Are Numbers Real?

The Uncanny Relationship of Mathematics and the Physical World

Author: Brian Clegg

Publisher: Macmillan

ISBN: 1250081041

Category: Mathematics

Page: 304

View: 1036

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Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity, to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader’s eyes to the hidden reality of the strange yet familiar entities that are numbers.

Which Numbers Are Real?

Author: Michael Henle

Publisher: MAA

ISBN: 0883857774

Category: Mathematics

Page: 219

View: 9320

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Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics.Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book.Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

Real Numbers

Management Accounting in a Lean Organization

Author: Jean E. Cunningham,Orest J. Fiume,Emily Adams

Publisher: N.A

ISBN: 9780972809900

Category: Business & Economics

Page: 184

View: 5684

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Are your accounting data and reports providing a true and timely picture of your company's performance? Are your lean operations personnel complaining that the numbers "lie"? This explosive issue and its implications are fully explored in "Real Numbers." Traditional "accountingese" is not used, and it is written for all professionals desiring an understanding of the application of lean accounting and the results that can be achieved from its use. The authors, each a former chief financial executive, describe how management accounting evolved to this point and how simplicity and clarity can be restored -- particularly in a lean organization. The anecdotal presentation from their personal experiences vividly illustrates the "Whys" and "Hows" of lean accounting. The management accounting model illustrated in "Real Numbers" points the way to unlocking the true profit potential of lean. Real Numbers is required reading for SME Lean Silver Certification. It was the first lean accounting book and remains the ideal starting point for investigating this methodology.

A Dictionary of Real Numbers

Author: Jonathan Borwein

Publisher: Springer Science & Business Media

ISBN: 1461585104

Category: Mathematics

Page: 434

View: 2912

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How do we recognize that the number . 93371663 . . . is actually 2 IoglQ(e + 7r)/2 ? Gauss observed that the number 1. 85407467 . . . is (essentially) a rational value of an elliptic integral-an observation that was critical in the development of nineteenth century analysis. How do we decide that such a number is actually a special value of a familiar function without the tools Gauss had at his disposal, which were, presumably, phenomenal insight and a prodigious memory? Part of the answer, we hope, lies in this volume. This book is structured like a reverse telephone book, or more accurately, like a reverse handbook of special function values. It is a list of just over 100,000 eight-digit real numbers in the interval [0,1) that arise as the first eight digits of special values of familiar functions. It is designed for people, like ourselves, who encounter various numbers computationally and want to know if these numbers have some simple form. This is not a particularly well-defined endeavor-every eight-digit number is rational and this is not interesting. However, the chances of an eight digit number agreeing with a small rational, say with numerator and denominator less than twenty-five, is small. Thus the list is comprised primarily of special function evaluations at various algebraic and simple transcendental values. The exact numbers included are described below. Each entry consists of the first eight digits after the decimal point of the number in question.

Ten Billion Tomorrows

How Science Fiction Technology Became Reality and Shapes the Future

Author: Brian Clegg

Publisher: St. Martin's Press

ISBN: 1466861924

Category: Science

Page: 320

View: 6734

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Science fiction is a vital part of popular culture, influencing the way we all look at the world. TV shows like Star Trek and movies from Forbidden Planet to Inception have influenced scientists to enter the profession and have shaped our futures. Science fiction doesn't set out to predict what will happen - it's far more about how human beings react to "What if?..." - but it is fascinating to see how science fiction and reality sometimes converge, sometimes take extraordinarily different paths. Ten Billion Tomorrows brings to life a whole host of science fiction topics, from the virtual environment of The Matrix and the intelligent computer HAL in 2001, to force fields, ray guns and cyborgs. We discover how science fiction has excited us with possibilities, whether it is Star Trek's holodeck inspiring makers of iconic video games Doom and Quake to create the virtual interactive worlds that transformed gaming, or the strange physics that has made real cloaking devices possible. Mixing remarkable science with the imagination of our greatest science fiction writers, Ten Billion Tomorrows will delight science fiction lovers and popular science devotees alike.

The Real Numbers and Real Analysis

Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

ISBN: 0387721762

Category: Mathematics

Page: 553

View: 8295

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This rigorous, detailed introduction to real analysis presents the fundamentals clearly and includes definitions, theorems and proofs. Mirroring the structure of standard calculus courses makes it especially accessible to university students of mathematics.

