He proposes his solution.

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in CALCULUS: THE CLASSIC EDITION, 5th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.

    do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    Numbers and the Making of Us is a sweeping account of how numbers radically enhanced our species' cognitive capabilities and sparked a revolution in human culture. Caleb Everett brings new insights in psychology, anthropology, primatology, linguistics, and other disciplines to bear in explaining the myriad human behaviors and modes of thought numbers have made possible, from enabling us to conceptualize time in new ways to facilitating the development of writing, agriculture, and other advances of civilization.Number concepts are a human invention--a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.Everett examines the various types of numbers that have developed in different societies, showing how most number systems derived from anatomical factors such as the number of fingers on each hand. He details fascinating work with indigenous Amazonians who demonstrate that, unlike language, numbers are not a universal human endowment. Yet without numbers, the world as we know it would not exist.

    Now, two science professors give us the tools to dismantle misinformation and think clearly in a world of fake news and bad data.It's increasingly difficult to know what's true. Misinformation, disinformation, and fake news abound. Our media environment has become hyperpartisan. Science is conducted by press release. Startup culture elevates bullshit to high art. We are fairly well equipped to spot the sort of old-school bullshit that is based in fancy rhetoric and weasel words, but most of us don't feel qualified to challenge the avalanche of new-school bullshit presented in the language of math, science, or statistics. In Calling Bullshit, Professors Carl Bergstrom and Jevin West give us a set of powerful tools to cut through the most intimidating data.You don't need a lot of technical expertise to call out problems with data. Are the numbers or results too good or too dramatic to be true? Is the claim comparing like with like? Is it confirming your personal bias? Drawing on a deep well of expertise in statistics and computational biology, Bergstrom and West exuberantly unpack examples of selection bias and muddled data visualization, distinguish between correlation and causation, and examine the susceptibility of science to modern bullshit.We have always needed people who call bullshit when necessary, whether within a circle of friends, a community of scholars, or the citizenry of a nation. Now that bullshit has evolved, we need to relearn the art of skepticism.

    Even with access to compelling theories and approaches such as multicultural education, culturally responsive teaching, culturally relevant instruction, culturally sustaining pedagogy, schools still struggle to implement equitable change that reshapes the academic experiences of students marginalized by the prevailing history, culture, and traditions in public education. Instead of getting it right with equity implementation, many schools and districts remain trapped in a cycle of equity dysfunction.In Belonging through a Culture of Dignity, Cobb and Krownapple argue that the cause of these struggles are largely based on the failure of educators to consider the foundational elements upon which educational equity is based, belonging and dignity. Through this work, the authors make these concepts accessible and explain their importance in the implementation of educational equity initiatives.Though the importance of dignity and belonging might appear to be self-evident at first glance, it's not until these concepts are truly unpacked, that educators realize the dire need for belonging through dignity. Once these fundamental human needs are understood, educators can gain clarity of the barriers to meaningful student relationships, especially across dimensions of difference such as race, class, and culture. Even the most relational and responsive educators need this clarity due to the normalization of what the authors refer to as dignity distortions. Cobb and Krownapple challenge that normalization and offer three concepts as keys to successful equity initiatives: inclusion, belonging, and dignity. Through their work, the authors aim to equip educators with the tools necessary to deliver the promise of democracy through schools by breaking the cycle of equity dysfunction once and for all.

    They’re also fearful about opening up a dialogue. Not Orenstein. A contributing writer to the New York Times Magazine and the New York Times best-selling author of books like Cinderella Ate My Daughter, Orenstein spoke to psychologists, academics, and other experts in the field and yes, 70 young women, to offer an in-depth picture of “girls and sex” today.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    Research has shown that by the time they graduate, as many as one in three women and almost one in six men will have been sexually assaulted. But why is sexual assault such a common feature of college life? And what can be done to prevent it? Drawing on the Sexual Health Initiative to Foster Transformation (SHIFT) at Columbia University, the most comprehensive study of sexual assault on a campus to date, Jennifer S. Hirsch and Shamus Khan present an entirely new framework that emphasizes sexual assault’s social roots—transcending current debates about consent, predators in a “hunting ground,” and the dangers of hooking up.Sexual Citizens is based on years of research interviewing and observing college life—with students of different races, genders, sexual orientations, and socioeconomic backgrounds. Hirsch and Khan’s landmark study reveals the social ecosystem that makes sexual assault so predictable, explaining how physical spaces, alcohol, peer groups, and cultural norms influence young people’s experiences and interpretations of both sex and sexual assault. Through the powerful concepts of “sexual projects,” “sexual citizenship,” and “sexual geographies,” the authors offer a new and widely-accessible language for understanding the forces that shape young people’s sexual relationships. Empathetic, insightful, and far-ranging, Sexual Citizens transforms our understanding of sexual assault and offers a roadmap for how to address it.

    It’s time to think this through.“Cancel” or “call-out” culture is a source of much tension and debate in American society. The infamous "Harper’s Letter,” signed by public intellectuals of both the left and right, sought to settle the matter and only caused greater division. Originating as a way for marginalized and disempowered people to address harm and take down powerful abusers, often with the help of social media, call outs are seen by some as having gone too far. But what is “too far” when you’re talking about imbalances of power and patterns of harm? And what happens when people in social justice movements direct their righteous anger inward at one another?In We Will Not Cancel Us, movement mediator Adrienne Maree Brown reframes the discussion for us, in a way that points to possible paths beyond this impasse. Most critiques of cancel culture come from outside the milieus that produce it, sometimes even from from its targets. However, Brown explores the question from a Black, queer, and feminist viewpoint that gently asks, how well does this practice serve us? Does it prefigure the sort of world we want to live in? And, if it doesn’t, how do we seek accountability and redress for harm in ways that reflect our values?

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

    In x + y, Cheng argues that her mathematical specialty -- category theory -- reveals why. Category theory deals more with context, relationships, and nuanced versions of equality than with intrinsic characteristics. Category theory also emphasizes dimensionality: much as a cube can cast a square or diamond shadow, depending on your perspective, so too do gender politics appear to change with how we examine them. Because society often rewards traits that it associates with males, such as competitiveness, we treat the problems those traits can create as male. But putting competitive women in charge will leave many unjust relationships in place. If we want real change, we need to transform the contexts in which we all exist, and not simply who we think we are.