Success with STEM: Ideas for the classroom, STEM clubs and beyond

 Sue Howarth e Linda Scott 

Routledge | 2014 | 188 páginas | rar - pdf | 1,33 Mb

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Success with STEM is an essential resource, packed with advice and ideas to support and enthuse all those involved in the planning and delivery of STEM in the secondary school. It offers guidance on current issues and priority areas to help you make informed judgements about your own practice and argue for further support for your subject in school. It explains current initiatives to enhance STEM teaching and offers a wide range of practical activities to support exciting teaching and learning in and beyond the classroom.

Illustrated with examples of successful projects in real schools, this friendly, inspiring book explores:

• Innovative teaching ideas to make lessons buzz

• Activities for successful practical work

• Sourcing additional funding

• Finding and making the most of the best resources

• STEM outside the classroom

• Setting-up and enhancing your own STEM club

• Getting involved in STEM competitions, fairs and festivals

• Promoting STEM careers and tackling stereotypes

• Health, safety and legal issues

• Examples of international projects

• An wide-ranging list of project and activity titles

Enriched by the authors’ extensive experience and work with schools, Success with STEM is a rich compendium for all those who want to develop outstanding lessons and infuse a life-long interest in STEM learning in their students. The advice and guidance will be invaluable for all teachers, subject leaders, trainee teachers and NQTs.

The European Mathematical Awakening: A Journey Through the History of Mathematics from 1000 to 1800

Frank J. Swetz

Dover Publications | 2013 - Reprint edition | 224 páginas | rar - epub | 18,5 Mb

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A global survey of the history of mathematics, this collection of 32 articles traces the subject from AD 1000 to 1800. Newly corrected and updated, the highly readable essays by such distinguished educators as Carl Boyer and Morris Kline introduce fascinating studies by Fibonacci, Descartes, Cardano, Kepler, Galileo, Pascal, Newton, Euler, and others. Suitable for readers with no background in math. Reprint of selected material from From Five Fingers to Infinity: A Journey Through the History of Mathematics, Open Court Publishing Company, Chicago, 1994.

Table of Contents
Preface
PERSPECTIVE: THE EUROPEAN MATHEMATICAL AWAKENING
HISTORICAL EXHIBIT 1 The Growth of Mathematical Knowledge
1.Counters: Computing if You Can Count to Five
VERA SANFORD
HISTORICAL EXHIBIT 2 Bede’s Finger Mathematics
2.Gerbert’s Letter to Adelbold
G. A. MILLER
HISTORICAL EXHIBIT 3 The Geometry of Gothic Church Windows
3.The Arithmetic of Medieval Universities
DOROTHY V. SCHRADER
4.The Craft of Nombryng
E. R. SLEIGHT
5.Leonardo Fibonacci
CHARLES KING
6.Leonardo of Pisa and his Liber quadratorum
R. B. McCLENON
7.Some Uses of Graphing before Descartes
THOMAS M. SMITH
8.Adam Riese
DOROTHY I. CARPENTER
9.Tangible Arithmetic: Finger Reckoning and Other Devices
PHILLIP S. JONES
10.The Cardano-Tartaglia Dispute
RICHARD W. FELDMANN
HISTORICAL EXHIBIT 5 Cardano’s Technique for the Solution of a Reduced Cubic Equation
11.Complex Numbers: An Example of Recurring Themes in the Development of Mathematics—I
PHILLIP S.JONES
12.Robert Recorde’s Whetstone of Witte, 1557
VERA SANFORD
13.The Teaching of Arithmetic in England from 1550 until 1800 as Influenced by Social Change
JAMES KING BIDWELL
14.Tangible Arithmetic: Napier’s and Genaille’s Rods
ILLIP S. JONES
15.The Life and Times of Johann Kepler
BERNARD H. TUCK
HISTORICAL EXHIBIT 6 Multiplication Algorithms of the Fifteenth and Sixteenth Centuries
16.Simon Steven and the Decimal Fractions
D. J. STRUIK
HISTORICAL EXHIBIT 7 Mathematical Considerations on the Trajectory of a Cannon Ball
17.Viète’s Use of Decimal Fractions
CARL B. BOYER
18.John Napier and His Logarithms
C. B. READ
HISTORICAL EXHIBIT 8 The Evolution of Algebraic Symbolism
19.Projective Geometry
MORRIS KLINE
20.Pisa, Galileo, Rome
EDMOND R. KIELY
HISTORICAL EXHIBIT 9 Torricelli’s Wine Glass
21.Analytic Geometry: The Discovery of Fermat and Descartes
CARL B. BOYER
22.The Young Pascal
HAROLD MAILE BACON
HISTORICAL EXHIBIT 10 Roberval’s Quadrature of the Cycloid
23.Isaac Newton: Man, Myth, and Mathematics
V. FREDERICK RICKEY
HISTORICAL EXHIBIT 11 Newton’s Method of Fluxions
24.The Newton-Leibniz Controversy Concerning the Discovery of the Calculus
DOROTHY V. SCHRADER
HISTORICAL EXHIBIT 12 Mengoli’s Proof for the Divergence of the Harmonic Series
25.The Bernoulli Family
HOWARD EVES
26.The Bernoullis and the Harmonic Series
WILLIAM DUNHAM
27.The First Calculus Textbooks
CARL B. BOYER
28.The Origin of L’Hopital’s Rule
D. J. STRUIK
29.Euler, the Master Calculator
JERRY D. TAYLOR
0.Gaspard Monge and Descriptive Geometry
LEO GAFNEY
31.Mathematicians of the French Revolution
CARL B. BOYER
32.The Ladies Diary… Circa 1700
TERI PERL
HISTORICAL EXHIBIT 13 Women in Mathematics
Epilogue: The Process Continues
Suggested Readings