Calculating the Cosmos

How Mathematics Unveils the Universe

Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465096115

Category: Mathematics

Page: 360

View: 9413

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A prize-winning popular science writer uses mathematical modeling to explain the cosmos. In Calculating the Cosmos, Ian Stewart presents an exhilarating guide to the cosmos, from our solar system to the entire universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it's all going to end. He considers parallel universes, the fine-tuning of the cosmos for life, what forms extraterrestrial life might take, and the likelihood of life on Earth being snuffed out by an asteroid. Beginning with the Babylonian integration of mathematics into the study of astronomy and cosmology, Stewart traces the evolution of our understanding of the cosmos: How Kepler's laws of planetary motion led Newton to formulate his theory of gravity. How, two centuries later, tiny irregularities in the motion of Mars inspired Einstein to devise his general theory of relativity. How, eighty years ago, the discovery that the universe is expanding led to the development of the Big Bang theory of its origins. How single-point origin and expansion led cosmologists to theorize new components of the universe, such as inflation, dark matter, and dark energy. But does inflation explain the structure of today's universe? Does dark matter actually exist? Could a scientific revolution that will challenge the long-held scientific orthodoxy and once again transform our understanding of the universe be on the way? In an exciting and engaging style, Calculating the Cosmos is a mathematical quest through the intricate realms of astronomy and cosmology.

Real Nigga Etiquette

Author: The God 720

Publisher: BookBaby

ISBN: 194382004X

Category: Philosophy

Page: 71

View: 4625

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Real Nigga Etiquette Is the Proverbs Addendum to The Black Man’s Bible. It is THE GOD 720’s First Philosophical Work. Real Nigga Etiquette is a Short Composite of the many rules and regulations that The God 720 lives by. It is A Self Help reference Book. That is needed and can be used everywhere you go inclusive with and situation or circumstance you might find yourself in. Wisdom & Understanding on everything from Cops, Home, Women, The World can all be found in this book. The Onyx Tablet is the Album that goes with this book.

Algebra for College Students

Author: Bernard Kolman,Arnold Shapiro

Publisher: Elsevier

ISBN: 1483271218

Category: Mathematics

Page: 550

View: 7762

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Algebra for College Students, Revised and Expanded Edition is a complete and self-contained presentation of the fundamentals of algebra which has been designed for use by the student. The book provides sufficient materials for use in many courses in college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, sets and set notation, matrices and their application in solving linear systems, and notation of functions. The theory of polynomial equations, formulas for factoring a sum and a difference of cubes, roots of polynomials, and the geometric definition of each conic are likewise included in the book. College students will find the book very useful and invaluable.

The Real Numbers

An Introduction to Set Theory and Analysis

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 331901577X

Category: Mathematics

Page: 244

View: 9260

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While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

Cooking by the Numbers

Author: Cecilia Minden

Publisher: Cherry Lake

ISBN: 1602791422

Category: Juvenile Nonfiction

Page: 32

View: 5516

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From adjusting recipes to measuring ingredients, cooks use math skills every day. Readers will discover how preparing healthy meals for themselves and their families can be fun and practical way to use math!

Statistics Hacks

Tips & Tools for Measuring the World and Beating the Odds

Author: Bruce Frey

Publisher: "O'Reilly Media, Inc."

ISBN: 9780596553999

Category: Mathematics

Page: 358

View: 303

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Want to calculate the probability that an event will happen? Be able to spot fake data? Prove beyond doubt whether one thing causes another? Or learn to be a better gambler? You can do that and much more with 75 practical and fun hacks packed into Statistics Hacks. These cool tips, tricks, and mind-boggling solutions from the world of statistics, measurement, and research methods will not only amaze and entertain you, but will give you an advantage in several real-world situations-including business. This book is ideal for anyone who likes puzzles, brainteasers, games, gambling, magic tricks, and those who want to apply math and science to everyday circumstances. Several hacks in the first chapter alone-such as the "central limit theorem,", which allows you to know everything by knowing just a little-serve as sound approaches for marketing and other business objectives. Using the tools of inferential statistics, you can understand the way probability works, discover relationships, predict events with uncanny accuracy, and even make a little money with a well-placed wager here and there. Statistics Hacks presents useful techniques from statistics, educational and psychological measurement, and experimental research to help you solve a variety of problems in business, games, and life. You'll learn how to: Play smart when you play Texas Hold 'Em, blackjack, roulette, dice games, or even the lottery Design your own winnable bar bets to make money and amaze your friends Predict the outcomes of baseball games, know when to "go for two" in football, and anticipate the winners of other sporting events with surprising accuracy Demystify amazing coincidences and distinguish the truly random from the only seemingly random--even keep your iPod's "random" shuffle honest Spot fraudulent data, detect plagiarism, and break codes How to isolate the effects of observation on the thing observed Whether you're a statistics enthusiast who does calculations in your sleep or a civilian who is entertained by clever solutions to interesting problems, Statistics Hacks has tools to give you an edge over the world's slim odds.

