They were preparing to compete in a poker tournament with million-dollar stakes, but those numbers meant nothing to them.  They were accustomed to risking billions.     At the card table that night was Peter Muller, an eccentric, whip-smart whiz kid who’d studied theoretical mathematics at Princeton and now managed a fabulously successful hedge fund called PDT…when he wasn’t playing his keyboard for morning commuters on the New York subway.  With him was Ken Griffin, who as an undergraduate trading convertible bonds out of his Harvard dorm room had outsmarted the Wall Street pros and made money in one of the worst bear markets of all time.  Now he was the tough-as-nails head of Citadel Investment Group, one of the most powerful money machines on earth. There too were Cliff Asness, the sharp-tongued, mercurial founder of the hedge fund AQR, a man as famous for his computer-smashing rages as for his brilliance, and Boaz Weinstein, chess life-master and king of the credit default swap, who while juggling $30 billion worth of positions for Deutsche Bank found time for frequent visits to Las Vegas with the famed MIT card-counting team.     On that night in 2006, these four men and their cohorts were the new kings of Wall Street.  Muller, Griffin, Asness, and Weinstein were among the best and brightest of a  new breed, the quants.  Over the prior twenty years, this species of math whiz --technocrats who make billions not with gut calls or fundamental analysis but with formulas and high-speed computers-- had usurped the testosterone-fueled, kill-or-be-killed risk-takers who’d long been the alpha males the world’s largest casino.  The quants believed that a dizzying, indecipherable-to-mere-mortals cocktail of differential calculus, quantum physics, and advanced geometry held the key to reaping riches from the financial markets.  And they helped create a digitized money-trading machine that could shift billions around the globe with the click of a mouse.     Few realized that night, though, that in creating this unprecedented machine, men like Muller, Griffin, Asness and Weinstein had sowed the seeds for history’s greatest financial disaster.     Drawing on unprecedented access to these four number-crunching titans, The Quants tells the inside story of what they thought and felt in the days and weeks when they helplessly watched much of their net worth vaporize – and wondered just how their mind-bending formulas and genius-level IQ’s had led them so wrong, so fast.  Had their years of success been dumb luck, fool’s gold, a good run that could come to an end on any given day?  What if The Truth they sought -- the secret of the markets -- wasn’t knowable? Worse, what if there wasn’t any Truth?   In The Quants, Scott Patterson tells the story not just of these men, but of Jim Simons, the reclusive founder of the most successful hedge fund in history; Aaron Brown, the quant who used his math skills to humiliate Wall Street’s old guard at their trademark game of Liar’s Poker, and years later found himself with a front-row seat to the rapid emergence of mortgage-backed securities; and gadflies and dissenters such as Paul Wilmott, Nassim Taleb, and Benoit Mandelbrot.     With the immediacy of today’s NASDAQ close and the timeless power of a Greek tragedy, The Quants is at once a masterpiece of explanatory journalism, a gripping tale of ambition and hubris…and an ominous warning about Wall Street’s future.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    Darrell Huff runs the gamut of every popularly used type of statistic, probes such things as the sample study, the tabulation method, the interview technique, or the way the results are derived from the figures, and points up the countless number of dodges which are used to fool rather than to inform.

    However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    

    R has traditionally been difficult for non-statisticians to learn, and most R books assume far too much knowledge to be of help. R for Everyone is the solution. Drawing on his unsurpassed experience teaching new users, professional data scientist Jared P. Lander has written the perfect tutorial for anyone new to statistical programming and modeling. Organized to make learning easy and intuitive, this guide focuses on the 20 percent of R functionality you'll need to accomplish 80 percent of modern data tasks. Lander's self-contained chapters start with the absolute basics, offering extensive hands-on practice and sample code. You'll download and install R; navigate and use the R environment; master basic program control, data import, and manipulation; and walk through several essential tests. Then, building on this foundation, you'll construct several complete models, both linear and nonlinear, and use some data mining techniques. By the time you're done, you won't just know how to write R programs, you'll be ready to tackle the statistical problems you care about most. COVERAGE INCLUDES - Exploring R, RStudio, and R packages - Using R for math: variable types, vectors, calling functions, and more - Exploiting data structures, including data.frames, matrices, and lists - Creating attractive, intuitive statistical graphics - Writing user-defined functions - Controlling program flow with if, ifelse, and complex checks - Improving program efficiency with group manipulations - Combining and reshaping multiple datasets - Manipulating strings using R's facilities and regular expressions - Creating normal, binomial, and Poisson probability distributions - Programming basic statistics: mean, standard deviation, and t-tests - Building linear, generalized linear, and nonlinear models - Assessing the quality of models and variable selection - Preventing overfitting, using the Elastic Net and Bayesian methods - Analyzing univariate and multivariate time series data - Grouping data via K-means and hierarchical clustering - Preparing reports, slideshows, and web pages with knitr - Building reusable R packages with devtools and Rcpp - Getting involved with the R global community

