Math Stuff

Theoni Pappas 

 Wide World Publishing, Tetra | 2002 | 225 páginas | rar - pdf | 6,7 Mb

link (password: matav)

Whether one is adjusting the settings of a camera, doing financial planning, or just talking about the weather, everyone is involved in mathematics every day. Theoni Pappas explores some of the many areas in which one least expects to find "math stuff." Readers learn how computers get stressed out, how epaper works, and how codes and numbers affect the body.

TABLE OF CONTENTS
Introduction ix
The pea counts 2
mathematics behind your genes
The mathematics of peace 12
The millennium clock 16
Chaos theory 21
Cricket math 26
Mathematical private eyes 27
ratios hold the clues
Holyhedrons 30
Fractals, fractals everywhere 32
Smart dust, MEMS 40
What’s it all about?
Starcage 44
the works of Akio Hizume
In search of AI 50
mathematics & artificial intelligence
Art in nature/nature in art 60
Andy Goldsworthy
Do bees count? 64
e-paper & mathematics 65
Mathematics mints a coin 70
The sound of mathematics 72
music & mathematics
Mathematics engineers your finances 82
Numbers, numbers everywhere 85
You’ve come a long way ! 89
Icosa shelters 95
mathematically designed shelters
Computers get stressed out too! 98
lock-up, crash, freeze
mathematics & the pomegranate 101
rhombic dodecahedron & sphere packing

The Best Writing on Mathematics 2013

 

Mircea Pitici 

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

link (password : matav)

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

Outros livros da mesma coleção:

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.

Nature and Numbers a mathematical photo shooting

Georg Glaeser

Ambra Verlag | 2014 | 377 páginas | rar - pdf | 137 Mb

link (password : matav)

Mathematicians with special interest in biology, physics, geography, astronomy, architecture, design, etc., and being prepared to take pictures at any time, might try to answer unusual questions like the followings: What do a zebra, a tiger shark, and a hard coral have in common? How is this with drying mud, wings of dragon flies, and the structures of leaves? What is the "snail king" and is there also a "worm king"? Which curves stay of the same type after being photographed? Do fishes see like we do if we look through a fisheye lens? Which geometric properties of an object have physical consequences? Which kinds of geometric patterns appear when waves are interfering?
In Nature and Numbers you can find 180 double pages with at least as many questions of this kind. The principle to attack a problem is often similar: It starts with a photo that is for some reasons remarkable. In a short description an explanation is offered, including relevant Internet links. Additionally one can frequently find computer simulations in order to illustrate and confirm.

The New York Times Book of Mathematics

Gina Kolata e Paul Hoffman 

Sterling | 2013 | 496 páginas | epub | 3,1 Mb

link

From the archives of the world's most famous newspaper comes a collection of its very best writing on mathematics. Big and informative, The New York Times Book of Mathematics gathers more than 110 articles written from 1892 to 2010 that cover statistics, coincidences, chaos theory, famous problems, cryptography, computers, and many other topics. Edited by Pulitzer Prize finalist and senior Times writer Gina Kolata, and featuring renowned contributors such as James Gleick, William L. Laurence, Malcolm W. Browne, George Johnson, and John Markoff, it's a must-have for any math and science enthusiast!

CONTENTS

Foreword Paul Hoffman

Introduction Gina Kolata

CHAPTER 1 What Is Mathematics?

Useful Invention or Absolute Truth: What Is Math?, George Johnson

But Aren’t Truth and Beauty Supposed to be Enough?, James Gleick

Mathematicians Meet Computerized Ideas, Gina Kolata

Mathematicians Finally Log On, James Gleick

With Major Math Proof, Brute Computers Show Flash of Reasoning Power, Gina Kolata

