Teaching Statistics and Probability

(Yearbook - National Council of Teachers of Mathematics)
Albert P. Shulte e James R. Smart

National Council of Teachers of Mathematics | 1981 | 258 páginas | rar - pdf | 7,22 Mb

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This 1981 yearbook of the National Council of Teachers of Mathematics (NCTM) offers classroom ideas for teaching statistics and probability, viewed as important topics in the school mathematics curriculum. Statistics and probability are seen as appropriate because they: (1) provide meaningful applications of mathematics at all levels; (2) provide methods for dealing with uncertainty; (3) give us some understanding of the statistical arguments, good and bad, with which we are continually bombarded; (4) help consumers distinguish sound use of statistical procedures for unsound or deceptive uses; and (5) are inherently interesting, exciting, and motivating topics for most students. The text is divided into eight parts, labeled: (1) The Case for Teaching Statistics and Probability; (2) Samples of Existing Courses or Programs; (3) Classroom Activities; (4) Teaching and Learning Specific Topics; (5) Applications; (6) Statistical Inference; (7) Monte Carlo Techniques and Simulation; and (8) Using Computers. The yearbook concludes with a bibliography and a list of suggested class projects

Will You Be Alive 10 Years from Now?: And Numerous Other Curious Questions in Probability

Paul J. Nahin

Princeton University Press | 2013 | 250 páginas | rar - pdf | 1,35 Mb

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What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the one-of-a-kind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book.
Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the past--from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton--and also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book.
Nahin then presents twenty-five unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB® Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

Contents
Preface xv
Introduction: Classic Puzzles from the Past 1
I.1 A Gambling Puzzle of Gombaud and Pascal 1
I.2 Galileo’s Dice Problem 3
I.3 Another Gombaud-Pascal Puzzle 4
I.4 Gambler’s Ruin and De Moivre 6
I.5 Monte Carlo Simulation of Gambler’s Ruin 10
I.6 Newton’s Probability Problem 13
I.7 A Dice Problem That Would Have Surprised Newton 17
I.8 A Coin-Flipping Problem 18
I.9 S impson’s Paradox, Radio-Direction Finding, and the Spaghetti Problem 21
Challenge Problems 30
1 Breaking Sticks 36
1.1 The Problem 36
1.2 Theoretical Analysis 36
1.3 Computer Simulation 38
2 The Twins 42
2.1 The Problem 42
2.2 Theoretical Analysis 43
2.3 Computer Simulation 44
3 Steve’s Elevator Problem 47
3.1 The Problem 47
3.2 Theoretical Analysis by Shane Henderson 48
3.3 Computer Simulation 51
4 Three Gambling Problems Newton Would “Probably” Have Liked 52
4.1 The Problems 52
4.2 Theoretical Analysis 1 54
4.3 Computer Simulation 1 55
4.4 Theoretical Analysis 2 57
4.5 Computer Simulation 2 58
4.6 Theoretical Analysis 3 59
5 Big Quotients—Part 1 62
5.1 The Problem 62
5.2 Theoretical Analysis 62
5.3 Computer Simulation 64
6 Two Ways to Proofread 66
6.1 The Problem 66
6.2 Theoretical Analysis 67
7 Chain Letters That Never End 70
7.1 The Problem 70
7.2 Theoretical Analysis 70
8 Bingo Befuddlement 74
8.1 The Problem 74
8.2 Computer Simulation 75
9 Is Dreidel Fair? 79
9.1 The Problem 79
9.2 Computer Simulation 80
10 Hollywood Thrills 83
10.1 The Problem 83
10.2 Theoretical Analysis 83
11 The Problem of the n-Liars 87
11.1 The Problem 87
11.2 Theoretical Analysis 87
11.3 Computer Simulation 89
12 The Inconvenience of a Law 90
12.1 The Problem 90
12.2 Theoretical Analysis 90
13 A Puzzle for When the Super Bowl is a Blowout 93
13.1 The Problem 93
13.2 Theoretical Analysis 94
14 Darts and Ballistic Missiles 96
14.1 The Problem 96
14.2 Theoretical Analysis 97
15 Blood Testing 103
15.1 The Problem 103
15.2 Theoretical Analysis 103
16 Big Quotients—Part 2 107
16.1 The Problem 107
16.2 Theoretical Analysis 107
17 To Test or Not to Test? 117
17.1 The Problem 117
17.2 Theoretical Analysis 119
18 Average Distances on a Square 126
18.1 The Problem(s) 126
18.2 Theoretical Analyses 127
18.3 Computer Simulations 136
19 When Will the Last One Fail? 139
19.1 The Problem 139
19.2 Theoretical Analyses 142
20 Who’s Ahead? 147
20.1 The Problem 147
20.2 Theoretical Analysis 148
21 Plum Pudding 151
21.1 The Problem 151
21.2 Computer Simulation 152
21.3 Theoretical Analysis 153
22 Ping-Pong, Squash, and Difference Equations 156
22.1 Ping-Pong Math 156
22.2 Squash Math Is Harder! 161
23 Will You Be Alive 10 Years from Now? 168
23.1 The Problem 168
23.2 Theoretical Analysis 169
24 Chickens in Boxes 176
24.1 The Problem (and Some Warm-ups, Too) 176
24.2 Theoretical Analysis 180
25 Newcomb’s Paradox 183
25.1 Some History 183
25.2 Decision Principles in Conflict 186
Challenge Problem Solutions 189
Technical Note on MATLAB®’s Random
Number Generator 213
Acknowledgments 217
Index 219

