More Fallacies, Flaws & Flimflam

(Spectrum) 

 Edward Barbeau

The Mathematical Association of America | 2013 | páginas | rar - pdf |966 kb

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Mistakes in mathematical reasoning can range from outlandish blunders to deep and subtle oversights that evade even the most watchful eye. This book represents the second collection of such errors to be compiled by Edward Barbeau. Like Barbeau's previous book, Mathematical Fallacies, Flaws and Flimflam, material is drawn from a variety of sources including the work of students, textbooks, the media, and even professional mathematicians. The errors presented here serve both to entertain, and to emphasize the need to subject even the most "obvious" assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. Each item is carefully analysed and the source of the error is exposed. All students and teachers of mathematics, from school to university level, will find this book both enlightening and entertaining.

Contents
Arithmetic
School algebra
Geometry
Limits, sequences and series
Differential calculus
Integral calculus
Combinatorics
Probability and statistics
Complex analysis
Linear and modern algebra
Miscellaneous

Outros livros do mesmo autor:

Challenging mathematics in and beyond the classroom : the 16th ICMI study por Edward Barbeau; P J Taylor; International Commission on Mathematical Instruction.; Idioma: Inglês   Editora: New York ; London : Springer, ©2009.

Mathematical fallacies, flaws, and flimflam por Edward Barbeau Idioma: Inglês   Editora: Washington, DC : Mathematical Association of America, ©2000.

Five hundred mathematical challenges por Edward Barbeau; Murray S Klamkin; W O J Moser Idioma: Inglês   Editora: [Washington, DC] : Mathematical Association of America, ©1995.

Elementary Mathematics in Context

Charlene Sheets

Information Age Publishing | 2013 | 123 páginas | rar - pdf | 4,7 Mb

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These materials were developed, in part, by a grant from the federally-funded Mathematics and Science Partnership through the Center for STEM Education. Some of the activities were adapted from the National Council of Teachers of Mathematics Illuminations, the National Library of Virtual Manipulatives, Hands-On Math Projects with Real Applications by Judith A. Muschla and Gary R. Muschla, Learning Math with Calculators: Activities for Grades 3-8 by Len Sparrow and Paul Swan, and Mathematical Ideas by Charles D. Miller, Vern E. Heeren and John Hornsby. 

CONTENTS
GRADE K
Investigations, Unit 3 - What Comes Next? Patterns and Functions .... 1
Investigations, Unit 6 - How Many Do You Have? Addition, Subtraction and the Number System .... 9
GRADE 1
Investigations, Unit 7 - Color, Shape and Number Patterns/Patterns and Functions .13
Investigations, Unit 8 - Twos, Fives, and Tens: Addition, Subtraction and the Number System .19
GRADE 2
Investigations, Unit 5 - How Many Floors? How Many Rooms? Patterns, Functions and Change .31
Investigations, Unit 7 - Parts of a Whole, Parts of a Group/Fractions ..37
GRADE 3
Investigations, Unit 6 - Stories, Tables and Graphs/Patterns, Functions and Change..41
Investigations, Unit 8 - How Many Hundreds? How Many Miles? Addition, Subtraction and the Number System ...57
GRADE 4
Investigations, Unit 4 - Landmarks and Large Numbers: Addition, Subtraction and the Number System .. 63
Investigations, Unit 9 - Penny Jars And Plant Growth: Patterns, Functions and Change .67
GRADE 5
Investigations, Unit 4 - What’s that Portion? Fractions and Percent . 97
Investigations, Unit 5 - Growth Patterns—Patterns, Functions and Change..101

Euclid-The Creation of Mathematics

Benno Artmann 

Springer | 2013 -  reprint of the original 1st ed. 1999 edition | 350 páginas | 26 Mb