Computers Still Can’t Do Beautiful Mathematics, Gina Kolata

100 Quadrillion Calculations Later, Eureka!, Gina Kolata

Theorist Applies Computer Power to Uncertainty in Statistic, Gina Kolata

CHAPTER 2 Statistics, Coincidences and Surprising Facts

1-in-a-Trillion Coincidence, You Say? Not Really, Experts Find, Gina Kolata

Sometimes Heavier Objects Go to the Top: Here’s Why, James Gleick

Behind Monty Hall’s Doors: Puzzle, Debate and Answer?, John Tierney

What If They Closed 42d Street and Nobody Noticed?, Gina Kolata

Down for the Count; Why Some Numbers Are Only Very Good Guesses, Gina Kolata

Could It Be? Weather Has Nothing to Do with Your Arthritis Pain?,Gina Kolata

Electronics to Aid Weather Figuring, Sidney Shalett

Insurance as a Study; Something of the Men Who Figure Business by Algebra Leontief’s Contribution, Leonard Silk

Many Small Events May Add Up to One Mass Extinction, Malcolm W. Browne

Metric Mania, John Allen Paulos

In Shuffling Cards, 7 Is a Winning Number, Gina Kolata

Can Game Theory Predict When Iran Will Get the Bomb?, Clive Thompson

In Modeling Risk, the Human Factor Was Left Out, Steve Lohr

Playing the Odds, George Johnson

Monday Puzzle: Solution to Birthday Problem, Pradeep Mutalik

Just What Are Your Odds in Genetic Roulette? Go Figure, Gina Kolata

The 2000 Election: The Science of Counting, Gina Kolata

Prospectus; Can a Computer Program Figure Out the Market? A Former Analyst and a Mathematician Are Betting That Theirs Can, Janet Stites

New Tools for the I.R.S. to Sniff Out Tax Cheats, David Cay Johnston

CHAPTER 3 Famous Problems, Solved and As Yet Unsolved

New Mathematics Links Two Worlds, William L. Laurence

An Elusive Proof and Its Elusive Prover, Dennis Overbye

Ask Science: Poincaré’s Conjecture, Dennis Overbye

Grigori Perelman’s Beautiful Mind, Jascha Hoffman

A Math Problem Solver Declines a $1 Million Prize, Dennis Overbye

“Four-Color Problem” Attacked, William L. Laurence

Four-Color Proof

Goldbach’s Conjecture; This One May Be Provable, but We May Never Know, George Johnson

