Pythagoras: His Life and Teachings

 Thomas Stanley, James Wasserman, J. Daniel Gunther e Manly P. Hall

 Ibis Press | 2010 | 352 páginas | epub | 2,5 Mb

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The timeless brilliance of this exhaustive survey of the best classical writers of antiquity on Pythagoras was first published in 1687 in Thomas Stanley's massive tome, The History of Philosophy. It remains as contemporary today as it was over three hundred years ago. The text of the 1687 book has been reset and modernized to make it more accessible to the modern reader. Spelling has been regularized, obsolete words not found in a modern dictionary have been replaced, and contemporary conventions of punctuation have been used. Biographical sketches of Thomas Stanley and Pythagoras by Manly Palmer Hall, founder of the Philosophical Research Society, have been included, along with a profound overview of Pythagorean philosophy by Platonic scholar Dr. Henry L. Drake. The extensive Greek language references throughout the text have been corrected and contextualized, and reset in a modern Greek font. Each quotation has been verified with the source document in Greek. An extensive annotated appendix of these classical sources is included. A complete bibliography details all the reference works utilized, and a small Glossary defines a number of terms, especially those from musical theory, which may be unfamiliar to the non-technical reader.

Contents
Foreword by James Wasserman and J. Daniel Gunther
Preface by Manly P. Hall
Introduction by Dr. Henry L. Drake
PART ONE: THE LIFE OF PYTHAGORAS
1. The Country, Parents, and Time of Pythagoras
2. His First Education and Masters
3. How He Traveled to Phoenicia
4. How He Traveled to Egypt
5. How He Went to Babylon
6. How He Returned to Samos
7. Travels to Delos, Delphi, Crete, and Sparta
8. How He Went to Olympia and Phlius
9. How He Lived at Samos
10. His Voyage to Italy
11. His Arrival at Crotona
12. His Oration to the Young Men
13. His Oration to the Senators
14. His Oration to the Boys
15. His Oration to the Women
16. His Institution of a Sect in Private and Public
17. His Authority in Civil Affairs
18. Wonders Related of Him
19. His Death
20. His Person and Virtues
21. His Wife, Children, and Servants
2. His Writings
23. His Disciples
24. The Succession of His School
PART TWO: DISCIPLINES AND DOCTRINES OF THE PYTHAGOREANS
1. The Great Authority and Esteem of Pythagoras
2. The Two Sorts of Auditors
3. Purificative Institution by Sufferings
4. Silence
5. Abstinence, Temperance, and Other Ways of Purification
6. Community of Estates
7. Admission or Rejection
8. Distinction
9. How They Disposed the Day
10. How They Examined Their Actions
11. Secrecy
PART THREE: THE DOCTRINE OF PYTHAGORAS
Section I. Mathematical Sciences
The Mathematical Sciences Preparative to Philosophy
Arithmetic
1. Number Its Kinds: Intellectual
2. The Other Kind of Number: Sciential
3. The Two Kinds of Sciential Number
4. Symbolic Numbers
5. The Monad
6. The Duad
7. The Triad
8. The Tetrad
9. The Pentad
10. The Hexad
11. The Heptad
12. The Ogdoad
13. The Ennead
14. The Decad
15. Divination by Numbers
Music
1. Voice, Its Kinds
2. First Music in the Planets
3. The Octochord
4. The Arithmetical Proportions of Harmony
5. The Division of the Diapason
6. The Cannon of the Monochord
7. Institution by Music
8. Medicine by Music
Geometry
1. Of a Point, Line, Superficies and Solid
2. Propositions
3. How He Determined the Stature of Hercules
Astronomy
1. The System of the Spheres
2. The Motions of the Planets
3. The Intervals and Harmony of the Spheres
4. Of the Planet Venus
Section II: Philosophy
Philosophy: Its Name, Definition, Parts, Method
Practical Philosophy: Its Parts; and First of Education
1. Institution, Silence, Abstinence
2. Fortitude
3. Temperance and Continence
4. Sagacity and Wisdom
Of Politics: The Other Part of Practical Philosophy
1. Common Conversation
2. Friendship
3. Worship of the Gods
4. Piety to the Dead
5. Reverence of Parents, and Obedience to the Law
6. Lawmaking
Theoretical Philosophy: Its Parts
1. Of the Supreme God
2. Of Gods, Daemons, Heroes
3. Of Fate and Fortune
4. Divination
Physic
1. Principles
2. Of the World
3. Of the Superior or Aetherial Parts of the World
Of the Sublunary Parts of the World
1. Of Living, and Animate Creatures
2. Of the Generation of Animate Creatures
3. The Soul: Its Parts, and First of the Irrational Part
4. Of the Rational Part of the Soul: The Mind
5. Of the Transmigration of the Soul
6. The Separate Life of the Soul
Medicine
1. Dietetics
2. Therapeutic
Section III. Symbols
1. Pythagoras: His Symbolic Way of Teaching
2. The Symbols of Pythagoras According to Iamblichus
3. Explication of the Pythagorean Symbols by Iamblichus
4. The Same Symbols Explained by Others
5. Other Symbols
6. The Golden Verses of Pythagoras
PART FOUR: PYTHAGOREAN COMMENTATORS
Of the Soul of the World by Timaeus the Locrian
The Doctrine of Pythagoras by John Reuchlin
1. Of Pythagoras: His Way of Teaching,
2. The Triple Word
3. The Supreme World
4. The Intelligible World
5. The Sensible World
6. The State of the Soul after Death
7. Of the Pythagorean Transmigration
Glossary
Endnotes
Additional Notes to the Text by J. Daniel Gunther
Bibliography

