Adventures in Mathematical Reasoning


Author: Sherman Stein
Publisher: Courier Dover Publications
ISBN: 0486814114
Category: Mathematics
Page: 192
View: 4322

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Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.

Adventures in Mathematical Reasoning


Author: Sherman Stein
Publisher: Courier Dover Publications
ISBN: 0486806448
Category: Mathematics
Page: 192
View: 5933

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Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.

Mathematics and the Aesthetic

New Approaches to an Ancient Affinity
Author: Nathalie Sinclair,William Higginson
Publisher: Springer Science & Business Media
ISBN: 9780387381459
Category: Mathematics
Page: 288
View: 9317

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Strategies for Teaching Mathematics


Author: N.A
Publisher: Default- TCM
ISBN: 1425891152
Category: Electronic books
Page: 320
View: 4918

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Enhance mathematics instruction and build students' understanding of mathematical concepts with this exceptional resource notebook. Choose from a wide range of easy-to-implement strategies that enhance mathematical content. Topics include developing students' mathematical vocabulary and problem-solving abilities, assessing students' mathematics thinking, and using manipulatives. Highlights include tips on planning instruction and managing the mathematics classroom, plus differentiation strategies for each lesson. Includes Teacher Resource CD with reproducibles including rubrics and assessment.

Math Teacher's Survival Guide: Practical Strategies, Management Techniques, and Reproducibles for New and Experienced Teachers, Grades 5-12


Author: Judith A. Muschla,Gary Robert Muschla,Erin Muschla
Publisher: John Wiley & Sons
ISBN: 9780470574997
Category: Education
Page: 352
View: 9887

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Classroom-tested strategies to help new and experienced math teachers thrive Math teachers must not only instruct their students in basic mathematical skills and concepts, they must also prepare them for standardized tests, provide instruction in the use of technology, and teach problem-solving and critical-thinking skills. At the same time, they must also manage their other responsibilities – taking attendance, planning, grading, record-keeping, disciplining, and communicating with parents and administrators. This book provides efficient and practical information on the management skills necessary to succeed in this most challenging profession. Offers realistic suggestions and strategies for planning and delivering effective math instruction Helps math teachers achieve excellence and continue to be enthusiastic and successful in their teaching careers Includes reproducible forms to help math teachers stay on top of everything they need to do The Math Teacher's Survival Guide contains a wealth of useful tools and strategies that can help any math teacher succeed in the classroom.

Strength in Numbers

Discovering the Joy and Power of Mathematics in Everyday Life
Author: Sherman K. Stein
Publisher: Wiley
ISBN: 9781620456965
Category: Mathematics
Page: 288
View: 9517

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An engaging survey of the fundamental concepts of mathematics and the many ways math is used in everyday life. This is a stimulating and simple reintroduction to all the math we all learned in high school but have forgotten, using many examples of how math applies to the real world. Highlights the math topics that are most relevant to everyday concerns, such as how statistics can be misleading and how interest on savings accounts accrues at different interest rates. Also explores the most fundamental mysteries and amazing properties, such as why two negative numbers multiplied together make a positive number and why fractions can be easily multiplied but not easily added. Uses a multitude of examples from real life such as how extremely large numbers are used to write unbreakable computer codes and how the slope of a curve is used by biologists to calculate the rate of growth of species. It walks the reader step by step through simple solutions to each problem explored.

The Phantom Tollbooth


Author: Norton Juster
Publisher: Knopf Books for Young Readers
ISBN: 0375985298
Category: Juvenile Fiction
Page: 288
View: 3628

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With almost 4 million copies sold over 50 years after its original publication, generations of readers have now journeyed with Milo to the Lands Beyond in this beloved classic that Philip Pullman says “comes up bright and new every time I read it . . . it will continue to charm and delight for a very long time yet. And teach us some wisdom, too.” Enriched by Jules Feiffer’s splendid illustrations, the wit, wisdom, and wordplay of Norton Juster’s offbeat fantasy are as beguiling as ever. For Milo, everything’s a bore. When a tollbooth mysteriously appears in his room, he drives through only because he’s got nothing better to do. But on the other side, things seem different. Milo visits the Island of Conclusions (you get there by jumping), learns about time from a ticking watchdog named Tock, and even embarks on a quest to rescue Rhyme and Reason. Somewhere along the way, Milo realizes something astonishing. Life is far from dull. In fact, it’s exciting beyond his wildest dreams!

