His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    In Standard Deviations, economics professor Gary Smith walks us through the various tricks and traps that people use to back up their own crackpot theories. Sometimes, the unscrupulous deliberately try to mislead us. Other times, the well-intentioned are blissfully unaware of the mischief they are committing. Today, data is so plentiful that researchers spend precious little time distinguishing between good, meaningful indicators and total rubbish. Not only do others use data to fool us, we fool ourselves.With the breakout success of Nate Silver’s The Signal and the Noise, the once humdrum subject of statistics has never been hotter. Drawing on breakthrough research in behavioral economics by luminaries like Daniel Kahneman and Dan Ariely and taking to task some of the conclusions of Freakonomics author Steven D. Levitt, Standard Deviations demystifies the science behind statistics and makes it easy to spot the fraud all around.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    We are bombarded with more information each day than our brains can process—especially in election season. It's raining bad data, half-truths, and even outright lies. New York Times bestselling author Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them. It's becoming harder to separate the wheat from the digital chaff. How do we distinguish misinformation, pseudo-facts, distortions, and outright lies from reliable information? Levitin groups his field guide into two categories—statistical infomation and faulty arguments—ultimately showing how science is the bedrock of critical thinking. Infoliteracy means understanding that there are hierarchies of source quality and bias that variously distort our information feeds via every media channel, including social media. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they so often aren't. We need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning—not passively accepting information, repeating it, and making decisions based on it. Readers learn to avoid the extremes of passive gullibility and cynical rejection. Levitin's charming, entertaining, accessible guide can help anyone wake up to a whole lot of things that aren't so. And catch some lying weasels in their tracks!

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

      Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence -- and even more so if we hope to participate in the future, rather than being simple bystanders. In The Art of Statistics, world-renowned statistician David Spiegelhalter shows readers how to derive knowledge from raw data by focusing on the concepts and connections behind the math. Drawing on real world examples to introduce complex issues, he shows us how statistics can help us determine the luckiest passenger on the Titanic, whether a notorious serial killer could have been caught earlier, and if screening for ovarian cancer is beneficial. The Art of Statistics not only shows us how mathematicians have used statistical science to solve these problems -- it teaches us how we too can think like statisticians. We learn how to clarify our questions, assumptions, and expectations when approaching a problem, and -- perhaps even more importantly -- we learn how to responsibly interpret the answers we receive. Combining the incomparable insight of an expert with the playful enthusiasm of an aficionado, The Art of Statistics is the definitive guide to stats that every modern person needs.

    What will it take to turn this opportunity into reality in every classroom, school, and district? Continuing its tradition of mathematics education leadership, NCTM has defined and described the principles and actions, including specific teaching practices, that are essential for a high-quality mathematics education for all students. Principles to Actions: Ensuring Mathematical Success for All offers guidance to teachers, specialists, coaches, administrators, policymakers, and parents: Builds on the Principles articulated in Principles and Standards for School Mathematics to present six updated Guiding Principles for School MathematicsSupports the first Guiding Principle, Teaching and Learning, with eight essential, research-based Mathematics Teaching PracticesDetails the five remaining Principles--the Essential Elements that support Teaching and Learning as embodied in the Mathematics Teaching PracticesIdentifies obstacles and unproductive and productive beliefs that all stakeholders must recognize, as well as the teacher and student actions that characterize effective teaching and learning aligned with the Mathematics Teaching PracticesWith Principles to Actions, NCTM takes the next step in shaping the development of high-quality standards throughout the United States, Canada, and worldwide.