Thabit ibn Qurra, Science and Philosophy in Ninth-Century Baghdad

Roshdi Rashed

Walter de Gruyter | 2009 | 801 páginas | pdf | 9 Mb

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Thabit ibn Qurra (826-901) was one of history´s most original thinkers and displayed expertise in the most difficult disciplines of this time: geometry, number theory, and astronomy as well as ontology, physics, and metaphysics. Approximately a dozen of this shorter mathematical and philosophical writings are collected in this volume. Critically edited with accompanying commentary, these writings show how Thabit Ibn Qurra developed and reconceived the intellectual inheritance of ancient Greece in all areas of knowledge.

Contents
VOLUME 1
SOMMAIRE
Roshdi RASHED : Preface V
INTRODUCTION
Roshdi RASHED: Thabit ibn Qurra, Scholar and Philosopher (826-901) 3
Roshdi RASHED: Thabit ibn Qurra : From Harran to Baghdad 15
CHAPITRE I : THEORIE DES PARALLELES
Roshdi RASHED et Christian HOUZEL : Thabit ibn Qurra et la theorie des paralleles 27
Textes et traduction:
1. Si on mene deux droites suivant deux angles inferieurs adeux droits, elles se rencontrent  42
2. Sur la demonstration du celebre postulat d'Euclide 64
CHAPITRE II : THEORIE DES NOMBRES ET ALGEBRE GEOMETRIQUE
Roshdi RASHED et Christian HOUZEL : Theorie des nombres amiables 77
Texte et traduction: Sur la determination des nombres amiables 90
Roshdi RASHED: Resolution geometrique des equations du second degre 153
Texte et traduction: Retablir les problemes de I'algebre par les demonstrations geometriques 160
CHAPITRE III : RECHERCHES GEOMETRIQUES
Roshdi RASHED : Thabit ibn Qurra et I' art de la mesure 173
Texte et traduction : Sur la mesure des figures planes et solides  178
Roshdi RASHED: Lemmes geometriques de Thabit ibn Qurra 211
Texte et traduction: Lemmes 240
Helene BELLOSTA: Le Livre des hypotheses 255
Texte et traduction : Le livre des hypotheses 270
Katia ASSELAH : Thabit ibn Qurra : Construction d'un polyedre semi-regulier aquatorze faces, 8 triangles equilateraux et 6 carres 317
Texte et traduction : Construction d'une figure solide aquatorze faces 324
CHAPITRE IV
LA FIGURE SECTEUR ET LA COMPOSITION DES RAPPORTS
Helene BELLOSTA : Le traite de Thabit ibn Qurra sur La figure secteur 335
Traduction: Sur la figure secteur 365
Pascal CROZET: Thabit ibn Qurra et la composition des rapports 391
Texte et traduction: Livre sur la composition des rapports 428
Eberhard KNOBLOCH: La traduction latine du livre de Thabit ibn Qurra sur la figure secteur 537
Texte et traduction: Le livre sur la figure secteur 554
CHAPITRE V : COSMOLOGIE ET METAPHYSIQUE
Regis MORELON : The Astronomy of Thabit ibn Qurra 601
Marwan RASHED: Thabit ibn Qurra sur l'existence et l'infini : les Reponses aux questions posees par Ibn Usayyid 619
Texte et traduction : Questions posees aThabit ibn Qurra deJarran 625
Commentaire 646