Outros livros de Paul J. Nahin:

The logician and the engineer : how George Boole and Claude Shannon created the information age por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, [2013] ©2013

Chases and escapes : the mathematics of pursuit and evasion por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, 2012, ©2007.

Mrs. Perkins's electric quilt : and other intriguing stories of mathematical physics por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, ©2009.

Digital dice : computational solutions to practical probability problems por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, ©2008.

Dr. Euler's fabulous formula : cures many mathematical ills por Paul J Nahin Idioma: Inglês   Editora: Princeton, NJ : Princeton University Press, ©2006.

When least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2004.

Duelling idiots and other probability puzzlers por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2000.

An imaginary tale : the story of [the square root of minus one] por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©1998.

Digital Dice: Computational Solutions to Practical Probability Problems

Paul J. Nahin

Princeton University Press | 2013 | 289 páginas | rar - pdf | 1,7 Mb

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Edição de 2008

Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.
Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.
The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.
Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

Contents
Preface to the Paperback Edition xiii
Introduction 1
The Problems 35
1. The Clumsy Dishwasher Problem 37
2. Will Lil and Bill Meet at the Malt Shop? 38
3. A Parallel Parking Question 40
4. A Curious Coin-Flipping Game 42
5. The Gamow-Stern Elevator Puzzle 45
6. Steve’s Elevator Problem 48
7. The Pipe Smoker’s Discovery 51
8. A Toilet Paper Dilemma 53
9. The Forgetful Burglar Problem 59
10. The Umbrella Quandary 61
11. The Case of the Missing Senators 63
12. How Many Runners in a Marathon? 65
13. A Police Patrol Problem 69
14. Parrondo’s Paradox 74
15. How Long Is the Wait to Get the Potato Salad? 77
16. The Appeals Court Paradox 81
17. Waiting for Buses 83
18. Waiting for Stoplights 85
19. Electing Emperors and Popes 87
20. An Optimal Stopping Problem 91
21. Chain Reactions, Branching Processes, and Baby Boys 96
MATLAB Solutions To The Problems 101
1. The Clumsy Dishwasher Problem 103
2. Will Lil and Bill Meet at the Malt Shop? 105
3. A Parallel Parking Question 109
4. A Curious Coin-Flipping Game 114
5. The Gamow-Stern Elevator Puzzle 120
6. Steve’s Elevator Problem 124
7. The Pipe Smoker’s Discovery 129
8. A Toilet Paper Dilemma 140
9. The Forgetful Burglar Problem 144
10. The Umbrella Quandary 148
11. The Case of the Missing Senators 153
12. How Many Runners in a Marathon? 157
13. A Police Patrol Problem 160
14. Parrondo’s Paradox 169
15. How Long is the Wait to Get the Potato Salad? 176
16. The Appeals Court Paradox 184
17. Waiting for Buses 187
18. Waiting for Stoplights 191
19. Electing Emperors and Popes 197
20. An Optimal Stopping Problem 204
21. Chain Reactions, Branching Processes, and Baby Boys 213
Appendix 1. One Way to Guess on a Test 221
Appendix 2. An Example of Variance-Reduction in the
Monte Carlo Method 223
Appendix 3. Random Harmonic Sums 229
Appendix 4. Solving Montmort’s Problem by Recursion 231
Appendix 5. An Illustration of the Inclusion-Exclusion Principle 237
Appendix 6. Solutions to the Spin Game 244
Appendix 7. How to Simulate Kelvin’s Fair Coin with a Biased Coin 248
Appendix 8. How to Simulate an Exponential Random Variable 252
Appendix 9. Index to Author-Created MATLAB m-Files in the Book 255
Glossary 257
Acknowledgments 259
Index 261
Also by Paul J. Nahin 265

