Gödel, Escher, Bach: Una Eterna Trenza Dorada

 Douglas R. Hofstadter

Consejo nacional de ciencia - versão em castelhano | 1979 | 915 páginas | pdf | 44 Mb

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epub - 170 Mb - epubbud.com

versão em inglês

El Autor es Douglas R. Hofstadter y es un libro ganador del Premio Pulitzer. Aunque en la primera edición en español su titulo fue “Gödel, Escher, Bach: una eterna trenza dorada”, posteriormente fue cambiado por el actual.
El libro toma la forma de una interacción entre varias narrativas. Los capítulos principales se alternan con diálogos entre los personajes imaginarios, inspirados por la narración de Lewis Carroll Lo que le dijo la tortuga a Aquiles, que aparece en el libro. En éste, Aquiles y la tortuga discuten una paradoja relativa a los modus ponens. Hofstadter basa los otros diálogos en éste, presentando al cangrejo y a un genio, entre otros. Estas narrativas se sumergen con frecuencia en la autorreferencia y la metaficción.
Un diálogo particularmente significativo en el libro está ingeniosamente escrito en la forma de un canon en espejo, en el cual cada línea antes del punto medio corresponde a una línea idéntica pasado el punto medio, si bien la conversación da una sensación extraña debido al uso de frases comunes que pueden ser usadas como saludos o despedidas (“buen día”) y la colocación de las líneas que, bajo cercana inspección, dobla como una respuesta a una pregunta en la línea siguiente.
El libro fue considerado un tiempo como intraducible, dado que da gran énfasis en los así llamados “retruécanos estructurales”, como en el diálogo del canon en espejo, que se lee exactamente igual, oración por oración, tanto en forma normal como al revés, exceptuando el voilá del primer fragmento que es sustituido por viola en el segundo.
En este libro hay muchos campos tratados y es un libro “denso” que requiere varias relecturas y echar mano de la enciclopedia Internet para comprender ciertas partes, algunos de los campos que toca son:
* Metamatemática* Simetría* Inteligencia artificial* Sistema formal, Teoría de la computabilidad* Paradoja* Zen* Genética* Biología molecular* Lógica, Teoría de números* Tipografía y sintaxis* Cerebro, Mente y Cognición* Sintaxis vs. Semántica* Libre albedrío vs. Determinismo* Holismo vs. reduccionismo* El lenguaje de programación Lisp* Isomorfismos y significado* Capas yuxtapuestas de significado, contrapunto, semiótica, códigos* Autorreferencia, recursión, Bucles extraños* Auto-organización, sensación emergente de identidad: consciente (por Ej. “Yo soy una oración verdadera, y lo que declaro es que no puedo ser comprobado dentro de este sistema al que pertenezco” o “Yo soy verdadero, pero mi verdad transciende este universo”)

Sacred Geometry: Philosophy & Practice

 Robert Lawlor

Thames & Hudson | 1982 | 112 páginas | pdf | 17 Mb

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Art and Imagination: These large-format, gloriously-illustrated paperbacks cover Eastern and Western religion and philosophy, including myth and magic, alchemy and astrology. The distinguished authors bring a wealth of knowledge, visionary thinking and accessible writing to each intriguing subjecArt and Imagination: These large-format, gloriously-illustrated paperbacks cover Eastern and Western religion and philosophy, including myth and magic, alchemy and astrology. The distinguished authors bring a wealth of knowledge, visionary thinking and accessible writing to each intriguing subjec

An introduction to the geometry which, as modern science now confirms, underlies the structure of the universe.

The thinkers of ancient Egypt, Greece and India recognized that numbers governed much of what they saw in their world and hence provided an approach to its divine creator. Robert Lawlor sets out the system that determines the dimension and the form of both man-made and natural structures, from Gothic cathedrals to flowers, from music to the human body. By also involving the reader in practical experiments, he leads with ease from simple principles to a grasp of the logarithmic spiral, the Golden Proportion, the squaring of the circle and other ubiquitous ratios and proportions. 