The Meaning of It All

Thoughts of a Citizen-Scientist
Author: Richard P. Feynman
Publisher: Basic Books
ISBN: 0786739142
Category: Science
Page: 192
View: 5866

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Many appreciate Richard P. Feynman's contributions to twentieth-century physics, but few realize how engaged he was with the world around him—how deeply and thoughtfully he considered the religious, political, and social issues of his day. Now, a wonderful book—based on a previously unpublished, three-part public lecture he gave at the University of Washington in 1963—shows us this other side of Feynman, as he expounds on the inherent conflict between science and religion, people's distrust of politicians, and our universal fascination with flying saucers, faith healing, and mental telepathy. Here we see Feynman in top form: nearly bursting into a Navajo war chant, then pressing for an overhaul of the English language (if you want to know why Johnny can't read, just look at the spelling of “friend”); and, finally, ruminating on the death of his first wife from tuberculosis. This is quintessential Feynman—reflective, amusing, and ever enlightening.

Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics


Author: Robert B. Banks
Publisher: Princeton University Press
ISBN: 1400846749
Category: Mathematics
Page: 344
View: 9688

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Although we seldom think of it, our lives are played out in a world of numbers. Such common activities as throwing baseballs, skipping rope, growing flowers, playing football, measuring savings accounts, and many others are inherently mathematical. So are more speculative problems that are simply fun to ponder in themselves--such as the best way to score Olympic events. Here Robert Banks presents a wide range of musings, both practical and entertaining, that have intrigued him and others: How tall can one grow? Why do we get stuck in traffic? Which football player would have a better chance of breaking away--a small, speedy wide receiver or a huge, slow linebacker? Can California water shortages be alleviated by towing icebergs from Antarctica? What is the fastest the 100-meter dash will ever be run? The book's twenty-four concise chapters, each centered on a real-world phenomenon, are presented in an informal and engaging manner. Banks shows how math and simple reasoning together may produce elegant models that explain everything from the federal debt to the proper technique for ski-jumping. This book, which requires of its readers only a basic understanding of high school or college math, is for anyone fascinated by the workings of mathematics in our everyday lives, as well as its applications to what may be imagined. All will be rewarded with a myriad of interesting problems and the know-how to solve them. Some images inside the book are unavailable due to digital copyright restrictions.

Plato's Camera

How the Physical Brain Captures a Landscape of Abstract Universals
Author: Paul M. Churchland
Publisher: MIT Press
ISBN: 0262300826
Category: Philosophy
Page: 304
View: 3726

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In Plato's Camera, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures.

Our Mathematical Universe

My Quest for the Ultimate Nature of Reality
Author: Max Tegmark
Publisher: Vintage
ISBN: 038535049X
Category: Science
Page: 432
View: 2768

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Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

How the Body Shapes the Way We Think

A New View of Intelligence
Author: Rolf Pfeifer,Josh Bongard
Publisher: MIT Press
ISBN: 0262288524
Category: Computers
Page: 424
View: 3232

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How could the body influence our thinking when it seems obvious that the brain controls the body? In How the Body Shapes the Way We Think, Rolf Pfeifer and Josh Bongard demonstrate that thought is not independent of the body but is tightly constrained, and at the same time enabled, by it. They argue that the kinds of thoughts we are capable of have their foundation in our embodiment -- in our morphology and the material properties of our bodies.This crucial notion of embodiment underlies fundamental changes in the field of artificial intelligence over the past two decades, and Pfeifer and Bongard use the basic methodology of artificial intelligence -- "understanding by building" -- to describe their insights. If we understand how to design and build intelligent systems, they reason, we will better understand intelligence in general. In accessible, nontechnical language, and using many examples, they introduce the basic concepts by building on recent developments in robotics, biology, neuroscience, and psychology to outline a possible theory of intelligence. They illustrate applications of such a theory in ubiquitous computing, business and management, and the psychology of human memory. Embodied intelligence, as described by Pfeifer and Bongard, has important implications for our understanding of both natural and artificial intelligence.

The Real Story of Risk

Adventures in a Hazardous World
Author: Glenn Croston
Publisher: Prometheus Books
ISBN: 1616146613
Category: Science
Page: 294
View: 3539