Revisão: MAA

The Hard Mathematical Olympiad Problems And Their Solutions

Steve Dinh

AuthorHouse | 2011 | 320 páginas

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This book shows the approaches to solving many difficult Mathematical Olympiad and other international problems posted at the www.mathlinks.ro, the largest mathematical webpage that has most of the problems used to select the talented students of the world. At the time of this book's publication, the solutions to many of these problems are not yet available.

Soluções de alguns problemas do livro: link

A pedido de Hugo Delatorre

Infinity and the Mind: The Science and Philosophy of the Infinite

 Rudy Rucker

Princeton University Press | 2005 | 368 páginas | rar - epub | 8,4 Mb

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djvu - 5,9  Mb
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link1

pdf - 28,7 Mb - link 

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.
Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Contents

Preface to the 2005 Edition ix

Preface to the Paperback Edition xvii

Preface xix

Chapter One: Infinity 1

A Short History of Infinity
Physical Infinities; 
Temporal Infinities; Spatial Infinities; Infinities in the Small; Conclusion

Infinities in the Mindscape 35

The Absolute Infinite 44

Connections 49

Puzzles and Paradoxes 51
Chapter Two: All the Numbers 53
From Pythagoreanism to Cantorism 53
Transfinite Numbers 64
From Omega to Epsilon-Zero; The Alefs
Infinitesimals and Surreal Numbers 78
Higher Physical Infinities 87
Puzzles and Paradoxes 91
Chapter Three: The Unnameable 93
The Berry Paradox 93
Naming Numbers; Understanding Names
Random Reals 107
Constructing Reals; The Library of Babel ; Richard’s Paradox; Coding the World 
What is Truth? 143
Conclusion 152
Puzzles and Paradoxes 155
Chapter Four: Robots and Souls 157
Gödel’s Incompleteness Theorem 157
Conversations with Gödel 164
Towards Robot Consciousness171
Formal Systems and Machines;  The Liar Paradox and the Non-Mechanizability of Mathematics; Artificial Intelligence via Evolutionary Processes; Robot Consciousness
Beyond Mechanism?185
Puzzles and Paradoxes187
Chapter Five: The One and the Many189
The Classical One/Many Problem189
What is a Set?191
The Universe of Set Theory196
Pure Sets and the Physical Universe; Proper Classes and Metaphysical Absolutes
Interface Enlightenment206
One/Many in Logic and Set Theory; Mysticism and Rationality; Satori
Puzzles and Paradoxes219
Excursion One: The Transfinite Cardinals 221
On and Alef-One 221
Cardinality 226
The Continuum 238
Large Cardinals 253
Excursion Two: Gödel’s Incompleteness Theorems 267
Formal Systems 267
Self-Reference 280
Gödel’s Proof 285
A Technical Note on Man-Machine Equivalence 292
Answers to the Puzzles and Paradoxes 295
Notes 307
Bibliography 329

The Fifty-Nine Icosahedra

(Lecture Notes in Statistics)

 H. S. M. Coxeter, P. DuVal, H. T. Flather e J. F. Petrie

Springer | 2013 -  reprint of the original 1st ed. 1982 edition | 52 páginas | rar - pdf | 1,7 Mb

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Edição anterior - 1938 (link)

This is a completely new edition of the classic book which has been out of print for many years. The plans and illustrations of all 59 of the stellations of the icosahedron have been redrawn by Kate and David Krennell and there is a new introduction by Professor Coxeter. For a thorough understanding of the process of stellation and for splendid examples of polyhedra, this book will be a valuable addition to any mathematics library.

