Nature and Numbers a mathematical photo shooting

Georg Glaeser

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

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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.

A Female Genius: How Ada Lovelace Started the Computer Age

James Essinger

Gibson Square | 2013 | 304 páginas | rar - epub | 1,45 Mb

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The daughter of Lord Byron, Ada was the visionary who recognised the true potential of Babbage's of cog-wheel computer, The Analytical Engine. She demonstrated to the world that computers wouldn't merely be adding machines, but that they would be able to think.

Contents
Preface
1. Poetic Beginnings
2. Lord Byron: A Scandalous Ancestry
3. Annabella: Anglo-Saxon Attitudes
4. The Manor of Parallelograms
5. The Art of Flying
6. Love
7. Silken Threads
8. When Ada Met Charles
9. The Thinking Machine
10. Kinship
11. Mad Scientist
12. A Window on the Future
13. The Jacquard Loom
14. A Mind with a View
15. Ada’s Offer to Babbage
16. The Enchantress of Number
17. A Horrible Death
18. Redemption
Afterword
Acknowledgement

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