Mathematics Expert May Soon Resolve A 350-Year Problem, James Gleick

Fermat’s Theorem Solved? Not This Time, James Gleick

Fermat’s Last Theorem Still Has 0 Solutions ,James Gleick

At Last, Shout of “Eureka!” in Age-Old Math Mystery, Gina Kolata

Fermat’s Theorem, James Gleick

Flaw Is Found in Math Proof, but Repairs Are Under Way, Gina Kolata

A Year Later Fermat’s Puzzle Is Still Not Quite Q.E.D., Gina Kolata

How a Gap in the Fermat Proof Was Bridged, Gina Kolata

Two Key Mathematics Questions Answered after Quarter Century, John A. Osmundsen

Mathematical Theory of Poker Is Applied to Business Problems, Will Lissner

Soap Bubbles Get a New Role in Old Mathematics Problem, Joseph Williams

Math Advance Penetrates Secrets of Knots, James Gleick

Packing Tetrahedrons, and Closing in on a Perfect Fit ,Kenneth Chang

Finding Order in the Apparent Chaos of Currents, Bina Venkataraman

In Bubbles and Metal, the Art of Shape-Shifting, Kenneth Chang

The Scientific Promise of Perfect Symmetry, Kenneth Chang

143-Year-Old Problem Still Has Mathematicians Guessing, Bruce Schechter

What Is the Most Important Problem in Math Today?, Gina Kolata

Solution to Old Puzzle: How Short a Shortcut?, Gina Kolata

CHAPTER 4 Chaos, Catastrophe and Randomness

Chaos Is Defined by New Calculus

Experts Debate the Prediction of Disasters, Malcolm W. Browne

Solving the Mathematical Riddle of Chaos, James Gleick

The Man Who Reshaped Geometry, James Gleick

Snowflake’s Riddle Yields to Probing of Science, James Gleick

Tales of Chaos: Tumbling Moons and Unstable Asteroids, James Gleick

Fluid Math Made Simple—Sort Of, James Gleick

When Chaos Rules the Market, James Gleick

New Appreciation of the Complexity in a Flock of Birds, James Gleick

Indestructible Wave May Hold Key to Superconductors , James Gleick

The Quest for True Randomness Finally Appears Successful, James Gleick

Coin-Tossing Computers Found to Show Subtle Bias, Malcolm W. Browne

Science Squints at a Future Fogged by Chaotic Uncertainty, Malcolm W. Browne

Probing Disease Clusters: Easier to Spot Than Prove, Gina Kolata

The Odds of That, Lisa Belkin

Fractal Vision, James Gleick

CHAPTER 5 Cryptography and the Emergence of Truly Unbreakable Codes

Harassment Alleged over Code Research, Malcolm W. Browne

Researchers to Permit Pre-Publication Review by U.S., Richard Severo

Tighter Security Rules for Advances in Cryptology, Walter Sullivan

A New Approach to Protecting Secrets Is Discovered, James Gleick

Brief U.S. Suppression of Proof Stirs Anger

A Most Ferocious Math Problem Tamed, Malcolm W. Browne

Biggest Division a Giant Leap in Math, Gina Kolata

Scientists Devise Math Tool to Break a Protective Code, John Markoff

Tied Up in Knots, Cryptographers Test Their Limits, Gina Kolata

A Public Battle over Secret Codes, John Markoff

U.S. Code Agency Is Jostling for Civilian Turf, John Markoff

Researchers Demonstrate Computer Code Can Be Broken, Sara Robinson

Nick Patterson; A Cold War Cryptologist Takes a Crack at Deciphering DNA’s Deep Secrets, Ingfei Chen

Adding Math to List of Security Threats, John Markoff

Prizes Aside, the P-NP Puzzler Has Consequences, John Markoff

CHAPTER 6 Computers Enter the World of Mathematics

“Thinking Machine” Does Higher Mathematics; Solves Equations That Take Humans Months
New Giant “Brain” Does Wizard Work
“Brain” Speeded Up for War Problems, Will Lissner
The Electronic Digital Computer: How It Started, How It Works and What It Does, Henry L. Lieberman and Dr. Louis Robinson
New Shortcut Found for Long Math Proofs, Gina Kolata
New Technique Stores Images More Efficiently, Gina Kolata
Giant Computer Virtually Conquers Space and Time, George Johnson
Rear Adm. Grace M. Hopper Dies; Innovator in Computers Was 85, John Markoff
Frances E. Holberton, 84, Early Computer Programmer, Steve Lohr
Squeezing Data like an Accordion, Peter Wayner
A Digital Brain Makes Connections, Anne Eisenberg
A Soviet Discovery Rocks World of Mathematics, Malcolm W. Browne
The Health Care Debate: Finding What Works, Gina Kolata
Step 1: Post Elusive Proof. Step 2: Watch Fireworks, John Markoff
CHAPTER 7 Mathematicians and Their World
Paul Erdos, 83, a Wayfarer in Math’s Vanguard, Is Dead, Gina Kolata
Journeys to the Distant Fields of Prime, Kenneth Chang
Highest Honor in Mathematics Is Refused, Kenneth Chang
Scientist at Work: John H. Conway; At Home in the Elusive World of Mathematics, Gina Kolata
Claude Shannon, B. 1916—Bit Player, James Gleick
An Isolated Genius Is Given His Due , James Gleick
Scientist at Work: Andrew Wiles; Math Whiz Who Battled 350-Year-Old, Problem Gina Kolata
Scientist at Work: Leonard Adleman; Hitting the High Spots of Computer Theory, Gina Kolata
Dr. Kurt Gödel, 71, Mathematician, Peter B. Flint
Genius or Gibberish? The Strange World of the Math Crank, George Johnson
Contributors’ Biographies
Photography and Illustration Credits

Love and Math: The Heart of Hidden Reality

Edward Frenkel

Basic Books | 2013 | 306 páginas | epub | 9 Mb

link

mobi - 10 Mb - link 

pdf - 28 mb - link

What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.