Outros livros de Paul J. Nahin:

The logician and the engineer : how George Boole and Claude Shannon created the information age por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, [2013] ©2013

Chases and escapes : the mathematics of pursuit and evasion por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, 2012, ©2007.

Dr. Euler's fabulous formula : cures many mathematical ills por Paul J Nahin Idioma: Inglês   Editora: Princeton, NJ : Princeton University Press, ©2006.

When least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2004.

Duelling idiots and other probability puzzlers por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2000.

An imaginary tale : the story of [the square root of minus one] por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©1998.

Help Your Kids with Math: A visual problem solver for kids and parents

 

Barry Lewis

DK Publishing | 2010 | 258 páginas | rar - pdf | 9,7 Mb

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Studying math is often a source of great anxiety for children and also proves troublesome for parents helping with their homework.

Using uniquely accessible illustrated stress-free approach, Help Your Kids with Math looks at every aspect of math, from simple sums to simultaneous equations, and explains each facet in easily understandable language so that adults and kids can master the subject together.

In Help Your Kids with Math tricky concepts are explored and examined step-by-step, so that even the most math-phobic individual will be able to approach and solve complex problems with confidence.

Contents
NUMBERS
Introducing numbers ; Addition ; Subtraction ; Multiplication ; Division ; Prime numbers ; Units of measurement ; Positive and negative numbers ; Powers and roots ; Standard form ; Decimals in action; Fractions, Ratio and proportion, Percentages, Converting fractions, decimals, and percentages ; Mental math ; Rounding off ; Using a calculator ; Personal finance ; Business finance
GEOMETRY
What is geometry?; Angles; Straight lines; Symmetry; Coordinates; Vectors; Translations ; Rotations; Reflections; Enlargements; Scale drawings; Bearings; Constructions; Loci ; Triangles; Constructing triangles; Congruent triangles; Area of a triangle; Similar triangles ; Pythagorean Theorem ; Quadrilaterals; Polygons ; Circles ; Circumference and diameter ; Area of a circle ; Angles in a circle; Chords and cyclic quadrilaterals ; Tangents ; Arcs ; Sectors ; Solids ; Volumes ; Surface area 148
TRIGONOMETRY
What is trigonometry? ; Working with trigonometry ; Finding missing sides ; Finding missing angles 
ALGEBRA
What is algebra?; Sequences; Working with expressions; Expanding and factorizing expressions; Quadratic expressions; Formulas; Solving equations; Linear graphs; Simultaneous equations; Factorizing quadratic equations; The quadratic formula; Quadratic graphs ; Inequalities 
STATISTICS
What is statistics? ; Collecting and organizing data ; Bar charts ; Pie charts ; Line graphs;  Averages; Moving Averages ; Measuring spread ; Histograms ; Scatter diagrams 
PROBABILITY
What is probability? , Expectation and reality ; Multiple probability ; Dependent events ; Tree diagrams 
Reference section 232
Glossary 244
Index 252
Acknowledgments 256