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The philosopher Immanuel Kant writes in the popular introduction to his philosophy: "There is no single book about metaphysics like we have in mathematics. If you want to know what mathematics is, just look at Euclid's Elements." (Prolegomena Paragraph 4) Even if the material covered by Euclid may be considered elementary for the most part, the way in which he presents essential features of mathematics in a much more general sense, has set the standards for more than 2000 years. He displays the axiomatic foundation of a mathematical theory and its conscious development towards the solution of a specific problem. We see how abstraction works and how it enforces the strictly deductive presentation of a theory. We learn what creative definitions are and how the conceptual grasp leads to the classification of the relevant objects. For each of Euclid's thirteen Books, the author has given a general description of the contents and structure of the Book, plus one or two sample proofs. In an appendix, the reader will find items of general interest for mathematics, such as the question of parallels, squaring the circle, problem and theory, what rigour is, the history of the platonic polyhedra, irrationals, the process of generalization, and more. This is a book for all lovers of mathematics with a solid background in high school geometry, from teachers and students to university professors. It is an attempt to understand the nature of mathematics from its most important early source.

Content: 
Front Matter....Pages i-xvi
General Historical Remarks....Pages 1-2
The Contents of the Elements....Pages 3-10
The Origin of Mathematics 1: The Testimony of Eudemus....Pages 11-16
Euclid Book I: Basic Geometry....Pages 17-46
The Origin of Mathematics 2: Parallels and Axioms....Pages 47-50
The Origin of Mathematics 3: Pythagoras of Samos....Pages 51-60
Euclid Book II: The Geometry of Rectangles....Pages 61-71
The Origin of Mathematics 4: Squaring the Circle....Pages 73-78
Euclid Book III: About the Circle....Pages 79-91
The Origin of Mathematics 5: Problems and Theories....Pages 93-95
Euclid Book IV: Regular Polygons....Pages 97-107
The Origin of Mathematics 6: The Birth of Rigor....Pages 109-111
The Origin of Mathematics 7: Polygons After Euclid....Pages 113-120
Euclid Book V: The General Theory of Proportions....Pages 121-134
Euclid Book VI: Similarity Geometry....Pages 135-149
The Origin of Mathematics 8: Be Wise, Generalize....Pages 151-159
Euclid Book VII: Basic Arithmetic....Pages 161-182
The Origin of Mathematics 9: Nicomachus and Diophantus....Pages 183-191
Euclid Book VIII: Numbers in Continued Proportion, the Geometry of Numbers..
Pages 193-201
The Origin of Mathematics 10: Tools and Theorems....Pages 203-206
Euclid Book IX: Miscellaneous Topics from Arithmetic....Pages 207-211
The Origin of Mathematics 11: Math Is Beautiful....Pages 213-221
Euclid Book X: Incommensurable Magnitudes....Pages 223-228
The Origin of Mathematics 12: Incommensurability and Irrationality....Pages 229-253
Euclid Book XI: Solid Geometry....Pages 255-265
The Origin of Mathematics 13: The Role of Definitions....Pages 267-269
Euclid Book XII: Volumes by Limits....Pages 271-278
The Origin of Mathematics 14: The Taming of the Infinite....Pages 279-282
Euclid Book XIII: Regular Polyhedra....Pages 283-302
The Origin of Mathematics 15: Symmetry Through the Ages....Pages 303-316
The Origin of Mathematics 16: The Origin of the Elements....Pages 317-320

The New York Times Book of Mathematics

Gina Kolata e Paul Hoffman 

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

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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