In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.

At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

Contents
Preface
A Guide for the Reader
1 A Mysterious Beast
2 The Essence of Symmetry
3 The Fifth Problem
4 Kerosinka
5 Threads of the Solution
6 Apprentice Mathematician
7 The Grand Unified Theory
8 Magic Numbers
9 Rosetta Stone
10 Being in the Loop
11Conquering the Summit
12Tree of Knowledge
13Harvard Calling
14Tying the Sheaves of Wisdom
15A Delicate Dance
16Quantum Duality
17Uncovering Hidden Connections
18Searching for the Formula of Love
Epilogue
Acknowledgments
Notes
Glossary of Terms
Index

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

Max Tegmark

Knopf  | 2014 | 432 paginas | epub | 25 Mb

link

mobi - 8 Mb - link

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.

Contents
Preface
  1 What Is Reality?
Not What It Seems • What’s the Ultimate Question? • The Journey Begins
Part One: Zooming Out
  2 Our Place in Space
Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space?
  3 Our Place in Time
Where Did Our Solar System Come From? • Where Did the Galaxies Come From? • Where Did the Mysterious Microwaves Come From? • Where Did the Atoms Come From?
  4 Our Universe by Numbers
Wanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From?
  5 Our Cosmic Origins
What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation
  6 Welcome to the Multiverse
The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup
Part Two: Zooming In
  7 Cosmic Legos
Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion
  8 The Level III Multiverse
The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words?
Part Three: Stepping Back
  9 Internal Reality, External Reality and Consensus Reality
External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality
10 Physical Reality and Mathematical Reality
Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure?
11 Is Time an Illusion?
How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You?
12 The Level IV Multiverse
Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses • Testing the Level IV Multiverse
13 Life, Our Universe and Everything
How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life • The Future of You—Are You Insignificant?
Acknowledgments
Suggestions for Further Reading
Index
A Note About the Author

Six Sources of Collapse A Mathematician’s Perspective on How Things Can Fall Apart in the Blink of an Eye

Charles R. Hadlock

The Mathematical Association of America | 2012 | 222 páginas | rar - pdf |4 Mb

link (password: matav)

Beginning with one of the most remarkable ecological collapses of recent time, that of the passenger pigeon, Hadlock goes on to survey collapse processes across the entire spectrum of the natural and man-made world. He takes us through extreme weather events, technological disasters, evolutionary processes, crashing markets and companies, the chaotic nature of Earth's orbit, revolutionary political change, the spread and elimination of disease, and many other fascinating cases.

His key thesis is that one or more of six fundamental dynamics consistently show up across this wide range. These "six sources of collapse" can all be best described and investigated using fundamental mathematical concepts. They include low probability events, group dynamics, evolutionary games, instability, nonlinearity, and network effects, all of which are explained in readily understandable terms. Almost the entirety of the book can be understood by readers with a minimal mathematical background, but even professional mathematicians are likely to get rich insights from the range of examples. The author tells his story with a warmly personal tone and weaves in many of his own experiences, whether from his consulting career of racing around the world trying to head off industrial disasters to his story of watching collapse after collapse in the evolution of an ecosystem on his New Hampshire farm.

Creative teachers could use this book for anything from a liberal arts math course to a senior capstone seminar, and one reviewer suggested that it should be required reading for any mathematics graduate student heading off into a teaching career. This book will also be of interest to readers in the fields under discussion, such as business, engineering, ecology, political science, and others.