Contents
Introduction 4
The Practice of Geometry 7
Sacred Geometry : Metaphor of Universal Order 16
The Primal Act: The Division of Unity 23
Workbook 1 : The Square Cut by its Diagonal; square root 2 25-27
Workbook 2: The square root 3 and the Vesica Piscis 32-33
Workbook 3: The square root 5 36-37
Alternation
Workbook 4: Alternation 4W1
Proportiorl andthe Golden Section
Workbook 5: The Golden Proportion 48-52
Gnomonic Expan~iona nd the Creation of Spirals
Workbook 6: Gnomonic spirals 67-70
The Squaring of the Circle
Workbook 7: Squaring the circle 7479
Mediation : Geometry becomes Music
Workbook 8: Geometry and Music 83-85
Anthropos I
The Genesis of Cosmic Volumes
Workbook 9: The Platonic Solids 98-1 02
Bibliography

Sources of Illustrations

A Guide to Complex Variables

(Dolciani Mathematical Expositions)

Steven G. Krantz

Mathematical Association of America | 2008 |202 páginas | 1 Mb

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This is a book about complex variables that gives the reader a quick and accessible introduction to the key topics. While the coverage is not comprehensive, it certainly gives the reader a solid grounding in this fundamental area. There are many figures and examples to illustrate the principal ideas, and the exposition is lively and inviting. An undergraduate wanting to have a first look at this subject or a graduate student preparing for the qualifying exams, will find this book to be a useful resource.


In addition to important ideas from the Cauchy theory, the book also include sthe Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping and dozens of other central topics.
Readers will find this book to be a useful companion to more exhaustive texts in the field. It is a valuable resource for mathematicians and non-mathematicians alike.

Table of Contents
Preface
1. The complex plane
2. Complex line integrals
3. Applications of the Cauchy theory
4. Isolated singularities and Laurent series
5. The argument principle
6. The geometric theory of holomorphic functions
7. Harmonic functions
8. Infinite series and products
9. Analytic continuation.

Teaching Young Children Mathematics

Janice Minetola, Robert G. Ziegenfuss e J. Kent Chrisman

Routledge | 2013 | 331 páginas | rar - pdf | 3 Mb

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Teaching Young Children Mathematics provides a comprehensive overview of mathematics instruction in the early childhood classroom. Taking into account family differences, language barriers, and the presence of special needs students in many classrooms throughout the U.S., this textbook situates best practices for mathematics instruction within the larger frameworks of federal and state standards as well as contemporary understandings of child development.

Key topics covered include: developmental information of conceptual understanding in mathematics from birth through 3rd grade, use of national and state standards in math, including the new Common Core State Standards, information for adapting ideas to meet special needs and English Language Learners, literacy connections in each chapter, ‘real-world’ connections to the content, and information for family connections to the content.

Imagine Math 2: Between Culture and Mathematics

Michele Emmer (Editor) 

Springer | 2013 | 262 páginas | PDF | 3,15 Mb


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Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms.  The new volume in the series “Imagine Math” is intended to contribute to grasping how much that is interesting and new is happening in the relationships between mathematics, imagination and culture.

The present book begins with the connections between mathematics, numbers, poetry and music, with the latest opera by Italian composer Claudio Ambrosini. Literature and narrative also play an important role here. There is cinema too, with the “erotic” mathematics films by Edward Frenkel, and the new short “Arithmétique “ by  Munari and Rovazzani. The section on applications of mathematics features a study of ants, as well as the refined forms and surfaces generated by algorithms used in the performances by Adrien Mondot and Claire Bardainne. Last but not least, in honour of the hundredth anniversary of his birth, a mathematical, literary and theatrical homage to Alan Turing, one of the outstanding figures of the twentieth century.

Contents

Introduction . . 1

Mathematics, Numbers and Music

The Fascination of Numbers, between Music and Poetry

Michele Emmer . . 5

The Solitude of Last Words

Claudio Ambrosini . . 11

Mathematics, Poetry and Literature

Godel’s Childhood and Other Algorithms

Vincenzo Della Mea . . 23

The Wild Number Problem: Math or Fiction?

