In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    . . . It's a keeper."--ForbesWe live in a society where kids and parents are obsessed with early achievement, from getting perfect scores on SATs to getting into Ivy League colleges to landing an amazing job at Google or Facebook--or even better, creating a start-up with the potential to be the next Google or Facebook or Uber. We see software coders become millionaires or billionaires before age thirty and feel we are failing if we are not one of them.Late bloomers, on the other hand, are undervalued in popular culture by educators and employers, and even unwittingly by parents. Yet the fact is, a lot of us - most of us - do not explode out of the gates in life. We have to discover our passions and talents and gifts. That was true for author Rich Karlgaard, who had a mediocre academic career at Stanford (which he got into by a fluke) and, after graduating, worked as a dishwasher and nightwatchman before finally finding the inner motivation and drive that ultimately led him to start up a high-tech magazine in Silicon Valley, and eventually to become the publisher of Forbes magazine.There is a scientific explanation for why so many of us bloom later in life. The executive function of our brains doesn't mature until age twenty-five - and later for some. In fact, our brain's capabilities peak at different ages. We actually experience multiple periods of blooming in our lives. Moreover, late bloomers enjoy hidden strengths due to taking the time to discover their way in life - strengths coveted by many employers and partners, including curiosity, insight, compassion, resilience, and wisdom.Based on years of research, personal experience, interviews with neuroscientists, psychologists, and countless people at different stages of their careers, Late Bloomers reveals how and when we achieve our full potential, and why today's focus on early success is so misguided, and even harmful.Praise for Late Bloomers"The underlying message that we should 'consider a kinder clock for human development' is a compelling one."-- Financial Times "Late Bloomers spoke to me deeply as a parent of two millennials and as a coach to many new college grads (the children of my friends and associates). It's a bracing tonic for the anxiety they are swimming through, with a facts-based approach to help us all calm down."--Robin Wolaner, founder of Parenting magazine

    Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems.This book can serve as a complete Algebra I course, and also includes many concepts covered in Algebra II. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of algebra will find this book an instrumental part of their mathematics libraries.656About the author: Richard Rusczyk is a co-author of Art of Problem Solving, Volumes 1 and 2, the author of Art of Problem Solving's Introduction to Geometry. He was a national MATHCOUNTS participant, a USA Math Olympiad winner, and is currently director of the USA Mathematical Talent Search.

    

    Rare Book

    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.

    That’s what we tell ourselves when facing a tricky problem or a difficult project. But a growing body of research indicates that we’ve got it exactly backwards. What we need to do, says acclaimed science writer Annie Murphy Paul, is think outside the brain. A host of “extra-neural” resources—the feelings and movements of our bodies, the physical spaces in which we learn and work, and the minds of those around us— can help us focus more intently, comprehend more deeply, and create more imaginatively. The Extended Mind outlines the research behind this exciting new vision of human ability, exploring the findings of neuroscientists, cognitive scientists, psychologists, and examining the practices of educators, managers, and leaders who are already reaping the benefits of thinking outside the brain. She excavates the untold history of how artists, scientists, and authors—from Jackson Pollock to Jonas Salk to Robert Caro—have used mental extensions to solve problems, make discoveries, and create new works. In the tradition of Howard Gardner’s Frames of Mind or Daniel Goleman’s Emotional Intelligence, The Extended Mind offers a dramatic new view of how our minds work, full of practical advice on how we can all think better.

    Pose the same question to students and many will use words like "boring", "useless", and even "humiliating". In  Becoming the Math Teacher You Wish You'd Had , author Tracy Zager helps teachers close this gap by making math class more like mathematics. Tracy has spent years working with highly skilled math teachers in a diverse range of settings and grades. You'll find this book jam-packed with new ideas from these vibrant classrooms.  How to Teach Student-Centered Mathematics: Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learningBig Ideas, Practical Application: This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborateKey Topics for Elementary and Middle School Teachers:  Becoming the Math Teacher You Wish You'd Had  offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachersAll teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.

    Building on the concepts of professional competence that he introduced in his classic The Reflective Practitioner, Schon offers an approach for educating professional in all areas that will prepare them to handle the complex and unpredictable problems of actual practice with confidence, skill, and care.