Contents

Preface ix

Acknowledgements xi

1 Introduction 1

1.1 What is a collapse?. . 1

1.2 Shades of Hitchcock, and other tales . . 2

1.3 What might tomorrow bring?  . . 6

1.4 What this book aims to do  . . 13

2 Predicting Unpredictable Events 15

2.1 Like a thief in the night?. . 15

2.2 Chance and regularity. . 17

2.3 A quick statistics primer  . . 18

2.4 Normal regularity: the good, the bad, and the miraculous. . 22

2.5 Abnormal regularity: extreme value statistics  . . 25

2.6 Getting things right with heavy-tailed distributions . . 31

2.7 The dangers from getting your probabilities wrong . . 35

3 Group Behavior: Crowds, Herds, and Video Games 41

3.1 Fire! . . 41

3.2 Birds, boids, and bicycles . . 44

3.3 The Monte Carlo world. . 48

3.4 Models with probabilities . . 50

3.5 People, properties, and political systems  . . 54

3.6 Connections to other chapters . . . 59

4 Evolution and Collapse: Game Playing in a ChangingWorld 61

4.1 My New Hampshire. . 61

4.2 Strategies and games. . 63

4.3 Iterated and evolutionary game playing .. . 68

4.4 Modeling the evolution of species and cultures . . 74

4.5 Implications for understanding collapse. . 80

5 Instability, Oscillation, and Feedback 85

5.1 Sharing an electric blanket and other challenges. . . 85

5.2 Primer on differential equations . . 91

5.3 Stable and unstable equilibriumpoints and related concepts . 97

5.4 The dynamics of interacting populations. . 100

5.5 Structural collapses and related processes. . 106

5.6 The science of trying to maintain control . . 112

5.7 The Chernobyl disaster  . . 115

6 Nonlinearity: Invitation to Chaos and Catastrophe 121

6.1 The elephant’s toenail . . 121

6.2 Local linearity . . 122

6.3 Bifurcations, tipping points, and catastrophes . . . 127

6.4 Hysteresis: where there may be no simple turning back . . 134

6.5 Chaos: beginning with a butterfly . . 138

7 It’s All About Networks 145

7.1 How’s your networking? . . 145

7.2 Network fundamentals . . 147

7.3 Important variations in network macrostructure . . 152

7.4 Unexpected network crashes. . 157

7.5 Interactive dynamics across networks  . . 161

7.6 Spreading processes through networks . . 165

7.7 A surprising game on a network  . . 167

7.8 Networks in an evolutionary context  . . 169

8 Putting It All Together: Looking at Collapse Phenomena in “6-D” 173

8.1 A quick review  . . 173

8.2 The utility of multiple perspectives in understanding the risk of collapse . 175

8.3 Where to go from here: the modern field of complexity theory . . 186

References 189

Index 201

About the Author 207

Out of the Labyrinth: Setting Mathematics Free

 Ellen Kaplan e Robert Kaplan

Bloomsbury Press |  2014 | 256 páginas | rar - epub | 18,3 Mb

link (password : matav)

edição de 2006

Who hasn’t feared the math Minotaur in its labyrinth of abstractions? The subject can seem convoluted and forbidding. Yet to do mathematics is to wrestle with “accessible mysteries”—and Out of the Labyrinth shows how exhilarating the challenge can be. Robert and Ellen Kaplan are founders of the Math Circle, a pioneering learning program begun at Harvard in 1994 and now spreading around the world. In their classrooms students ages six to sixty have discovered mathematics as the highest form of intellectual play, while exploring topics that range from Roman numerals to quantum mechanics. 
The Kaplans reveal the secrets of their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics. Stocked with puzzles, colorful anecdotes, and insights from the authors’ own teaching experience, Out of the Labyrinth is both an engaging and practical guide for parents and educators, and a treasure chest of mathematical discoveries. For any reader who has felt the excitement of mathematical discovery—or tried to convey it to someone else—this volume will be a delightful and valued companion.