Plato and Pythagoreanism

Phillip Sidney Horky 

 Oxford University Press | 2013 | 328 páginas | rar - pdf | 2,1 Mb

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Was Plato a Pythagorean? Plato's students and earliest critics thought so, but scholars since the nineteenth century have been more skeptical. With this probing study, Phillip Sidney Horky argues that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, exercised a decisive influence on fundamental aspects of Plato's philosophy. The progenitor of mathematical Pythagoreanism was the infamous Pythagorean heretic and political revolutionary Hippasus of Metapontum, a student of Pythagoras who is credited with experiments in harmonics that led to innovations in mathematics. The innovations of Hippasus and other mathematical Pythagoreans, including Empedocles of Agrigentum, Epicharmus of Syracuse, Philolaus of Croton, and Archytas of Tarentum, presented philosophers like Plato with novel ways to reconcile empirical knowledge with abstract mathematical theories. Plato and Pythagoreanism demonstrates how mathematical Pythagoreanism established many of the fundamental philosophical questions Plato dealt with in his central dialogues, including Cratylus, Phaedo, Republic, Timaeus, and Philebus. In the process, it also illuminates the historical significance of the mathematical Pythagoreans, a group whose influence on the development of philosophical and scientific methods has been obscured since late antiquity. The picture that results is one in which Plato inherits mathematical Pythagorean method only to transform it into a powerful philosophical argument about the essential relationships between the cosmos and the human being.

CONTENTS
Preface ix
Acknowledgments xv
Abbreviations xix
1. Aristotle on Mathematical Pythagoreanism in the Fourth Century bce 3
2. Hippasus of Metapontum and Mathematical Pythagoreanism 37
3 . Exoterism and the History of Pythagorean Politics 85
4 . Mathematical Pythagoreanism and Plato’s Cratylus 125
5 . What Is Wisest? Mathematical Pythagoreanism and Plato’s Phaedo 167
6 . Th e Method of the Gods: Mathematical Pythagoreanism and Discovery 201
Afterword 261
Bibliography 265
Index Locorum 281

General Index 295

Basic Math & Pre-Algebra Workbook

Mark Zegarelli 

For Dummies | 2014 -2ª edição | 315 Páginas | rar - PDF | 4,6 Mb

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1ª edição - 2012/2007

Basic Math and Pre-Algebra Workbook For Dummies, 2nd Edition helps take the guesswork out of solving math equations and will have you unraveling the mystery of FOIL in no time. Whether you need to brush up on the basics of addition, subtraction, multiplication, and division or you’re ready to tackle algebraic expressions and equations, this handy workbook will demystify math so you can get back to having fun in math class.

• Properly use negative numbers, units, inequalities, exponents, square roots, and absolute value

• Round numbers and estimate answers

• Solve problems with fractions, decimals, and percentages

• Navigate basic geometry

• Complete algebraic expressions and equations

• Understand statistics and sets

• Sample questions with step-by-step explanation

• Answers to practice problems so you can check your work

Let Basic Math and Pre-Algebra Workbook For Dummies, 2nd Edition take the guessing out of math and help you discover your problem solving potential.

