Everyday Calculus: Discovering the Hidden Math All around Us

Oscar E. Fernandez 

Princeton University Press | 2014 | 165 páginas | rar - pdf | 1,5 Mb

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Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.

Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations--how hot coffee cools down, for example--and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful--determining which seat at the theater leads to the best viewing experience, for instance--and fascinating--exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.

Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

CONTENTS

Preface ix

Calculus Topics Discussed by Chapter xi

CHAPTER 1 Wake Up and Smell the Functions 1

What’s Trig Got to Do with Your Morning? 2

How a Rational Function Defeated Thomas Edison, and Why Induction Powers the World 5

The Logarithms Hidden in the Air 10

The Frequency of Trig Functions 14

Galileo’s Parabolic Thinking 17

CHAPTER 2 Breakfast at Newton’s 21

Introducing Calculus, the CNBC Way 21

Coffee Has Its Limits 25

A Multivitamin a Day Keeps the Doctor Away 30

Derivatives Are about Change 34

CHAPTER 3 Driven by Derivatives 35

Why Do We Survive Rainy Days? 36

Politics in Derivatives, or Derivatives in Politics? 39

What the Unemployment Rate Teaches Us about the Curvature of Graphs 41

America’s Ballooning Population 44

Feeling Derivatives 46

The Calculus of Time Travel 47

CHAPTER 4 Connected by Calculus 51

E-Mails, Texts, Tweets, Ah! 51

The Calculus of Colds 53

What Does Sustainability Have to Do with Catching a Cold? 56

What Does Your Retirement Income Have to Do with Traffic? 58

The Calculus of the Sweet Tooth 61

CHAPTER 5 Take a Derivative and You’ll Feel Better 65

I “Heart” Differentials 65

How Life (and Nature) Uses Calculus 67

The Costly Downside of Calculus 73

The Optimal Drive Back Home 75

Catching Speeders Efficiently with Calculus 77

CHAPTER 6 Adding Things Up, the Calculus Way 81

The Little Engine That Could . . . Integrate 82

The Fundamental Theorem of Calculus 90

Using Integrals to Estimate Wait Times 93

CHAPTER 7 Derivatives Integrals: The Dream Team 97

Integration at Work—Tandoori Chicken 98

Finding the Best Seat in the House 101

Keeping the T Running with Calculus 104

Look Up to Look Back in Time 108

The Ultimate Fate of the Universe 109

The Age of the Universe 113

Epilogue 116

Appendix A Functions and Graphs 119

Appendices 1–7 125

Notes 147

Index 149

Naked Statistics: Stripping the Dread from the Data

Charles Wheelan


W. W. Norton & Company | 2014 | 304 páginas | epub | 1 Mb

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Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called “sexy.” From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. 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 showLet’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.

Contents

Introduction: Why I hated calculus but love statistics

1 What’s the Point?

2 Descriptive Statistics: Who was the best baseball player of all time?

3 Deceptive Description: “He’s got a great personality!” and other true but grossly misleading statements

4 Correlation: How does Netflix know what movies I like?

5 Basic Probability: Don’t buy the extended warranty on your $99 printer

5½ The Monty Hall Problem

6 Problems with Probability: How overconfident math geeks nearly destroyed the global financial system

7 The Importance of Data: “Garbage in, garbage out”

8 The Central Limit Theorem: The Lebron James of statistics

9 Inference: Why my statistics professor thought I might have cheated

10 Polling: How we know that 64 percent of Americans support the death penalty (with a sampling error ± 3 percent)

11 Regression Analysis: The miracle elixir

12 Common Regression Mistakes: The mandatory warning label

13 Program Evaluation: Will going to Harvard change your life?

Conclusion: Five questions that statistics can help answer

Appendix: Statistical software

Notes

Acknowledgments

Statistics in Plain English

Timothy C Urdan

Routledge | 2010 - 3.ª edição  | 223 páginas | rar - epub | 1,24 Mb

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(novo formato)

PDF | 2,6 Mb
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This inexpensive paperback provides a brief, simple overview of statistics to help readers gain a better understanding of how statistics work and how to interpret them correctly. Each chapter describes a different statistical technique, ranging from basic concepts like central tendency and describing distributions to more advanced concepts such as t tests, regression, repeated measures ANOVA, and factor analysis. Each chapter begins with a short description of the statistic and when it should be used. This is followed by a more in-depth explanation of how the statistic works. Finally, each chapter ends with an example of the statistic in use, and a sample of how the results of analyses using the statistic might be written up for publication.

Lawrence Erlbaum | 2005 - 2ª edição | PDF | 199 páginas | 12,56 Mb

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Statistics in Plain English, 2/e provides a brief, simple overview of statistics to help readers gain a better understanding of how statistics work and how to interpret them correctly. It presents brief explanations of statistical concepts and techniques in simple, everyday language. Each self-contained chapter consists of three sections. The first describes the statistic, including how it is used and what information it provides. The second section reviews how it works, how to calculate the formula, the strengths and weaknesses of the technique, and the conditions needed for its use. The final section provides examples that use and interpret the statistic. A glossary of terms and symbols is also included.