Leveled Texts for Mathematics Data Analysis and Probability

Stephanie Paris

Shell Education | 2011 | 147 páginas | rar -pdf | 23 Mb

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Highlighting data analysis and probability, this resource provides the know-how to use leveled texts to differentiate instruction in mathematics. A total of 15 different topics are featured in and the high-interest text is written at four different reading levels with matching visuals. Practice problems are provided to reinforce what is taught in the passage. The included Teacher Resource CD features a modifiable version of each passage in text format and full-color versions of the texts and image files. This resource is correlated to the Common Core State Standards.

Table of Contents
What Is Differentiation?......4
How to Differentiate Using This Product.......5
General Information About the Student Populations........6
Below-Grade-Level Students........6
English Language Learners.......6
On-Grade-Level Students........7
Above-Grade-Level Students........7
Strategies for Using the Leveled Texts......8
Below-Grade-Level Students.......8
English Language Learners....... 11
Above-Grade-Level Students..... 14
How to Use This Product...... 16
Readability Chart........ 16
Components of the Product......... 17
Tips for Managing the Product....... 18
Correlation to Mathematics Standards..... 19
Leveled Texts......... 21
Collecting Data...... 21
Creating Pictographs...... 29
Analyzing Pictographs...... 37
Creating Bar Graphs...... 45
Analyzing Bar Graphs..... 53
Creating Line Graphs...... 61
Analyzing Line Graphs....... 69
Creating Circle Graphs...... 77
Analyzing Circle Graphs...... 85
Comparing Graphs.......... 93
What Does Mean Mean?....... 101
Median in the Middle...... 109
Mode and Range.......... 117
Probability of Events....... 125
Probability Experiments..... 133
Appendices...... 141
References Cited......... 141
Contents of Teacher Resource CD...... 142

The Drunkard's Walk: How Randomness Rules Our Lives

Leonard Mlodinow

Pantheon Books, New York | 2008 | 268 páginas | pdf |920 kb

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With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe.By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more informed decisions. From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

CONTENTS
Chapter 1: Peering through the Eyepiece of RandomnessThe hidden role of chance…when human beings can be outperformed by a rat.
Chapter 2: The Laws of Truths and Half-TruthsThe basic principles of probability and how they are abused…why a good story is often less likely to be true than a flimsy explanation.
Chapter 3: Finding Your Way through a Space of PossibilitiesA framework for thinking about random situations…from a gambler in plague-ridden Italy to Let’s Make a Deal.
Chapter 4: Tracking the Pathways to SuccessHow to count the number of ways in which events can happen, and why it matters…the mathematical meaning of expectation.
Chapter 5: The Dueling Laws of Large and Small NumbersThe extent to which probabilities are reflected in the results we observe…Zeno’s paradox, the concept of limits, and beating the casino at roulette.
Chapter 6: False Positives and Positive FallaciesHow to adjust expectations in light of past events or new knowledge…mistakes in conditional probability from medical screening to the O. J. Simpson trial and the prosecutor’s fallacy.
Chapter 7: Measurement and the Law of ErrorsThe meaning and lack of meaning in measurements…the bell curve and wine ratings, political polls, grades, and the position of planets.Chapter 8: The Order in ChaosHow large numbers can wash out the disorder of randomness…or why 200,000,000 drivers form a creature of habit.Chapter 9: Illusions of Patterns and Patterns of IllusionWhy we are often fooled by the regularities in chance events…can a million consecutive zeroes or the success of Wall Street gurus be random?Chapter 10: The Drunkard’s WalkWhy chance is a more fundamental conception than causality…Bruce Willis, Bill Gates, and the normal accident theory of life.

Outro livro do mesmo autor:

Euclid's window : the story of geometry from parallel lines to hyperspace por Leonard Mlodinow Idioma: Inglês   Editora: New York : Free Press, ©2001.

