Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

(Synthese Library) 

Ulianov Montano 

Springer | 2014 | 224 páginas | rar - pdf | 1,1 Mb

link (password: matav)

This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics.

The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as processtheory.

The theory comprises explications of three central topics: aesthetic experience (in mathematics), aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities.

Contents
Introduction.
Part 1. Antecedents.
Chapter 1. On Non-literal Approaches.
Chapter 2. Beautiful, Literally.
Chapter 3. Ugly, Literally.
Chapter 4. Problems of the Aesthetic Induction.
Chapter 5. Naturalizing the Aesthetic Induction.
Part 2. An Aesthetics of Mathematics.
Chapter 6. Introduction to a Naturalistic Aesthetic Theory.
Chapter 7. Aesthetic Experience.
Chapter 8. Aesthetic Value.
Chapter 9. Aesthetic Judgement I: Concept.
Chapter 10. Aesthetic Judgement II: Functions.
Chapter 11. Mathematical Aesthetic Judgements.
Part 3. Applications.
Chapter 12. Case Analysis I: Beauty.
Chapter 13. Case Analysis II: Elegance.
Chapter 14. Case Analysis III: Ugliness, Revisited.
Chapter 15. Issues of Mathematical Beauty, Revisited.

A History of Astronomy

Walter William Bryant

London Methuen 1907

online: archive.org

Routledge | 2013 | 434 páginas | rar - pdf | 5,52 Mb

link (password: matav)

A History of Astronomy, first published in 1907, offers a comprehensive introduction to the steady development of the science since its inception in the ancient world up to the momentous progress of the nineteenth century. It includes biographical material relating to the most famous names in the study of astronomy – Copernicus, Galileo, Newton, Herschel – and their contributions, clear and accessible discussions of key discoveries, as well as detailing the incremental steps in technology with which many of the turning points in astronomy were intimately bound up.

CONTENTS
CHAP. PAGE
I. EARLY NOTIONS
II. THE EASTERN NATIONS OF ANTIQUITY 8
III. THE GREEKS 14
IV. THE ARABS 25
V. THE REVIVAL-COPERNICUS-TYCHO BRAHE 28
VI. KEPLER-GALl LEO 39
'VII. NEWTON 47
VIII. NEWTON'S SUCCESSORS: LAPLACE 53
IX. FLAMSTEED-HALLEy-BRADLEy-HERSCHEL 63
X. THE EARLY NINETEENTH CENTURy-NEPTUNE 73
XI. HERSCHEL-BESSEL-STRUVE • 83
XII. COMETS • 96
XIII. THE SUN-EcLIPSES-PARALLAX 103
XIV. GENERAL ASTRONOMY AND CELESTIAL MECHANICS 118
XV. OBSERVATORIES AND INSTRUMENTS • 132
XVI. ADJUSTMENT OF OBSERVATIONS. PERSONAL ERRORS 141
XVII. THE SUN 146
XVIII. SOLAR SPECTROSCOPY 159
XIX. SOLAR ECLIPSES-SPECTROSCOPY 169
XX. THE MOON 183
XXI. THE EARTH 192
XXII. THE INTERIOR PLANETS 201
XXIII. MARS 209
XXIV. MINOR PLANETS 219
XXV. THE MAJOR PLANETS 226
XXVI. THE SOLAR SYSTEM • 24I
XXVII. COMETS, METEORS, ZODIACAL LIGHT 247
XXVIII. THE STARS-CATALOGUES-PROPER MOTION-PARALLAX-MAGNITUDE 27I
XXIX. DOUBLE STARS 292
XXX. VARIABLE STARS 303
XXXI. CLUSTERS-NEBULIE-MILKY WAY. 318
XXXII. STELLAR SPECTROSCOPY 327
XXXIII. CONCLUSION • 340

Learning Mathematics and Logo

Celia Hoyles e Richard Noss

The MIT Press | 1992 | 492 páginas | pdf | 22,4 Mb

link
link1

These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.
Essays in the first section discuss the link between Logo and the school mathematics curriculum, focusing on the ways in which pupils' Logo activities relate to and are influenced by the ideas they encounter in the context of school algebra and geometry.
In the second section the contributions take up pedagogical styles and strategies. They tackle such cognitive and metacognitive questions as, What range of learning styles can the Logo setting accommodate? How can teachers make sense of pupils' preferred strategies? And how can teachers help students to reflect on the strategies they are using?
Returning to the mathematical structures, essays in the third section consider a variety of mathematical ideas, drawing connections between mathematics and computing and showing the ways in which constructing Logo programs helps or does not help to illuminate the underlying mathematics.