Using and Applying Mathematics at Key Stage 2: A Guide to Teaching Problem Solving and Thinking Skills

Elaine Sellars e Sue Lowndes

David Fulton Publishers | 2003 | 105 páginas | rar - pdf | 3,1 Mb

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All pupils - able children included - need to be taught strategies to enable their thinking skills to progress. They also need help with developing different approaches to problem solving. A sustained piece of work that requires perseverance, logical strategies, and refinement of method and extension of the original task is not the same as a straightforward quick-fix type problem. Both types of problem solving need to be taught. This book presents a series of activities that can be used with whole classes to provide a curriculum for the teaching of problem solving and the development of thinking skills. Each tried and tested investigation is clearly explained with ideas on how to introduce the task to a class, full solutions and resource sheets.
Activities include prisoners: a fun way of generating square numbers; handshakes: exploring arithmetic progressions; T-shape: an activity to lead pupils from numerical calculations to algebraic generalizations; frogs: encouraging systematic working and listing; and opposite corners: an advanced piece of work for independent learners.

Contents
Introduction 1
1. Prisoners 5
2. Handshakes 11
3. Worms 17
4. T-shape 21
5. Pond Borders 33
6. Rotten Apples 43
7. Pilot 47
8. Painted Cube 59
9. Frogs I 64
10. Frogs II 71
11. Opposite Corners 87

Apollonius: Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banu Musa

(Sources in the History of Mathematics and Physical Sciences)

Gerald J. Toomer

Springer | 2011 - reprint of  1990 edition | 644 páginas | rar- pdf | 21,3 Mb

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This is the first edition of the original text of the advanced part of the most important work on conic sections written in antiquity and one of the most influential works in mathematics. It is also the first literal English translation of it ever to be published. The purpose of the work is to make available, to those interested in the history of science and to mathematicians, a version of the work as close to the original as possible. This part of Apollonius' Conics is lost in the original Greek, and only an Arabic translation made in the 9th century survives. This text has never been published previously, and all "editions" of this part of Apollonius' work are based on the Latin translation from the Arabic published by Edmund Halley in 1710, which suffers from Halley's insufficient knowledge of Arabic and his use of a single manuscript. The present edition is based on all known manuscripts. Its other improvements over Halley's edition are: 1) the Arabic text with a full critical apparatus; 2) an accurate English translation (until now only a loose paraphrase, based on Halley's translation, has been available in English); 3) a commentary to elucidate both mathematical and historical difficulties. This book will replace Halley's edition and all its derivatives as the standard edition of this part of Apollonius' work.

Mathematics Teaching in the Early Years: An Investigation of Teachers' Subject Knowledge

Carol Aubrey

Routledge | 1997 | 225 páginas | rar - pdf | 3,5 Mb

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Young children start school already able to do a surprising amount of mathematics. This book examines the nature and origin of subject knowledge and is based on information gathered from observing the interactions between teachers and their first-year pupils. It demonstrates the necessity of the classroom teacher to draw on many kinds of knowledge in order to deal with various issues surrounding classroom learning and teaching. Two important core areas are knowledge of lesson structure and of subject matter; this book address the area of subject matter and, as such, it should be of interest to classroom teachers and lecturers in education.

Contents
List of Tables vi
List of Figures Vll
Acknowledgments viii
Summary ix
1 Teachers' Subject Knowledge: Emerging Themes 1
2 Changing Models and Methods of Investigating Teachers' Subject Knowledge 11
3 Knowing and Understanding Mathematics: Concerning a Theory ofInstruction 31
4 The Construction and Early Learning of Mathematics in School and Out 57
5 Investigating the Mathematical Knowledge and Competences Which Young Children Bring into School 77
6 Reporting on Teachers' Classroom Practice 91
7 Teacher and Pupil Interactions in the Course of Mathematical Instruction 107
8 Teacher and Pupil Mathematical Subject Knowledge and the Processes of Instruction in Reception Classes 123
9 Towards a Deeper Understanding of Pedagogical Subject Development 153
Appendix 1: Extracts from Mathematical Assessment Tasks 169
Appendix 2: Copy of Field Notes Schedule 173
Appendix 3: Copy of Teacher Interview Schedule for Phase Four 179
Appendix 4: Extracts from Teacher Interviews 181
References
Index

Outro livro da mesma autora:

A developmental approach to early numeracy : helping to raise childrens̓ achievements and deal with difficulties in learning por Carol Aubrey Idioma: Inglês   Editora: Birmingham : Questions Pub. Co., 1999.

Numbers A Very Short Introduction

Peter M. Higgins

Oxford University Press | 2011 | 144 páginas | rar - epub | 365 kb

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Numbers are integral to our everyday lives and factor into almost everything we do. In this Very Short Introduction, Peter M. Higgins, a renowned popular-science writer, unravels the world of numbers, demonstrating its richness and providing an overview of all the number types that feature in modern science and mathematics. Indeed, Higgins paints a crystal-clear picture of the number world, showing how the modern number system matured over many centuries, and introducing key concepts such as integers, fractions, real and imaginary numbers, and complex numbers. Higgins sheds light on such fascinating topics as the series of primes, describing how primes are now used to encrypt confidential data on the internet. He also explores the infinite nature of number collections and explains how the so-called real numbers knit together to form the continuum of the number line. Written in the fashion of Higgins' highly popular science paperbacks, Numbers accurately explains the nature of numbers and how so-called complex numbers and number systems are used in calculations that arise in real problems.

Contents 
Preface
List of illustrations
1 How not to think about numbers
2 The unending sequence of primes
3 Perfect and not so perfect numbers
4 Cryptography: the secret life of primes
5 Numbers that count
6 Below the waterline of the number iceberg
7 To infinity and beyond!
8 Numbers but not as we know them
Further reading
Index