All My Friends Are Dead

Author: Avery Monsen,Jory John

Publisher: Chronicle Books

ISBN: 145213538X

Category: Humor

Page: 96

View: 8725

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If you're a dinosaur, all of your friends are dead. If you're a pirate, all of your friends have scurvy. If you're a tree, all of your friends are end tables. Each page of this laugh-out-loud illustrated humor book showcases the downside of being everything from a clown to a cassette tape to a zombie. Cute and dark all at once, this hilarious children's book for adults teaches valuable lessons about life while exploring each cartoon character's unique grievance and wide-eyed predicament. From the sock whose only friends have gone missing to the houseplant whose friends are being slowly killed by irresponsible plant owners (like you), All My Friends Are Dead presents a delightful primer for laughing at the inevitable.

The TB12 Method

How to Achieve a Lifetime of Sustained Peak Performance

Author: Tom Brady

Publisher: Simon and Schuster

ISBN: 1501180738

Category: Biography & Autobiography

Page: 320

View: 6476

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Quarterback Tom Brady offers the principles behind pliability, which is at the heart of a new paradigm shift and movement toward a more natural, healthier way of exercising, training, and living, and one that challenges some commonly held assumptions around health and wellness. Filled with lessons learned from Brady's own peak performance training, and step-by-step action steps to help readers develop and maintain their own peak performance, this book also advocates for more effective approaches to strength training, hydration, nutrition, supplementation, cognitive fitness, recovery, and other lifestyle choices.

Single Mothers are for Grown Men, ONLY!

Author: Tristan

Publisher: Shop Derrick Jaxn LLC

ISBN: N.A

Category: Self-Help

Page: 132

View: 9420

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Our understanding of single mothers is broken. Not like, "The x-ray came back and you may need a cast", broken; but, "It's time to evacuate. The levy has been demolished," broken.Mentally, our streets are flooded with ignorance, yet we simply paddle along as if this is the way things are going to be. All things common sense seem to be immersed under the murky waters of, "She should've known better," "She should've been married first," and "It's her fault he ran out. She's the one who chose him." It's bizarre that in a world where cars can drive themselves and phones can recognize thumb prints, we're still committed to such ignorance, but that's about to change.For the last few years I've posted articles, memes, poems, and even viral videos with tens of millions of views on this subject, but like sandbags to an ocean, they've gotten swallowed whole without us, as a society, moving forward one inch. So, I've decided to take things up a notch with Single Mothers are for Grown Men, ONLY! and drain the preconceived notions, biases, and stereotypes once and for all, particularly as they pertain to dating and relationships.This is not some pity-ridden manual about how single moms should feel sorry for themselves. They have nothing to feel sorry about. In fact, they should be feeling the exact opposite if despite what they have to put up with, they're still able to hold their heads up and put one foot in front of the other. This is 130 pages of facts, analogies, and practical examples of how single mothers have been framed for moral crimes they've never committed, and underappreciated for the should-be obvious positive qualities they possess. It's time for a perspective adjustment. If you agree, then you've found the right book. If you don't, then challenge me to change your mind, and yes, I accept.