Contents at a Glance

Introduction...... 1

Part I: Getting Started with Basic Math and Pre-Algebra.... 5

Chapter 1: We’ve Got Your Numbers......... 7

Chapter 2: Smooth Operators: Working with the Big Four Operations.. 23

Chapter 3: Getting Down with Negative Numbers..... 37

Chapter 4: It’s Just an Expression...... 49

Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples... 69

PartII: Slicing Things Up: Fractions, Decimals, and Percents...... 89

Chapter 6: Fractions Are a Piece of Cake........ 91

Chapter 7: Fractions and the Big Four...... 109

Chapter 8: Getting to the Point with Decimals...... 143

Chapter 9: Playing the Percentages.... 165

Part III: A Giant Step Forward: Intermediate Topics...... 177

Chapter 10: Seeking a Higher Power through Scientific Notation... 179

Chapter 11: Weighty Questions on Weights and Measures. 189

Chapter 12: Shaping Up with Geometry.. 203

Chapter 13: Getting Graphic: Xy-Graphs...... 223

Part IV: The X Factor: Introducing Algebra..... 235

Chapter 14: Expressing Yourself with Algebraic Expressions... 237

Chapter 15: Finding the Right Balance: Solving Algebraic Equations.....257

Part V: The Part of Tens...... 273

Chapter 16: Ten Alternative Numeral and Number Systems.... 275

Chapter 17: Ten Curious Types of Numbers..... 283

Index....... 289

The beginnings of Greek mathematics

A. Szabó e A.M. Ungar

Springer | 1978 | 363 páginas | pdf | 16 Mb

link

Table of contents : 
Title......Page 1
Contents......Page 2
Chronological Table......Page 4
Introduction......Page 5
1.1 Current views of the theory's development......Page 14
1.2 The concept of 'Dynamis'......Page 16
1.3 The mathematic part of the 'Theaetetus'......Page 18
1.4 The usage and chronology of 'Dynamis'......Page 20
1.5 'Tetragonismos'......Page 21
1.6 The mean proportional......Page 22
1.7 The mathematics lecture delivered by Theodorus......Page 25
1.8. The mathematical discoveries of Plato's Theaethetus......Page 28
1.9 The 'independence' of Theaetetus......Page 31
1.10 A glance at some rival theories......Page 33
1.11 The so called 'Theaetetus problem'......Page 35
1.12 The discovery of incommensurability......Page 40
1.13 The problem of doubling the square......Page 43
1.14 Doubling the square and the mean proportional......Page 46
2.1 Introduction......Page 47
2.2 A survey of the most important terms......Page 49
2.3 Consonances and intervals......Page 52
B. Diastema as interval......Page 53
2.4 The diastema between two numbers......Page 55
2.5 A digression on the theory of music......Page 57
2.6 End points and intervals pictured as straight lines......Page 60
2.7 'Diplasion', 'Hemiolion', 'Epitriton'......Page 62
2.8 The euclidean algorithm......Page 65
2.9 The canon......Page 66
2.10 Arithmetical operations on the canon......Page 68
2.12 'Aναλογια as 'geometric proportion'......Page 70
2.13 'Aνάλογον......Page 72
2.14 The preposition άνά......Page 73
2.15 The elliptic expression άνά λόγον......Page 75
2.16 The subsequent history of ανάλογον as a mathematical term......Page 76
2.17 Out of the canon and musical means......Page 78
2.18 The creation of the mathematical concept of λόγος......Page 81
2.19 A digression on the history of the word λόγος......Page 82
2.20 The appication of the theory of proportions to arithmetic and geometry..Page 83
2.21 The mean proportional in music, arithmetic and geometry......Page 85
2.22 The construction of the mean proportional......Page 86
2.23 Conclusion......Page 88
3.1 'Proof' in Greek mathematics......Page 90
3.2 The proof of incommensurability......Page 97
3.3 The origin of anti-empiricism and indirect proof......Page 106
3.4 Euclid's foundations......Page 108
3.5 Aristotle and foundations of mathematics......Page 111
3.6 'Hypotheseis'......Page 114
3.7 The 'assumptions' in dialectic......Page 116
3.8 How 'hypotheseis' were used......Page 117
3.9 'Hypotheseis' and the method of indirect proof......Page 119
3.10 A question of priority......Page 120
3.11 Zeno, the inventor of dialectic......Page 122
3.12 Plato and the Eleatics......Page 123
3.13 'Hypotheseis' and the foundations of mathematics......Page 124
3.14 The definition of 'Unit'......Page 126
3.15 Arithmetic and the teaching of the Eleatics......Page 128
3.16 The divisibility of numbers......Page 130
3.17 The problem of the 'aithemata'......Page 132
3.18 Euclid's postulates......Page 133
3.19 The construction of oenopides......Page 134
3.20 The first three postulates in the 'Elements'......Page 136
3.21 The 'Koinai Ennoiai'......Page 138
3.22 The word άξιωμα......Page 139
3.23 Plato's όμολογήματα and Euclid's άξιώματα......Page 141
3.24 "The whole is greater than the part"......Page 143
3.25 A complex of axioms......Page 147
3.26 The difference between postulates and axioms......Page 149
3.27 Arithmetic and geometry......Page 150
3.28 The science of space......Page 151
3.29 The foundations of geometry......Page 154
3.30 A reconsideration of some problems relating to early greek mathematics......Page 156
Postscript......Page 163
1. The prevailing view......Page 164
3. Elements of a pythagorean theory about the areas of parallelograms......Page 165
4. How to find a square with the same area as a given rectangle......Page 171
5. Conclusion......Page 174