Contents
Chapter One: A Glimpse Inside
Chapter Two: Cod Liver Oil
Chapter Three: The Myth of Talent
Chapter Four: Making Your Hats
1. Holding On
Stubbornness
Orneriness
A High Threshold of Frustration
The Jump-Cut Mind
Putting On Hold
2. Taking Apart
Method vs. Approach
Atomizing
Attention Without Tension
Precision
Rotating the Diamond
Breaking Apart
Pursuing the Possible
3. Putting Together
Play
Stubbornness Revisited
The Riddle of the Pygmy Shrew
Analogy
Holding Hypotheses Like Birds
Experimental Fervor
The Architectural Instinct
The Conductor
Chapter Five: The Great Barrier Reef
Language: Symbols
Language: Equations
Language: Third Person Remote
The Buddha, the Bodhisattva, and the Bo
Climbing a Tall Building
Alienation
Diamond Hard
Who Cares?
Chapter Six: How Math Has Been Taught
Behind the Phenomena
The Teaching Wars
Cookbooks, Song-Lines, and Games
Ancestral Voices Calling for Reform
Anticurriculum
The Curate’s Egg
Russian Math Circles
Chapter Seven: How Mathematicians Actually Work
hapter Eight: The Math Circle
Ends
Beginnings
The Students
The Leaders
The Math
Connecting
Intuition Grows
A Proof Takes Shape
Looking Leads to Seeing
Competition
Chapter Nine: Filling in the Details
Where’s the Kit?
Math Itself
Courses
Sample Outline of a Middle Course: Interesting Points in Triangles
Piecemeal Advice
Perilous Turnings and Pivotal Moments
From a Journal
What’s the Way Forward?
The Summer Institute
To Take with You
Acknowledgments
Footnotes
Appendix: Thoughts of a Young Teacher
A Note on Our Pronouns

Mathematical cranks

Underwood Dudley 

The Mathematical Association of America | 1992 | páginas | djvu |4,6  Mb

link

A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem); people who pray in matrices; people who find the American Revolution ruled by the number 57; people who have in common eccentric mathematical views, some mild (thinking we should count by 12s instead of 10s), some bizarre (thinking that second-order differential equations will solve all problems of economics, politics and philosophy). This is a truly unique book. It is written with wit and style and is a part of folk mathematics.

Contents
Introduction v 
Alphabet, Application of Pyramid Height to the 1 
American Revolution, The Role of 57 in the 4 
Applied Mathematics 9 
Base for the Number System, The Best - 20 
Bitterness, Cranks' 32 
Calculus, Celestial 38 
Cantor's Diagonal Process 40 
Congressional Record, Mathematics in the 46 
Constant Society, The 50 
Consultation, Lack of, of Cranks with Experts 53 
Crank, Case Study of a 55. 
Crank, The Making of a 67 
Deduction, The Joy of 78 
Duplication of the Cube 86 
Ellipse, Circumference of an 93 
Encouraging Cranks, The Folly of 97 
Equations, Solving 102 
Fermat's Last Theorem 105 
Fermat's Little Theorem 135 
Fifth Postulate, Euclid's 137 
Four-Color Theorem, The ." 159 
Godel's Theorem 167 
Goldbach Conjecture, The 171 
Greed 179 
Incomprehensibility of Crank's Works 182 
Infinity, Difficulties with 184 
Insanity 189 
Legislating Pi 192 
Linear Programming, Conspiracy Involving 198 
Magic Squares 200 
Mail, Crank 205 
Megalomania 208 
Money to be Made in Mathematics, Lack of 222 
Nines, Casting Out 226 
Nonagons, Regular 231 
Notation, Nonstandard 235 
Number Theory, The Lure of 239 
Perfect Numbers 242 
Phi 245 
Prayer, Matrix 251 
Primes, The Secret of the 254 
Primes, Twin, Existence of Infinitely Many 256 
Prolificity, Crank's 260 
Puzzle, A 269 
Pythagoreans, Neo- 271 
Pythagoreans, The Mystery of the 274 
Quadrature of the Circle 279 
Set Theory 322 
Signs, The Rule of 324 
Solution to a Puzzle 330 
Sphere, Philosophy of the 331 
Statistics, Parameter Estimation in 334 
Taxonomy, Mathematical 337 
Time, Wasted ....! 339 
Topology, Applied 341 
Trisection of the Angle 342 
Van der Pol's Equation 349 
Notes 353 

Index 363

Poincaré's prize : the hundred-year quest to solve one of math's greatest puzzles

George Szpiro

Plume | 2007 | 321 páginas | rar - pdf | 1,6 Mb

link (password: matav)

The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it

In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.
Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. 