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We live in a world of risk. It waits for us in our refrigerator and surrounds us on the freeway. It's lurking in our arteries and sitting in our 401(k) accounts. Given that we deal with risk on a constant basis, we should be good at it; as it turns out, though, we're not. We're blind to common risks like heart disease (one in five deaths), but we shrink in fear from rare events like shark attacks (one in a million) and airplane crashes (one in twenty thousand). What accounts for our poor ability to perceive and react to the risks that really matter? Starting from an evolutionary perspective, the author traces our distorted perception of risk back to our ancestors, reminding readers that we are all the culmination of a long line of survivors who fought life-and-death threats such as attacks from wild animals, starvation, and disease. The fact that we have covered Earth with seven billion people is a testament to our skill at overcoming these risks. But our spectacular success has also produced our contemporary artificial world with new threats like climate change, chili dogs, and online gambling. Our brains, which evolved to deal with the ancient world, are ill equipped to process the new threats we face. Croston examines the many facets of our hazardous modern environment that we only dimly perceive. He explains why we let our guard down for a beautiful face, why slow-moving risks (like rising seas) are hard to stop, how a good story (though false) can be more persuasive than dry statistics (even alarming ones), what we fear even more than death, and many other intriguing quirks about our built-in incompetence to adequately handle present-day risks. Offering a wealth of fascinating information about health, sex, money, safety, food, and the environment, this book illuminates an often-misunderstood but crucial aspect of daily life. From the Trade Paperback edition.

Soccermatics

Mathematical Adventures in the Beautiful Game
Author: David Sumpter
Publisher: Bloomsbury Publishing
ISBN: 1472924150
Category: Mathematics
Page: 288
View: 5345

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'Football looked at in a very different way' Pat Nevin, former Chelsea and Everton star and football media analyst Football – the most mathematical of sports. From shot statistics and league tables to the geometry of passing and managerial strategy, the modern game is filled with numbers, patterns and shapes. How do we make sense of them? The answer lies in the mathematical models applied in biology, physics and economics. Soccermatics brings football and mathematics together in a mind-bending synthesis, using numbers to help reveal the inner workings of the beautiful game. This new and expanded edition analyses the current big-name players and teams using mathematics, and meets the professionals working inside football who use numbers and statistics to boost performance. Welcome to the world of mathematical modelling, expressed brilliantly by David Sumpter through the prism of football. No matter who you follow – from your local non-league side to the big boys of the Premiership, La Liga, the Bundesliga, Serie A or the MLS – you'll be amazed at what mathematics has to teach us about the world's favourite sport.

The Mathematical Mechanic

Using Physical Reasoning to Solve Problems
Author: Mark Levi
Publisher: Princeton University Press
ISBN: 0691154562
Category: Science
Page: 186
View: 7849

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In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

The Drunkard's Walk

How Randomness Rules Our Lives
Author: Leonard Mlodinow
Publisher: Vintage
ISBN: 0307275175
Category: Mathematics
Page: 252
View: 2002

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An irreverent look at how randomness influences our lives, and how our successes and failures are far more dependent on chance events than we recognize.

An Illustrated Book of Bad Arguments


Author: Ali Almossawi
Publisher: The Experiment
ISBN: 1615192263
Category: Philosophy
Page: 64
View: 5505

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“A flawless compendium of flaws.” —Alice Roberts, PhD, anatomist, writer, and presenter of The Incredible Human Journey The antidote to fuzzy thinking, with furry animals! Have you read (or stumbled into) one too many irrational online debates? Ali Almossawi certainly had, so he wrote An Illustrated Book of Bad Arguments! This handy guide is here to bring the internet age a much-needed dose of old-school logic (really old-school, a la Aristotle). Here are cogent explanations of the straw man fallacy, the slippery slope argument, the ad hominem attack, and other common attempts at reasoning that actually fall short—plus a beautifully drawn menagerie of animals who (adorably) commit every logical faux pas. Rabbit thinks a strange light in the sky must be a UFO because no one can prove otherwise (the appeal to ignorance). And Lion doesn’t believe that gas emissions harm the planet because, if that were true, he wouldn’t like the result (the argument from consequences). Once you learn to recognize these abuses of reason, they start to crop up everywhere from congressional debate to YouTube comments—which makes this geek-chic book a must for anyone in the habit of holding opinions.

Calculus and Analytic Geometry


Author: Anthony Barcellos,Sherman K. Stein
Publisher: McGraw-Hill Science, Engineering & Mathematics
ISBN: 9780070612075
Category: Mathematics
Page: 245
View: 2545

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The Dyslexic Advantage

Unlocking the Hidden Potential of the Dyslexic Brain
Author: Brock Eide,Fernette Eide
Publisher: Penguin
ISBN: 0452297923
Category: Family & Relationships
Page: 283
View: 2417

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The neurolearning-expert creators of the award-winning blog by the same name reveal the unique brain structure and organization of dyslexic individuals, identifying how the differences responsible for reading challenges also enable specific mechanical, artistic, narrative and dynamic talents. Reprint.