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.

The History of Mathematics: A Very Short Introduction

Jacqueline Stedall

Oxford University Press | 2012 | 144 páginas | rar -epub |3,34 Mb

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This Very Short Introduction explores the rich historical and cultural diversity of mathematical practice, ranging from the distant past to the present. Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.

Contents 
Acknowledgements 
List of illustrations 
Introduction 
1 Mathematics: myth and history 
2 What is mathematics and who is a mathematician? 
3 How are mathematical ideas disseminated? 
4 Learning mathematics 
5 Mathematical livelihoods 
6 Getting inside mathematics 
7 The evolving historiography of mathematics

30 Mathematics Lessons Using the TI-10

(Graphing Calculator Strategies) 

 Pamela Dase 

Shell Education | 2009 | 250 páginas | rar - pdf | 2,1 Mb

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This book is designed for grades K-2 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-10 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data analysis and probability. 

A Guide to Groups, Rings, and Fields

Fernando Gouvêa

 Mathematical Association of America | 2012 | 328 páginas | rar - pdf |1,44 Mb

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This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs. Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.

Contents
Preface;
A guide to this guide;
1. Algebra: classical, modern, and ultramodern;
2. Categories;
3. Algebraic structures;
4. Groups and their representations;
5. Rings and modules;
6. Fields and skew fields;
Bibliography;
Index of notations;
Index

What Primary Teachers Should Know About Maths

 

Aileen Duncan

Hodder Education | 1996 - 2ª edição | 216 páginas | rar - pdf | 22,3 Mb

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This title offers support to those involved in teaching primary maths. This edition has been fully updated to accord with the new National Curriculum. Its question-and-answer format allows specific problem areas to be easily located. It explains unfamiliar mathematical terms and includes sample lesson plans.
Contents

Introduction 4
Section One —Aspects of mathematics

1 Introduction 6
2 About numbers 8
Whole numbers - cardinality, ordinality, counting; Whole numbers - place value ; Conservation ; Negative numbers ; Common fractions ; Decimal fractions ; Percentages 
3 Using numbers 31
Addition ; Subtraction ; Multiplication ; Division ; Number patterns ; Averages ; Probability ; Ratio ; Algebra - equations ; Money 
4 Measure 64
Length ; Area ; Weight ; Volume ; Time ; Scale
5 Shape, position and movement 88
Two-dimensional shapes: symmetry and tessellation; Triangles ; Quadrilaterals ; Circles ; 3D shapes; Lines ; Angles, compass points and bearings ; Networks and topology
6 Information handling 113
Pictorial representation ; Coordinates ; Graphs ; Databases and spreadsheets 126
Section Two - Teaching and learning7 Introduction 129
8 Focus on children listening and talking 130
Watching and listening to the teacher ; Talking with the teacher ; Talking with classmates; Devising and asking questions ; Reading
9 Focus on children doing and recording 144
Using resources ; Using a calculator ; Using a computer ; Playing a game; Writing practice examples;  Using a workcard, worksheet work/textbook; Recording mathematics; Problem solving 
Section Three - Sample lesson notes
10 Introduction 164
11 Lessons for 5 to 7-year-olds 165
12 Lessons for 7 to 11 -year-olds 181
Index 213