CONTENTS
1. Introduction... 3
2. Complete Enumeration of Stellated Icosahedra, by Considering the Possible Faces. . 8
3. An Alternative Enumeration, by Considering Solid Cells.... 15
4. Notes on the Plates. . 18

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

Sugestão de tibu

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.

Modelling and Mathematics Education: ICTMA 9: Applications in Science and Technology

J.F. Matos, S.K. Houston, Werner Blum e S.P. Carreira

Woodhead Publishing | 2002 | 433 páginas | PDF | 25 Mb

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The articles included in this book are from the ICTMA 9 conference held in Lisbon, attended by delegates from about 30 countries. This work records the 1999 Lisbon Conference of ICTMA. It contains the selected and edited content of the conference and makes a significant contribution to mathematical modelling which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships.

Contents
Preface ix
Section A. Mathematical modelling revisited
1 Enacting possible worlds: Making sense of (human) nature
Stephen R Campbell
2 The mountain is the utility - On the metaphorical nature of mathematical models
Susana Carreira
3 The theory of multiple intelligences and mathematical modelling
S Kenneth Houston
4 Modelling modelling: Where is the centre of gravity of-for-when teaching modelling?
John Mason
5 Fact, fiction, fiddle - Three types of models
Allan Tarp
6 Issues and problems of research on the teaching and leaming of applications and modelling
Mogens Niss
Section B. Mathematical aspects of modelling
7 Mathematical modelling by means of functional equations: The missing link in the leaming of functions
Claudi Alsina
8 Applications of simultaneous iteration
Neville T Neil
9 On the derivative of nondifferentiable fimctions
Miguel Ramos
10 Mathematics before or through applications. Top-down and bottom-up understandings of linear and exponential functions
Allan Tarp
Section C. Mathematical modelling and technology
Formulating and assessing a mathematical modelling problem in a technological environment
Roger Brown
The graphics calculator and mathematical modelling - Creating an integrated learning environment
Milton Fuller
Mobile classroom - A school project focussing on modelling
Hans- Wolfgang Henn
What should be asked of a computer program for mathematical modelling in primary/lower secondary school?
Inge B Larsen
Modelling and algebra: How ‘pure’ shall we be?
Henk van der Kooij
Section D. Mathematical modelling in higher education
16 Mathematical modelling in pre-service teacher education
Jonei Cerqueira Barbosa
17 Mathematical modelling in calculus courses
Jussara de Loiola Aratijo and Josk Antbnio Salvador
18 Mathematical modelling and technology in teacher education - Visions and reality
Thomas Lingejard and Mikael Holmquist
19 Modelling optimisation problems: From simple to realistic 216
Margarida P Mello and Sandra A Santos
20 Role of mathematical modelling and applications in university mathematics service courses: An across countries study
Sergiy Klymchuk and Tatyana Zverkova
21 A mathematics curriculum for undergraduate courses based on mathematical modelling and computer science
Regina Helena Franchi
22 Mathematical applications and modelling: A case study involving first year higher education students
Fernanda Tavares
23 Mathematical modelling with environmental students
Mike Hamson
24 Exploring different approaches to mathematical modelling in engineering calculus courses
Maria Ines Cavallaro and Marta Anaya
25 From mathematical modelling to mathematical experiments
Qiyuan Jiang
Section E. Pedagogical issues in mathematical modelling
26 Modelling: Good problems - not only a question of (good) taste
Eva Jablonka
27 Assumptions and context: Pursuing their role in modelling activity
P. Galbraith and G. Stillman
28 The effect of task organisation on classroom modelling activities 311
Iben Maj Christiansen
Aiming for success: Modelling sports problems with an aiming theme
Trevor Gethins
Context orientated teaching
Klaoudatos Nikos and Papastavridis Stavros
Enculturation in mathematical modelling
Susan J Lamon
Conceptual and procedural demands embedded in modelling tasks
Peter Galbraith and Christopher Haines
Mathematical modelling by the pupils themselves - Possibilities and limitations in school-leaving examination papers
Wolfiam Eid
Understanding students’ modelling skills
Christopher Haines, Rosalind Crouch and John Davies
The effects of students’ discussion in mathematical modelling
Toshikazu Ikeda and Max Stephens
Critical evaluation of models in relation to the modelling process
Iben Maj Christiansen
Mathematics of traffic safety - Composite real mathematics approach
Akira Yanagimoto and Noboru Yoshimura
Trigonometry with reference to modern land surveying techniques in maths lessons

Katja MaaJ