Statistics and Probability with Applications for Engineers and Scientists

Bhisham C. Gupta e Irwin Guttman 

Wiley | 2013 | 898 páginas | rar - pdf | 9,18 Mb

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An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences.

Unique among books of this kind, Statistics and Probability with Applications for Engineers and Scientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab® and Microsoft® Office Excel® to analyze various data sets. The book also features:

• Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices

• A clear presentation of nonparametric methods and simple and multiple linear regression methods, as well as a brief discussion on logistic regression method
• Comprehensive guidance on the design of experiments, including randomized block designs, one- and two-way layout designs, Latin square designs, random effects and mixed effects models, factorial and fractional factorial designs, and response surface methodology
• A companion website containing data sets for Minitab and Microsoft Office Excel, as well as JMP ® routines and results

Assuming no background in probability and statistics, Statistics and Probability with Applications for Engineers and Scientists features a unique, yet tried-and-true, approach that is ideal for all undergraduate students as well as statistical practitioners who analyze and illustrate real-world data in engineering and the natural sciences.

Mathematical Connections: A Companion for Teachers

(Classroom Resource Material) 

Al Cuoco

The Mathematical Association of America | 2005 | 261 páginas | pdf | 6,3 Mb

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This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self-study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book.

Contents
1. Difference tables and polynomial fits. Doing it with sums
Doing it with differences
Finding a formula: combinatorial polynomials
Making it formal: the [delta] operator
Going the other way: polynomials to tables
Conversions
From Newton to Lagrange
Agreeing to disagree
2. Form and function: the algebra of polynomials. Polynomials
The basic theorems
Coefficients and values
Up a level
Transformations
Coefficients and zeros.
3. Complex numbers, complex maps, and trigonometry. Complex numbers
The complex plane
The geometry behind multiplying
Trigonometric identities
Complex maps
Julia sets and the Mandelbrot set.
4. Combinations and locks. Combinatorial proofs and identities
The simplex lock
Some approaches to the simplex lock problem
Connections to the Mahler basis.
5. Sums of powers. Summatory polynomials
Bernoulli's method.

Children's Logical and Mathematical Cognition Progress in Cognitive Development Research

 C.J. Brainerd

Springer | 2011 - reprint of the original 1st ed. 1982 edition | páginas | pdf | 6,6 Mb

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Contents
Chapter 1 Conservation - Nonconservation: Alternative Explanations .. 1
Curt Acredolo
Conservation and the Appreciation of an Identity Rule ....
Operational and Nonoperational Conservation .. 2
Nonconservation and the Overreliance on Perceptual Cues .... 4
Pseudononconservation .... 5
Nonoperational Conservation .... 14
Conclusions ....... 21
Future Research: The Development of the Identity Rule ..... 24
Reference Notes ..... 27
References ...... 27
Chapter 2 The Acquisition and Elaboration of the Number Word Sequence .... 33
Karen C. Fuson, John Richards, and Diane J. Briars
Acquisition of the Sequence .... 35
Elaboration of the Sequence ... 55
Conclusion ......... 89
Reference Notes ...... 89
References ..... 91
Chapter 3 Children's Concepts of Chance and Probability
Harry W. Hoemann and Bruce M. Ross
Piagetian Theory ... 94
Subsequent Studies .... 99
Theoretical Implications ... 116
References .... 120
Chapter 4 The Development of Quantity Concepts: Perceptual and Linguistic Factors .. 123
Linda S. Siegel
Linguistic Factors and the Development of Quantity Concepts ..... 123
A Taxonomy of Quantity Concepts .... 124
The Relationship between Language and Thought in the Child .... 128
Study 1: Concept versus Language ....... 129
Study 2: Does Language Training Facilitate Concept Acquisition? ... 132
Study 3: Visual versus Verbal Functions .... 138
Study 4: Training of Cognitive and Language Abilities ...... 140
Study 5: Cognitive Development of Children with Impaired Language Development ... 141
Study 6: The Abstraction of the Concept of Number ....... 144
Conclusion ........ 152
Reference Notes... 153
References ..... 153
Chapter 5 Culture and the Development of Numerical Cognition: Studies among the Oksapmin of Papua New Guinea ... 157
Geoffrey B. Saxe
Methodology and Cross-Cultural Number Research .... 158
The Oksapmin Community ..... 159
Studies on Numerical Cognition among the Oksapmin ... 160
Concluding Remarks
Chapter 6 Children's Concept Learning as Rule-Sampling Systems with Markovian Properties . 177
Charles J. Brainerd
Concept Learning as Rule Sampling ....179
Some Questions about Concept Learning ... 185
Some Experimental Evidence ...192
Remark ......202
Appendix ... 203
References .. 208
Index ..... 213