A World of Work

Imagined Manuals for Real Jobs

Author: Ilana Gershon

Publisher: Cornell University Press

ISBN: 080145641X

Category: Social Science

Page: 248

View: 5220

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Ever wondered what it would be like to be a street magician in Paris? A fish farmer in Norway? A costume designer in Bollywood? This playful and accessible look at different types of work around the world delivers a wealth of information and advice about a wide array of jobs and professions. The value of this book is twofold: For young people or middle-aged people who are undecided about their career paths and feel constrained in their choices, A World of Work offers an expansive vision. For ethnographers, this book offers an excellent example of using the practical details of everyday life to shed light on larger structural issues. Each chapter in this collection of ethnographic fiction could be considered a job manual. Yet not any typical job manual—to do justice to the ways details about jobs are conveyed in culturally specific ways, the authors adopt a range of voices and perspectives. One chapter is written as though it was a letter from an older sister counseling her brother on how to be a doctor in Malawi. Another is framed as a eulogy for a well-loved village magistrate in Papua New Guinea who may have been killed by sorcery. Beneath the novelty of the examples are some serious messages that Ilana Gershon highlights in her introduction. These ethnographies reveal the connection between work and culture, the impact of societal values on the conditions of employment. Readers will be surprised at how much they can learn about an entire culture by being given the chance to understand just one occupation. Contributors: Lovleen Bains, Mumbai; Chiwoza Bandawe, University of Malawi; Joshua A. Bell, Smithsonian Institution; Michelle Bigenho, Colgate University; Warren Chamberlain, Vita Needle Company, Massachusetts; Melissa Demian, Australian National University; Ilana Gershon, Indiana University; Kathryn Graber, Indiana University; Graham M. Jones, MIT; Amanda Kemble, The George Washington University; Briel Kobak, The George Washington University; Corinna Kruse, Linköping University, Sweden; Joel Kuipers, The George Washington University; Carrie Lane, California State University, Fullerton; Jean Lave, University of California, Berkeley; John Law, Open University; Heather Levi, Temple University; Marianne Elisabeth Lien, University of Oslo; Caitrin Lynch, Olin College; Loïc Marquet, Paris; Winnifred Fallers Sullivan, Indiana University; Chris Swift, Leeds Teaching Hospitals; Claire Wendland, University of Wisconsin–Madison; Clare Wilkinson, University of Pennsylvania; Helena Wulff, Stockholm University

Factfulness

Ten Reasons We're Wrong About the World--and Why Things Are Better Than You Think

Author: Hans Rosling,Anna Rosling Rönnlund,Ola Rosling

Publisher: Flatiron Books

ISBN: 125012381X

Category: Business & Economics

Page: 288

View: 2549

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INSTANT NEW YORK TIMES BESTSELLER “One of the most important books I’ve ever read—an indispensable guide to thinking clearly about the world.” – Bill Gates “Hans Rosling tells the story of ‘the secret silent miracle of human progress’ as only he can. But Factfulness does much more than that. It also explains why progress is so often secret and silent and teaches readers how to see it clearly.” —Melinda Gates "Factfulness by Hans Rosling, an outstanding international public health expert, is a hopeful book about the potential for human progress when we work off facts rather than our inherent biases." - Former U.S. President Barack Obama Factfulness: The stress-reducing habit of only carrying opinions for which you have strong supporting facts. When asked simple questions about global trends—what percentage of the world’s population live in poverty; why the world’s population is increasing; how many girls finish school—we systematically get the answers wrong. So wrong that a chimpanzee choosing answers at random will consistently outguess teachers, journalists, Nobel laureates, and investment bankers. In Factfulness, Professor of International Health and global TED phenomenon Hans Rosling, together with his two long-time collaborators, Anna and Ola, offers a radical new explanation of why this happens. They reveal the ten instincts that distort our perspective—from our tendency to divide the world into two camps (usually some version of us and them) to the way we consume media (where fear rules) to how we perceive progress (believing that most things are getting worse). Our problem is that we don’t know what we don’t know, and even our guesses are informed by unconscious and predictable biases. It turns out that the world, for all its imperfections, is in a much better state than we might think. That doesn’t mean there aren’t real concerns. But when we worry about everything all the time instead of embracing a worldview based on facts, we can lose our ability to focus on the things that threaten us most. Inspiring and revelatory, filled with lively anecdotes and moving stories, Factfulness is an urgent and essential book that will change the way you see the world and empower you to respond to the crises and opportunities of the future. --- “This book is my last battle in my life-long mission to fight devastating ignorance...Previously I armed myself with huge data sets, eye-opening software, an energetic learning style and a Swedish bayonet for sword-swallowing. It wasn’t enough. But I hope this book will be.” Hans Rosling, February 2017.