Contents
Contributors vii
Series Foreword ix
Foreword by Seymour Papert xi
Preface xvii
Acknowledgments xxiii
LOGO IN THE CURRICULUM
Introduction to Part I 3
The Notion of Variable in the Context of Turtle Graphics 11
Joel Hillel
2 What Is Algebraic about Programming in Logo? 37
Rosamund Sutherland
3 Conceptually Defined Turtles 55
Herbert Loethe
4 The Turtle Metaphor as a ToOl for Children's Geometry 97
Chronis Kynigos
5 A Logo Microworld for Transformation Geometry 127
Laurie D. Edwards
II STYLES AND STRATEGIES
Introduction to Part II 159
6 LEGO-Logo: A Vehicle for Learning 165
Sylvia Weir
7 On Intra- and Interlndividual Differences in Children's Learning Styles 191
Tamara Lemerise
8 Mathematics in a Logo Environment: A Recursive Look at a Complex Phenomenon 223
Thomas E. Kieren
9 Between Logo and Mathematics: A Road of Tunnels and Bridges 247
Jean-Luc Gurtner
III EXPRESSING MATHEMATICAL STRUCTURES
Introduction to Part ", 27 1
10 Processes: A Dynamical Integration of Computer Science into Mathematical Education 279
Bruno Vitale
Of Geometry, Turtles, and Groups
Uri Leron and Rina Zazkis
Patterns, Permutations, and Groups
Trevor Fletcher
Avoiding Recursion 393
Brian Harvey
IV AFTERWORD
Introduction to Part IV 429
Looking Back and Looking Forward
Richard Noss and Celia Hoyles
Index 47 1

Eureka! Math Fun From Many Angles

David Lewis

Perigee Trade | 1955 | 199 páginas | pdf | 4,8 Mb

link

link1

djvu - 1,1 Mb

link

link1

Presents a variety of puzzles, problems, and paradoxes that test the reader's skills in logic and knowledge of mathematics

Contents

Fun and Games

1. Twisted Topology

2. A Bag of Tricks and Treats

3. A Score of Games

4. The Magic's There

5. Rubiquity

Nifty Numerics

6. Palindromesemordnilap

7. A Pole Vaulter

8. A Timely Switch

Fallacies and Logic

9. If This Is Not a Chapter, My Name Is Raymond Smullyan

10. Thrice Befuddled

11. Better Mixed-Up Than Lost

And Even Dissection of Solids

12. Archimedes Anderson and the Case of the Sinister Plot 93

13. How to Dissect a Square and Other Marvels of Modern Biology 96

14. Geometer's Heaven 105

15. Hole in the Sphere 108

16. Convexstasy 110

17. Great Unsolved Problems 113

18. Out of This World 115

Photons Are Light Matter, Too

19. Archimedes Anderson and the Gambling Candidate 119

20. Once Upon a Time. . . 122

21. A Problem Fly 123

22. The Leading Series of Pisa 124

23. The Early Something Catches the Whatever 127

Shortcuts

24. A Speedier System of Solving 129

25. A Letter Home 135

26. In Which We Are Initiated Into the Secret

Society of Square Root Solvers

27. Heads and Legs

28. Noble Bases

29. A Division in Ancient Rye

30. Getting at the Root of the Problem

31. Or is it 32? Remumbt:r Nembers

Neat Numbers

32. Prime Time 151

33. A Sense of Balance 159

34. Perfect Numbers and Some Not-So-Perfect Numbers 161

Cranium Crackers and Cheese: Problems to Munch On

35. Classy Problems 165

36. LEITERS + DIGITS = FRUSTRATION 174

FUNdamental Ratios

37. Expand Your Mind

38. E? Ah!

39. A Section of Gold

40. A Bundled-Up Buyer

41. A Piece of Pi

Bibliography

Writing Strategies for Mathematics

(Reading and Writing Strategies)