Philibert Schogt . . 31

A Play at Dusk. Mathematics in Literature

Carlo Toffalori. . 39

Mathematics according to Italo Calvino

Gabriele Lolli . . 49

The Mathematical Mind - Iconography of a Tension

Paolo Pagli  . . 57

Mathematics and Film

Spatial Rhythms in Cinema between the Avant-Garde and Entertainment

Gian Piero Brunetta  . . 69

Lessons in Mathematics, at the Cinema

Michele Emmer  . . 83

Mathematics, Love, and Tattoos

Edward Frenkel . . 93

Arithmetique

Giovanni Munari. . . 101

Mathematics and Art

L’art du Trait est l’attrait de l’Art

Sophie Skaf  . . 107

Mathematics and Morphology

Morphogenesis and Dynamical Systems. A View Instantiated by a Performative Design Approach

Sara Franceschelli  . . 117

Empirical Evidence that the World Is Not a Computer

James W. McAllister  . . 127

Mathematics, Art and Music

Numeri Malefici (Evil Numbers): Homage to Fabio Mauri

Michele Emmer . . 139

From Pollock’s Summertime to Jacksontime

Davide Amodio . . 151

Mathematics as a Tool for the Composition of Jacksontime

Chiara de Fabritiis. . 161

Mathematics and Applications

Extracting Information from Chaos: a Case in Climatological Analysis

Francesco Bonghi, Roberto Ferretti  . . 173

On the Tangible Boundary between Real and Virtual

Andrien Mondot  . . 181

Fort Marghera and the French and Austrian Plans of Defence

Mauro Scroccaro . . 185

Mathematics and Ants

Myrmedrome: Simulating the Life of an Ant Colony

Simone Cacace, Emiliano Cristiani, Dario D’Eustacchio. . 201

Ants Searching for a Minimum

Maurizio Falcone. . 211

Mathematics and Marco

Exotic Spheres and John Milnor

Marco Abate. . 221

Cellular Automata: the Game of Life

Gian Marco Todesco . . 231

Homage to Alan Turing

Alan M. Turing (1912-1954)

Gabriele Lolli. . 247

Alan Turing and the Poisoned Apple

Massimo Vincenzi . . 255

International Mathematical Olympiads and Forty Supplementary Problems

(New Mathematical Library) 

Murray S. Klamkin

The Mathematical Association of America |1986 | 155 páginas | rar -pdf | 5 Mb

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A compilation of problems of arresting ingenuity given to high school students competing in the International Mathematical Olympiads

Contents
Editor’s Note
Preface
Olympiad Problems
Supplementary Problems
Solutions of Olympiad Problems
Olympiad 20,1978
Olympiad 21,1979
Olympiad 22,1981
Olympiad 23,1982
Olympiad 24,1983
Olympiad 25,1984
Olympiad 26,1985
Solutions of Supplementary Problems
Algebra
Number Theory
Plane Geometry
Solid Geometry
Geometric Inequalities
Inequalities
Combinatorics
Appendix A

Mathematics Curriculum in School Education

(Advances in Mathematics Education)

 Yeping Li e Glenda Lappan

Springer | 2014 | 651 páginas | rar - pdf | 8,8 Mb

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• Identifying what is important in mathematics for teaching and learning in different education systems;

• Understanding mathematics curriculum and its changes that are valued over time in different education systems;

• Identifying and analyzing effective curriculum practices;

• Probing effective infrastructure for curriculum development and implementation.

Mathematics curriculum, which is often a focus in education reforms, has not received extensive research attention until recently. Ongoing mathematics curriculum changes in many education systems call for further research and sharing of effective curriculum policies and practices that can help lead to the improvement of school education.

This book provides a unique international perspective on diverse curriculum issues and practices in different education systems, offering a comprehensive picture of various stages along curriculum transformation from the intended to the achieved, and showing how curriculum changes in various stages contribute to mathematics teaching and learning in different educational systems and cultural contexts.

The book is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including:

Mathematics Curriculum in School Education brings new insights into curriculum policies and practices to the international community of mathematics education, with 29 chapters and four section prefaces contributed by 56 scholars from 14 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, curriculum developers, and graduate students interested in learning about recent curriculum development, research, and practices in different education systems.

It will help readers to reflect on curriculum policies and practices in their own education systems, and also inspire them to identify and further explore new areas of curriculum research for improving mathematics teaching and learning.

