewritten copyright and patent laws to stifle creativity and progress.Lessig weaves the history of technology and its relevant laws to make a lucid and accessible case to protect the sanctity of intellectual freedom. He shows how the door to a future of ideas is being shut just as technology is creating extraordinary possibilities that have implications for all of us. Vital, eloquent, judicious and forthright, The Future of Ideas is a call to arms that we can ill afford to ignore.

    "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."

    Along the way she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how this little symbol holds the biggest idea of all. "Beyond Infinity is a spirited and friendly guide--appealingly down to earth about math that's extremely far out." --Jordan Ellenberg, author of How Not to Be Wrong "Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board." --Natalie Angier, New York Times

    Book by Waring, Chris

    In Dataclysm, Christian Rudder uses it to show us who we truly are.   For centuries, we’ve relied on polling or small-scale lab experiments to study human behavior. Today, a new approach is possible. As we live more of our lives online, researchers can finally observe us directly, in vast numbers, and without filters. Data scientists have become the new demographers.   In this daring and original book, Rudder explains how Facebook "likes" can predict, with surprising accuracy, a person’s sexual orientation and even intelligence; how attractive women receive exponentially more interview requests; and why you must have haters to be hot. He charts the rise and fall of America’s most reviled word through Google Search and examines the new dynamics of collaborative rage on Twitter. He shows how people express themselves, both privately and publicly. What is the least Asian thing you can say? Do people bathe more in Vermont or New Jersey? What do black women think about Simon & Garfunkel? (Hint: they don’t think about Simon & Garfunkel.) Rudder also traces human migration over time, showing how groups of people move from certain small towns to the same big cities across the globe. And he grapples with the challenge of maintaining privacy in a world where these explorations are possible.   Visually arresting and full of wit and insight, Dataclysm is a new way of seeing ourselves—a brilliant alchemy, in which math is made human and numbers become the narrative of our time.

    It has been inspired by the scientific ferment that swept through Britain at the end of the 18th century, and which Holmes now radically redefines as 'the revolution of Romantic Science'.

    Bruno Latour's contention is that the word "social" as used by Social Scientists has become laden with assumptions to the point where it has become a misnomer. When the adjective is applied to a phenomenon, it is used to indicate a stabilized state of affairs, a bundle of ties that in due course may be used to account for another phenomenon. Latour also finds the word used as if it described a type of material, in a comparable way to an adjective such as "wooden" or "steely".Rather than simply indicating what is already assembled together, it is now used in a way that makes assumptions about the nature of what is assembled. It has become a word that designates two distinct things: a process of assembling: and a type of material, distinct from others. Latour shows why "the social" cannot be thought of as a kind of material or domain, and disputes attempts to provide a "social explanation" of other states of affairs. While these attempts have been productive (and probably necessary) in the past, the very success of the social sciences mean that they are largely no longer so. At the present stage it is no longer possible to inspect the precise constituents entering the social domain. Latour returns to the original meaning of "the social" to redefine the notion and allow it to trace connections again. It will then be possible to resume the traditional goal of the social sciences, but using more refined tools. Drawing on his extensive work examining the "assemblages" of nature, Latour finds it necessary to scrutinize thoroughly the exact content of what is assembled under the umbrella of Society. This approach, a "sociology of associations" has become known as Actor-Network-Theory, and this book is an essential introduction both for those seeking to understand Actor-Network-Theory, or the ideas of one of its most influential proponents.

    This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python.You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and concepts.Develop your understanding of probability and statistics by writing and testing codeRun experiments to test statistical behavior, such as generating samples from several distributionsUse simulations to understand concepts that are hard to grasp mathematicallyLearn topics not usually covered in an introductory course, such as Bayesian estimationImport data from almost any source using Python, rather than be limited to data that has been cleaned and formatted for statistics toolsUse statistical inference to answer questions about real-world data

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice-freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You'll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you've mastered these techniques, you'll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes - Learning the Bayesian "state of mind" and its practical implications - Understanding how computers perform Bayesian inference - Using the PyMC Python library to program Bayesian analyses - Building and debugging models with PyMC - Testing your model's "goodness of fit" - Opening the "black box" of the Markov Chain Monte Carlo algorithm to see how and why it works - Leveraging the power of the "Law of Large Numbers" - Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning - Using loss functions to measure an estimate's weaknesses based on your goals and desired outcomes - Selecting appropriate priors and understanding how their influence changes with dataset size - Overcoming the "exploration versus exploitation" dilemma: deciding when "pretty good" is good enough - Using Bayesian inference to improve A/B testing - Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.

    He believes that we should investigate what makes some countries more capable than others. Complex products—from films to robots, apps to automobiles—are a physical distillation of an economy’s knowledge, a measurable embodiment of its education, infrastructure, and capability. Economic wealth accrues when applications of this knowledge turn ideas into tangible products; the more complex its products, the more economic growth a country will experience.A radical new interpretation of global economics, Why Information Grows overturns traditional assumptions about the development of economies and the origins of wealth and takes a crucial step toward making economics less the dismal science and more the insightful one.

    Drawing on research by their team at the Center for Digital Business, they show that there's been no stagnation in technology -- in fact, the digital revolution is accelerating. Recent advances are the stuff of science fiction: computers now drive cars in traffic, translate between human languages effectively, and beat the best human Jeopardy! players.As these examples show, digital technologies are rapidly encroaching on skills that used to belong to humans alone. This phenomenon is both broad and deep, and has profound economic implications. Many of these implications are positive; digital innovation increases productivity, reduces prices (sometimes to zero), and grows the overall economic pie.But digital innovation has also changed how the economic pie is distributed, and here the news is not good for the median worker. As technology races ahead, it can leave many people behind. Workers whose skills have been mastered by computers have less to offer the job market, and see their wages and prospects shrink. Entrepreneurial business models, new organizational structures and different institutions are needed to ensure that the average worker is not left behind by cutting-edge machines.In Race Against the Machine Brynjolfsson and McAfee bring together a range of statistics, examples, and arguments to show that technological progress is accelerating, and that this trend has deep consequences for skills, wages, and jobs. The book makes the case that employment prospects are grim for many today not because there's been technology has stagnated, but instead because we humans and our organizations aren't keeping up.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.