Dice World

Science and Life in a Random Universe

Author: Brian Clegg

Publisher: Icon Books Ltd

ISBN: 1848315643

Category: Science

Page: 288

View: 7762

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LONGLISTED FOR THE 2014 WINTON ROYAL SOCIETY PRIZE FOR SCIENCE BOOKS As troubling as we pattern-seeking humans may find it, modern science has repeatedly shown us that randomness is the underlying heartbeat of nature. In Dice World, acclaimed science writer Brian Clegg takes readers on an incredible trip around our random universe, uncovering the truths and lies behind probability and statistics, explaining how chaotic intervention is behind every great success in business, and demonstrating the possibilities quantum mechanics has given us for creating unbreakable ciphers and undergoing teleportation. He explores how the ‘clockwork universe’ imagined by Newton, in which everything could be predicted given enough data, was disproved bit by bit, to be supplanted by chaos theory and quantum physics. Clegg reveals a world in which not only is accurate forecasting often impossible but probability is the only way for us to understand the fundamental nature of things. Forget the clockwork universe. Welcome to Dice World, a unique portrait of a startlingly complex cosmos, from the bizarre microscopic world of the quantum to the unfathomable mechanics of planetary movements, where very little is as it seems...

The Book of Revelation and the Work of the Priest

Eighteen Lectures, Conversations and Question-and-answer Sessions in Dornach from 5 to 22 September 1924, Reconstructed from Notes Taken by the Participants

Author: Rudolf Steiner

Publisher: Rudolf Steiner Press

ISBN: 1855840529

Category: Religion

Page: 282

View: 7734

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Lectures to 57 priests in Dornach Sept 5-22, 1924 (CW 346)John's Book of Revelation, the Apocalypse, has been subjected to countless theological and academic interpretations over the years, usually based on theories and abstract speculations. Rudolf Steiner, however, discussed the Book of Revelation through direct experience and knowledge of the spiritual truths contained in John's mysterious imagery. Rudolf Steiner had already presented his insights on the Apocalypse to various audiences, but in 1924 he presented a completely new perspective. This time, his comments were in response to requests from priests of The Christian Community, the movement for religious renewal, which itself had taken form on the basis of Steiner's insights. This book will be of value to anyone who would like a fresh perspective on the most enigmatic book of the New Testament. Includes eight color plates of blackboard drawings. Read Bobby Matherne's review of this book

What Happened

Author: Hillary Rodham Clinton

Publisher: Simon and Schuster

ISBN: 1501175572

Category: Biography & Autobiography

Page: 512

View: 8427

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“An engaging, beautifully synthesized page-turner” (Slate). The #1 New York Times bestseller and Time Magazine #1 Nonfiction Book of the Year: Hillary Rodham Clinton’s most personal memoir yet, about the 2016 presidential election. In this “candid and blackly funny” (The New York Times) memoir, Hillary Rodham Clinton reveals what she was thinking and feeling during one of the most controversial and unpredictable presidential elections in history. She takes us inside the intense personal experience of becoming the first woman nominated for president by a major party in an election marked by rage, sexism, exhilarating highs and infuriating lows, stranger-than-fiction twists, Russian interference, and an opponent who broke all the rules. “At her most emotionally raw” (People), Hillary describes what it was like to run against Donald Trump, the mistakes she made, how she has coped with a shocking and devastating loss, and how she found the strength to pick herself back up afterward. She tells readers what it took to get back on her feet—the rituals, relationships, and reading that got her through, and what the experience has taught her about life. In this “feminist manifesto” (The New York Times), she speaks to the challenges of being a strong woman in the public eye, the criticism over her voice, age, and appearance, and the double standard confronting women in politics. Offering a “bracing... guide to our political arena” (The Washington Post), What Happened lays out how the 2016 election was marked by an unprecedented assault on our democracy by a foreign adversary. By analyzing the evidence and connecting the dots, Hillary shows just how dangerous the forces are that shaped the outcome, and why Americans need to understand them to protect our values and our democracy in the future. The election of 2016 was unprecedented and historic. What Happened is the story of that campaign, now with a new epilogue showing how Hillary grappled with many of her worst fears coming true in the Trump Era, while finding new hope in a surge of civic activism, women running for office, and young people marching in the streets.