The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day

David J. Hand

Scientific American | 2014 | 288 páginas | rar - epub | 376 kb

link (matav)

In The Improbability Principle, the renowned statistician David J. Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.
But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.
Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.
An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

Contents
Title Page
Dedication
Epigraph
Preface
1. The Mystery
2. A Capricious Universe
3. What Is Chance?
4. The Law of Inevitability
5. The Law of Truly Large Numbers
6. The Law of Selection
7. The Law of the Probability Lever
8. The Law of Near Enough
9. The Human Mind
10. Life, the Universe, and Everything
11. How to Use the Improbability Principle
Epilogue
Appendix A: Mind-Numbingly Large and Mind-Bogglingly Small
Appendix B: Rules of Chance
Notes
Index
Also by David J. Hand
A Note About the Author

Outro livro do mesmo autor:

Statistics : a very short introduction por D J Hand Idioma: Inglês   Editora: Oxford ; New York : Oxford University Press, 2008.

The Game of Probability: Literature and Calculation From Pascal to Kleist

Rudiger Campe e Ellwood Wiggins

Stanford University Press | 2013 | 504 páginas | rar - pdf | 2,3 Mb

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There exist literary histories of probability and scientific histories of probability, but it has generally been thought that the two did not meet. Campe begs to differ. Mathematical probability, he argues, took over the role of the old probability of poets, orators, and logicians, albeit in scientific terms. Indeed, mathematical probability would not even have been possible without the other probability, whose roots lay in classical antiquity.
The Game of Probability revisits the seventeenth and eighteenth-century "probabilistic revolution," providing a history of the relations between mathematical and rhetorical techniques, between the scientific and the aesthetic. This was a revolution that overthrew the "order of things," notably the way that science and art positioned themselves with respect to reality, and its participants included a wide variety of people from as many walks of life. Campe devotes chapters to them in turn. Focusing on the interpretation of games of chance as the model for probability and on the reinterpretation of aesthetic form as verisimilitude (a critical question for theoreticians of that new literary genre, the novel), the scope alone of Campe's book argues for probability's crucial role in the constitution of modernity.

Contents
Introduction 1
part i. games for example: modeling probability
1 Theology and the Law: Dice in the Air 15
2 Numbers and Calculation in Context: The Game of Decision—Pascal 37
3 Writing the Calculation of Chances: Justice and Fair Game—Christiaan Huygens 73
4 Probability, a Postscript to the Theory of Chance: Logic and Contractual Law—Arnauld, Leibniz, Pufendorf 97
5 Probability Applied: Ancient Topoi and the Theory of Games of Chance—Jacob Bernoulli 118
6 Continued Proclamations: The Law of logica probabilium—Leibniz 147
7 Defoe’s Robinson Crusoe, or, The Improbability of Survival 172
part ii. verisimilitude spelled out: the appearance of truth
8 Numbers and Tables in Narration: Jurists and Clergymen and Their Bureaucratic Hobbies 195
9 Novels and Tables: Defoe’s A Journal of the Plague Year and Schnabel’s Die Insel Felsenburg 220
10 The Theory of Probability and the Form of the Novel: Daniel Bernoulli on Utility Value, the Anthropology of Risk, and Gellert’s Epistolary Fiction 248
11 “Improbable Probability”: The Theory of the Novel and Its Trope—Fielding’s Tom Jones and Wieland’s Agathon 273
12 The Appearance of Truth: Logic, Aesthetics, and Experimentation—Lambert 305
13 “Probable” or “Plausible”: Mathematical Formula Versus Philosophical Discourse—Kant 338
14 Kleist’s “Improbable Veracities,” or, A Romantic Ending 369
Conclusion 391
Notes 399
Bibliography 465