    Access to texts such as the Lost Book of Enoch, the Nag Hamadi Gospels, and the Book of Jubilees, among others is now widely available and, when synthesized and correlated with existing documents like the Bible and Qu'ran, merits rethinking Western civilization's origins and intent.Prepare yourself for a profound belief-challenging journey through ancient Persia, Sumer, Greece, and Atlantis; from Rome to the United States, HQ of the New Atlantis. This book is not like any other in the field: expect the winged-warrior aerial perspective of an Army Attack helicopter pilot, the BS filter of an Electrical Engineer, a Western Medicine-challenging Structural Integrator, and Southern California didgeridoo player all at the same time. Energy and matter, sound entrainment, slave control design methods using the electromagnetic spectrum, eternal life, gravity, and DMT are addressed herein.U.S. public school history ignores the Sumerians, although they are credited with all aspects of modern civilization, influencing both Egypt and Greece alike. Television series produced by the History Channel, like the "Ancient Aliens" Series is assisting the masses in waking up to the fact that the Anunnaki were not a myth, having left physical documents and artifacts backing up their claims to have created mankind, described in highly sophisticated language, as recorded by Atrahasis.It was in South Africa, where the idea was spawned to create a primitive worker, namely mankind, to operate the gold mines, provide temple building manpower, and generally serve every whim the Ancient Astronauts from Nibiru conceived of. Many of the Niburians, referenced in the Biblical Genesis as the Elohim, known to the Sumerians as the Anunnaki, were enthroned as Gods in Mesopotamia.Perhaps it is fitting for Westerners to look into the religious and historical origins for the kings and demigods of Sumer, the first culture to provide evidence of the cuneiform script language, complete with no antecedent. Not only were mundane records, detailed as they were, kept on clay tablets, tens of thousands of which survive to this day, but the history and direct experience accounts of some of the famed inhabitants, like king Gilgamesh of Uruk, introduce us to "Those who from Heaven to Earth Came." The Anunnaki astronauts hailed from a planet, Nibiru, in our own solar system, whose apogee resides in a 3,600 retrograde elliptical orbit beyond Pluto. According to their records, likely using spectroscopy as scientists do today, they located gold on planet Earth. Due to a failing atmosphere on Nibiru, Anu their king, dispatched his preeminent scientist and first-born son, Enki, on a space mission to Earth to recover enough gold that could be ionized in a layer of their atmosphere, as a solar radiation shieldAnunnaki gold mines in Africa have been found and carbon dated. Mining operations were occurring at the exact time and location that the "Genetic Eve Study" indicates: Womankind's genetic origins are undeniably linked to Enki's gold mining operation. Egyptian Queen Sheba's mines ring a bell? Michael Tellinger followed the Sumerian account to Africa, locating many of the mines, homes and temples used by the primitive workers and gods, our true ancestors.Additional source material and limited genealogy tables are included in the Bibliography and Appendix for the reader to explore. More exhaustive ones are available by contacting the author. Now consider your place in the unfolding New World Order. Will you choose the Enlilites or Enkiites to affiliate with, or do you have a choice? Enjoy this intellectual read, it is mind-bending, pineal-gland stimulating, and worth it! Available as Hardback, Audio Book, and Kindle Now!

    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.

    In this fun and accessible guide, McKellar—dubbed a “math superstar” by The New York Times—gives girls and their parents the tools they need to master the math concepts that confuse middle-schoolers most, including fractions, percentages, pre-algebra, and more. The book features hip, real-world examples, step-by-step instruction, and engaging stories of Danica's own childhood struggles in math (and stardom). In addition, borrowing from the style of today's teen magazines, it even includes a Math Horoscope section, Math Personality Quizzes, and Real-Life Testimonials—ultimately revealing why math is easier and cooler than readers think.

    Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system.Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

    Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on* the relationship between mathematical knots and DNA* how computers based on quantum logic can significantly speed up the factoring of large composite numbers* the relationship between four-dimensional geometry and physical theories of the nature of matter* the application of cellular automata models to social questions and the peregrinations of virtual ants* a novel mathematical model of quasicrystals based on decagon-shaped tilesBlazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.

    Told here for the first time, the dramatic tale of how the secrets of the brain were discovered in seventeenth-century England unfolds against a turbulent backdrop of civil war, the Great Fire of London, and plague. At the beginning of that chaotic century, no one knew how the brain worked or even what it looked like intact. But by the century's close, even the most common conceptions and dominant philosophies had been completely overturned, supplanted by a radical new vision of man, God, and the universe. Presiding over the rise of this new scientific paradigm was the founder of modern neurology, Thomas Willis, a fascinating, sympathetic, even heroic figure at the center of an extraordinary group of scientists and philosophers known as the Oxford circle. Chronicled here in vivid detail are their groundbreaking revelations and the often gory experiments that first enshrined the brain as the physical seat of intelligence -- and the seat of the human soul. Soul Made Flesh conveys a contagious appreciation for the brain, its structure, and its many marvelous functions, and the implications for human identity, mind, and morality.

    This book is intended to help readers understand and critique research in language learning. It presents a balanced and objective view of a range of methods - including formal experiments, introspective methods, interaction and transcript analysis, ethnography, and case studies. The book is highly accessible and does not assume specialist or technical knowledge. This volume will be of interest to students of applied linguistics and educational researchers, in addition to classroom teachers and teachers-in-training. Throughout the book, theoretical issues are drawn from published studies and reports. The book emphasizes the professional and practical value of reading published research.

    As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone--from those who fumble over fractions to those who solve complex equations in their heads--winds up marveling at what numbers can do.Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach them.