    A public figure since winning his first National Chess Championship at the age of nine, Waitzkin was catapulted into a media whirlwind as a teenager when his father's book "Searching for Bobby Fischer" was made into a major motion picture. After dominating the scholastic chess world for ten years, Waitzkin expanded his horizons, taking on the martial art Tai Chi Chuan and ultimately earning the title of World Champion. How was he able to reach the pinnacle of two disciplines that on the surface seem so different? "I've come to realize that what I am best at is not Tai Chi, and it is not chess," he says. "What I am best at is the art of learning."In his riveting new book, "The Art of Learning," Waitzkin tells his remarkable story of personal achievement and shares the principles of learning and performance that have propelled him to the top -- twice.With a narrative that combines heart-stopping martial arts wars and tense chess face-offs with life lessons that speak to all of us, "The Art of Learning" takes readers through Waitzkin's unique journey to excellence. He explains in clear detail how a well-thought-out, principled approach to learning is what separates success from failure. Waitzkin believes that achievement, even at the championship level, is a function of a lifestyle that fuels a creative, resilient growth process. Rather than focusing on climactic wins, Waitzkin reveals the inner workings of his everyday method, from systematically triggering intuitive breakthroughs, to honing techniques into states of remarkable potency, to mastering the art of performance psychology.Through his own example, Waitzkin explains how to embrace defeat and make mistakes work for you. Does your opponent make you angry? Waitzkin describes how to channel emotions into creative fuel. As he explains it, obstacles are not obstacles but challenges to overcome, to spur the growth process by turning weaknesses into strengths. He illustrates the exact routines that he has used in all of his competitions, whether mental or physical, so that you too can achieve your peak performance zone in any competitive or professional circumstance.In stories ranging from his early years taking on chess hustlers as a seven year old in New York City's Washington Square Park, to dealing with the pressures of having a film made about his life, to International Chess Championships in India, Hungary, and Brazil, to gripping battles against powerhouse fighters in Taiwan in the Push Hands World Championships, "The Art of Learning" encapsulates an extraordinary competitor's life lessons in a page-turning narrative.

    Jerry King is no exception. His informal, nontechnical book, as its title implies, is organized around what Bertrand Russell called the 'supreme beauty' of mathematics--a beauty 'capable of a stern perfection such as only the greatest art can show.'NATUREIn this clear, concise, and superbly written volume, mathematics professor and poet Jerry P. King reveals the beauty that is at the heart of mathematics--and he makes that beauty accessible to all readers. Darting wittily from Euclid to Yeats, from Poincare to Rembrandt, from axioms to symphonies, THE ART OF MATHEMATICS explores the difference between real, rational, and complex numbers; analyzes the intellectual underpinnings of pure and applied mathematics; and reveals the fundamental connection between aesthetics and mathematics. King also sheds light on how mathematicians pursue their research and how our educational system perpetuates the damaging divisions between the two cultures.

    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.

    Barash, there are even more things that we don't know, genuine evolutionary mysteries that perplex the best minds in biology. Paradoxically, many of these mysteries are very close to home, involving some of the most personalaspects of being human.Homo Mysterious examines a number of these evolutionary mysteries, exploring things that we don't yet know about ourselves, laying out the best current hypotheses, and pointing toward insights that scientists are just beginning to glimpse. Why do women experience orgasm? Why do men have a shorterlifespan than women? Why does homosexuality exist? Why does religion exist in virtually every culture? Why do we have a fondness for the arts? Why do we have such large brains? And why does consciousness exist? Readers are plunged into an ocean of unknowns--the blank spots on the human evolutionarymap, the terra incognita of our own species--and are introduced to the major hypotheses that currently occupy scientists who are attempting to unravel each puzzle (including some solutions proposed here for the first time). Throughout the book, readers are invited to share the thrill of science atits cutting edge, a place where we know what we don't know, and, moreover, where we know enough to come up with some compelling and seductive explanations.Homo Mysterious is a guide to creative thought and future explorations, based on the best, most current thinking by evolutionary scientists. It captures the allure of the not-yet-known for those interested in stretching their scientific imaginations.

     “You’re about as useful as a windshield wiper on a goat’s butt.” Keep this book handy, someday you’ll be glad you have it. “Let's play horse. I'll be the front end and you just be yourself.” Pick any of the many jaw-dropping insults then laugh at the look on your adversary’s face when you whip one out and use it on them. You’ll leave no doubt in their mind that you are a master of sarcastic insults! ADDED BONUS: In addition to the fresh and hilarious insults in this book, you’ll also find great sarcastic observations about life hidden inside this book’s pages, like… “I think the reason so many people have smart phones is because opposites attract!” You’re no idiot, so you need this book to start your new life as the master of sarcastic insults and put-downs! “Hey! Who left the Idiot Box open? Now they're everywhere!”

    However, such critiques imply that though intelligence tests may miss certain key noncognitive areas, they encompass most of what is important in the cognitive domain. In this book, Keith E. Stanovich challenges this widely held assumption.Stanovich shows that IQ tests (or their proxies, such as the SAT) are radically incomplete as measures of cognitive functioning. They fail to assess traits that most people associate with “good thinking,” skills such as judgment and decision making. Such cognitive skills are crucial to real-world behavior, affecting the way we plan, evaluate critical evidence, judge risks and probabilities, and make effective decisions. IQ tests fail to assess these skills of rational thought, even though they are measurable cognitive processes. Rational thought is just as important as intelligence, Stanovich argues, and it should be valued as highly as the abilities currently measured on intelligence tests.