Probability and Statistics: A Didactic Introduction

José I. Barragués, Adolfo Morais e Jenaro Guisasola

CRC Press | 2014 | páginas | rar - pdf | 6,35 Mb

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With contributions by leaders in the field, this book provides a comprehensive introduction to the foundations of probability and statistics. Each of the chapters covers a major topic and offers an intuitive view of the subject matter, methodologies, concepts, terms, and related applications. The book is suitable for use for entry level courses in first year university studies of Science and Engineering, higher level courses, postgraduate university studies and for the research community.

Contents
Preface vii
1. Descriptive Statistics 1
Nicholas Watier, Claude Lamontagne and Sylvain Chartier
2. Probability 38
José I. Barragués, Adolfo Morais and Jenaro Guisasola
3. Random Variables 124
Verônica Y. Kataoka, Irene M. Cazorla, Hugo Hernandez and
Claudia Borim da Silva
4. Sampling 176
Giovanni Boscaino and Ornella Giambalvo
5. Point Estimation and Statistical Intervals 210
Martin Griffiths
6. Tests of Hypotheses 252
Martin Griffiths
7. Analysis of Variance 293
David L. Trumpower and Sait Atas
8. Factor Analysis 330
Marta B. Quaglino and José A. Pagura
9. Discriminant Analysis 384
T. Ramayah, Joshua Ignatius, Jasmine Yeap Ai Leen and Lo May Chiun
10. Multiple Regression Analysis 416
María V. López, María C. Fabrizio and María C. Plencovich
Index 469
Color Plate Section 475

The Best Writing on Mathematics 2013

 

Mircea Pitici 

Princeton University Press | 2014 | 273 páginas | rar - pdf | 3,65 Mb

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This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field,The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more.

Contents
Foreword
Roger Penrose ix
Introduction
Mircea Pitici xv
The Prospects for Mathematics in a Multimedia Civilization
Philip J. Davis 1
Fearful Symmetry
Ian Stewart 23
E pluribus unum: From Complexity, Universality
Terence Tao 32
Degrees of Separation
Gregory Goth 47
Randomness
Charles Seife 52
Randomness in Music
Donald E. Knuth 56
Playing the Odds
Soren Johnson 62
Machines of the Infinite
John Pavlus 67
Bridges, String Art, and Bézier Curves
Renan Gross 77
Slicing a Cone for Art and Science
Daniel S. Silver 90
High Fashion Meets Higher Mathematics
Kelly Delp 109
The Jordan Curve Theorem Is Nontrivial
Fiona Ross and William T. Ross 120
Why Mathematics? What Mathematics?
Anna Sfard 130
Math Anxiety: Who Has It, Why It Develops, and How to Guard against It
Erin A. Maloney and Sian L. Beilock 143
How Old Are the Platonic Solids?
David R. Lloyd 149
Early Modern Mathematical Instruments
Jim Bennett 163
A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today
Frank Quinn 175
Errors of Probability in Historical Context
Prakash Gorroochurn 191
The End of Probability
Elie Ayache 213
An abc Proof Too Tough Even for Mathematicians
Kevin Hartnett 225
Contributors 231
Notable Texts 237
Acknowledgments 241
Credits 243

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The best writing on mathematics 2011 por Mircea Pitici; Idioma: Inglês   Editora: Princeton : Princeton University Press, ©2012.

The best writing on mathematics 2010 por Mircea Pitici; Idioma: Inglês   Editora: Princeton : Princeton University Press, ©2011.