Contents
Chapter 1: Fit for a King 1
Grigori Perelman’s unprecedented refusal of a Fields Medal for solving one of the greatest problems of our age. The king waits in vain.
Chapter 2: What Flies Know and Ants Don’t 8
The importance of dimensions for Christopher Columbus and for bugs.
Chapter 3: The Forensic Engineer 15
The life of Henri Poincaré, in particular his investigation of a tragedy in a coal mine.
Chapter 4: An Oscar for the Best Script 33
Poincaré’s prizewinning theory of the solar system’s stability...and the scandal.
Chapter 5: Geometry Without Euclid 53 Topology; how this mathematical discipline has developed since Euler.
Chapter 6 : From Copenhagen and Hamburg to Black Mountain, North Carolina 75
Poincaré’s first, incorrect attempt to prove the conjecture...and the parts he got right.
Chapter 7 : What the Conjecture Is Really All About 95
Imaging things that are unimaginable.
Chapter 8 : Dead Ends and a Mysterious Disease 112
Around the world with three-dimensional spheres.
Chapter 9 : Voyage to Higher Dimensions 142
A rock-collecting yippie amazes the world.
Chapter 10 : Inquisition—West Coast Style 172
How other hopefuls ended up with egg on their faces.
Chapter 11 : Watching Things Go “Pop” 186
Richard Hamilton gets going with the Ricci flow . . . and then gets stuck.
Chapter 12 : The Cigar Surgeon 205
The proof lands on the Internet. Swooping up Poincaré, Thurston, and Hamilton. History is made.
Chapter 13 : The Gang of Four, plus Two 226
Vetting the proof, a math professor pushes his protégés into the limelight.
Chapter 14 : The Prize 247
The minor matter of a million dollars. Does money motivate math?
Notes 263
Bibliography 285
Acknowledgments 295
Index 297

Outros livros do mesmo autor:

Numbers rule : the vexing mathematics of democracy, from Plato to the present por George Szpiro Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2010.

The secret life of numbers : 50 easy pieces on how mathematicians work and think por George Szpiro Idioma: Inglês   Editora: Washington, D.C. : Joseph Henry Press, ©2006.

The Art of the Infinite: Our Lost Language of Numbers

Robert Kaplan e Ellen Kaplan


Penguin | 2004 | 332 páginas | 

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It is easy to be wary of mathematics - but as this book shows, drawing on science, literature and philosophy, its patterns are evrywhere. In witty and eloquent prose, Robert and Ellen Kaplan take mathematics back to its estranged audience, bringing understanding and clarity to a traditionally difficult subject, and revealing the beauty behind the equations. Only by letting loose our curiosity can we learn to appreciate the wonder that can be found in mathematics - an 'art' invented by humans, which is also timeless.

Contents
Acknowledgements
An Invitation
Chapter one Time and the Mind
Chapter two How Do We Hold These Truths?
Chapter Three Designs on a locked Chest
Interlude The Infinite and the Indefinite
Chapter Four Skipping Stones
Chapter Five Euclid Alone
Interlude Longing and the Infinite
Chapter Six The eagle of algebra
Chapter Seven Into the Highlands
Interlude The Infinite and the unknown
Chapter Eight Back of Beyond
Chapter Nine The abyss
Appendix
Bibliography
Index

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Outros livros dos mesmos autores:

Hidden harmonies : the lives and times of the Pythagorean theorem por Robert Kaplan; Ellen Kaplan Idioma: Inglês   Editora: New York : Bloomsbury Press, 2011.

Out of the labyrinth : setting mathematics free por Robert Kaplan; Ellen Kaplan Idioma: Inglês   Editora: Oxford ; New York : Oxford University Press, 2007.

The art of the infinite : the pleasures of mathematics por Robert Kaplan; Ellen Kaplan Idioma: Inglês   Editora: Oxford ; New York : Oxford University Press, ©2003.

The nothing that is : a natural history of zero por Robert Kaplan Idioma: Inglês   Editora: Oxford ; New York : Oxford University Press, 2000.