Contents

Part I Introduction and Perspectives

Mathematics Curriculum in School Education: Advancing Research and Practice from an International Perspective .. . 3

Yeping Li and Glenda Lappan

Curriculum Design and Systemic Change . . 13

Hugh Burkhardt

Mathematics Curriculum Policies and Practices in the U.S.: The Common Core State Standards Initiative  . . 35

Barbara J. Reys

Reflections on Curricular Change. . 49

Alan H. Schoenfeld

Part II Curriculum and Policy

Mathematics Curriculum Policies: A Framework with Case Studies from Japan, Korea, and Singapore  . . 79

Khoon Yoong Wong, Masataka Koyama, and Kyeong-Hwa Lee

Decision Making in the Mathematics Curricula among the Chinese Mainland, Hong Kong, and Taiwan . . 93

Hak Ping Tam, Ngai-Ying Wong, Chi-Chung Lam, Yunpeng Ma, Lije Lu, and Yu-Jen Lu

Potential Impact of the Common Core Mathematics Standards on the American Curriculum . . 119

Hung-Hsi Wu

Brief Considerations on Educational Directives and Public Policies in Brazil Regarding Mathematics Education  . . 143

Antonio Vicente Marafioti Garnica

The Australian Curriculum: Mathematics—How Did it Come About? What Challenges Does it Present for Teachers and for the Teaching of Mathematics? . . 157

Max Stephens

Part III Curriculum Development and Analysis

Three Pillars of First Grade Mathematics, and Beyond  . . 183

Roger Howe

Forging New Opportunities for Problem Solving in Australian Mathematics Classrooms through the First National Mathematics Curriculum. . 209

Judy Anderson

Freedom of Design: The Multiple Faces of Subtraction in Dutch Primary School Textbooks . . 231

Marc van Zanten and Marja van den Heuvel-Panhuizen

Changes to the Korean Mathematics Curriculum: Expectations and Challenges . . 261

JeongSuk Pang

The Singapore Mathematics Curriculum Development—A Mixed Model Approach . . 279

Ngan Hoe Lee

School Mathematics Textbook Design and Development Practices in China . . 305

Yeping Li, Jianyue Zhang, and Tingting Ma

Part IV Curriculum, Teacher, and Teaching

Teachers as Participants in Textbook Development: The Integrated Mathematics Wiki-book Project . . . 333

Ruhama Even and Shai Olsher

Mathematics Teacher Development in the Context of District Managed Curriculum  . . 351

Mary Kay Stein, Julia Kaufman, and Miray Tekkumru Kisa

Curriculum, Teachers and Teaching: Experiences from Systemic and Local Curriculum Change in England  . . 377

Margaret Brown and Jeremy Hodgen

Teaching Mathematics Using Standards-Based and Traditional Curricula: A Case of Variable Ideas . . 391

Jinfa Cai, Bikai Nie, John C. Moyer, and Ning Wang

Supporting the Effective Implementation of a New Mathematics Curriculum: A Case Study of School-Based Lesson Study at a Japanese Public Elementary School . . 417

Akihiko Takahashi

Does Classroom Instruction Stick to Textbooks? A Case Study of Fraction Division . . 443

Rongjin Huang, Z. Ebrar Yetkiner Ozel, Yeping Li, and Rebecca V. Osborne

Part V Curriculum and Student Learning

Curriculum Intent, Teacher Professional Development and Student Learning in Numeracy . . 473

Vince Geiger, Merrilyn Goos, and Shelley Dole

The Impact of a Standards-Based Mathematics Curriculum on Classroom Instruction and Student Performance: The Case of Mathematics in Context . . 493

Mary C. Shafer

Curriculum and Achievement in Algebra 2: Influences of Textbooks and Teachers on Students’ Learning about Functions  . . 515

Sharon L. Senk, Denisse R. Thompson, and Jamie L.W. Wernet

Learning Paths and Learning Supports for Conceptual Addition and Subtraction in the US Common Core State Standards and in the Chinese Standards  . . 541

Karen C. Fuson and Yeping Li

The Virtual Curriculum: New Ontologies for a Mobile Mathematics . . 559

Nathalie Sinclair and Elizabeth de Freitas

Part VI Cross-national Comparison and Commentary

Forty-Eight Years of International Comparisons in Mathematics Education from a United States Perspective: What Have We Learned?  . . 581

Zalman Usiskin

(Mathematics) Curriculum, Teaching and Learning  . . 607

Ngai-Ying Wong, Qiaoping Zhang, and Xiaoqing Li

Improving the Alignment Between Values, Principles and Classroom Realities . . 621

Malcolm Swan

Index . . . 637

Author Index . . . . 643

Author Biographies. . . 649