    Over years of groundbreaking experiments, he has distilled remarkable discoveries significant enough to become the bedrock of a whole new scientific field: social physics. Humans have more in common with bees than we like to admit: We’re social creatures first and foremost. Our most important habits of action—and most basic notions of common sense—are wired into us through our coordination in social groups. Social physics is about idea flow, the way human social networks spread ideas and transform those ideas into behaviors. Thanks to the millions of digital bread crumbs people leave behind via smartphones, GPS devices, and the Internet, the amount of new information we have about human activity is truly profound. Until now, sociologists have depended on limited data sets and surveys that tell us how people say they think and behave, rather than what they actually do. As a result, we’ve been stuck with the same stale social structures—classes, markets—and a focus on individual actors, data snapshots, and steady states. Pentland shows that, in fact, humans respond much more powerfully to social incentives that involve rewarding others and strengthening the ties that bind than incentives that involve only their own economic self-interest. Pentland and his teams have found that they can study patterns of information exchange in a social network without any knowledge of the actual content of the information and predict with stunning accuracy how productive and effective that network is, whether it’s a business or an entire city. We can maximize a group’s collective intelligence to improve performance and use social incentives to create new organizations and guide them through disruptive change in a way that maximizes the good. At every level of interaction, from small groups to large cities, social networks can be tuned to increase exploration and engagement, thus vastly improving idea flow.  Social Physics will change the way we think about how we learn and how our social groups work—and can be made to work better, at every level of society. Pentland leads readers to the edge of the most important revolution in the study of social behavior in a generation, an entirely new way to look at life itself.

    In writing the book James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? Stewart's ESSENTIAL CALCULUS offers a concise approach to teaching calculus that focuses on major concepts and supports those concepts with precise definitions, patient explanations, and carefully graded problems. Essential Calculus is only 850 pages-two-thirds the size of Stewart's other calculus texts (CALCULUS, Fifth Edition and CALCULUS, EARLY TRANSCENDENTALS, Fifth Edition)-and yet it contains almost all of the same topics. The author achieved this relative brevity mainly by condensing the exposition and by putting some of the features on the website, www.StewartCalculus.com. Despite the reduced size of the book, there is still a modern flavor: Conceptual understanding and technology are not neglected, though they are not as prominent as in Stewart's other books. ESSENTIAL CALCULUS has been written with the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

    Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.Head First Statistics is ideal for high school and college students taking statistics and satisfies the requirements for passing the College Board's Advanced Placement (AP) Statistics Exam. With this book, you'll:Study the full range of topics covered in first-year statistics Tackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge Explore real-world scenarios, ranging from casino gambling to prescription drug testing, to bring statistical principles to life Discover how to measure spread, calculate odds through probability, and understand the normal, binomial, geometric, and Poisson distributions Conduct sampling, use correlation and regression, do hypothesis testing, perform chi square analysis, and moreBefore you know it, you'll not only have mastered statistics, you'll also see how they work in the real world. Head First Statistics will help you pass your statistics course, and give you a firm understanding of the subject so you can apply the knowledge throughout your life.

    The term “complexity” can be misleading, however, because what makes West’s discoveries so beautiful is that he has found an underlying simplicity that unites the seemingly complex and diverse phenomena of living systems, including our bodies, our cities and our businesses. Fascinated by issues of aging and mortality, West applied the rigor of a physicist to the biological question of why we live as long as we do and no longer. The result was astonishing, and changed science, creating a new understanding of energy use and metabolism: West found that despite the riotous diversity in the sizes of mammals, they are all, to a large degree, scaled versions of each other. If you know the size of a mammal, you can use scaling laws to learn everything from how much food it eats per day, what its heart-rate is, how long it will take to mature, its lifespan, and so on. Furthermore, the efficiency of the mammal’s circulatory systems scales up precisely based on weight: if you compare a mouse, a human and an elephant on a logarithmic graph, you find with every doubling of average weight, a species gets 25% more efficient—and lives 25% longer. This speaks to everything from how long we can expect to live to how many hours of sleep we need. Fundamentally, he has proven, the issue has to do with the fractal geometry of the networks that supply energy and remove waste from the organism's body. West's work has been game-changing for biologists, but then he made the even bolder move of exploring his work's applicability to cities. Cities, too, are constellations of networks and laws of scalability relate with eerie precision to them. For every doubling in a city's size, the city needs 15% less road, electrical wire, and gas stations to support the same population. More amazingly, for every doubling in size, cities produce 15% more patents and more wealth, as well as 15% more crime and disease. This broad pattern lays the groundwork for a new science of cities. Recently, West has applied his revolutionary work on cities and biological life to the business world. This investigation has led to powerful insights into why some companies thrive while others fail. The implications of these discoveries are far-reaching, and are just beginning to be explored. Scale is a thrilling scientific adventure story about the elemental natural laws that bind us together in simple but profound ways. Through the brilliant mind of Geoffrey West, we can envision how cities, companies and biological life alike are dancing to the same simple, powerful tune, however diverse and unrelated they are to each other.From the Hardcover edition.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    Contains complete worked solutions to all regular exercises and computer exercises in the text; additional test questions and their solutions; an online laboratory manual for the computer algebra system GAP, with exercises tied to the book and an instructor answer key; and links on the author's website to true/false questions, flash cards, essays, software downloads, and other abstract algebra-related materials.