Trisha Brummer e Sarah Kartchner Clark

Shell Education | 2013 - 2ª edição | 259 páginas | rar - PDF | 6,4 Mb

link (password: matav)

1ª edição - 2008

Help students write mathematics content! This 2nd edition resource was created to support Common Core State Standards, provides an in-depth research base about literacy instruction, and includes key strategies to help students write and comprehend mathematics content. Designed in an easy-to-use format, this resource offers details approaches and activities with classroom examples by grade ranges and includes graphic organizer templates and digital resources to help teachers implement quickly and easily. Specific suggestions for differentiating instruction are also provided to help English language learners, gifted students, and students reading below grade level.
Table of Contents
Introduction
What Is Writing? . . . . . . . . . . . . . . . . . . . . . . . . . 5
Motivating Students to Write . . . . . . . . . . . . . . . 10
The Writing Process . . . . . . . . . . . . . . . . . . . . . 16
Writing Across the Curriculum . . . . . . . . . . . . . 20
Writing Instruction . . . . . . . . . . . . . . . . . . . . . . 25
How to Use This Book . . . . . . . . . . . . . . . . . . . 28
Correlation to Standards . . . . . . . . . . . . . . . . . . 29
Part 1: Writing to Learn
Developing Vocabulary
Developing Vocabulary Overview . . . . . . . . . . . 31
Word Wall . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Frayer Model . . . . . . . . . . . . . . . . . . . . . . . . 39
Concept of De nition Map . . . . . . . . . . . . . 43
List-Group-Label . . . . . . . . . . . . . . . . . . . . . 48
Vocabulary Self-Collection . . . . . . . . . . . . . 53
Possible Sentences . . . . . . . . . . . . . . . . . . . . 55
Word Trails . . . . . . . . . . . . . . . . . . . . . . . . . 59
Previewing and Reviewing
Previewing and Reviewing Overview . . . . . . . . 63
KWL Chart . . . . . . . . . . . . . . . . . . . . . . . . . 66
Think Sheet . . . . . . . . . . . . . . . . . . . . . . . . . 72
Free-Association Brainstorming . . . . . . . . . 76
Probable Passages . . . . . . . . . . . . . . . . . . . . 80
Guided Free Write . . . . . . . . . . . . . . . . . . . . 85
End-of-Class Re ection . . . . . . . . . . . . . . . . 89
Reader-Response Writing Chart . . . . . . . . . 92
Journal Writing
Journal Writing Overview . . . . . . . . . . . . . . . . . 96
Vocabulary Journal . . . . . . . . . . . . . . . . . . . 99
Dialogue Journal . . . . . . . . . . . . . . . . . . . . 103
Highlighted Journal . . . . . . . . . . . . . . . . . . 106
Key Phrase Journal . . . . . . . . . . . . . . . . . . 109
Double-Entry Journal . . . . . . . . . . . . . . . . 112
Critical Incident Journal . . . . . . . . . . . . . . 116
Three-Part Journal . . . . . . . . . . . . . . . . . . 119
Note-Taking
Note-Taking Overview . . . . . . . . . . . . . . . . . . 123
Cornell Note-Taking System . . . . . . . . . . . 125
Note-Taking System for Learning . . . . . . . 129
T-List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Using Diagrams and Maps
Using Diagrams and Maps Overview . . . . . . . 137
Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Venn Diagram . . . . . . . . . . . . . . . . . . . . . . 143
Triangular Venn Diagram . . . . . . . . . . . . . 147
Cause-and-Effect Map . . . . . . . . . . . . . . . . 151
Semantic Word Map . . . . . . . . . . . . . . . . . 155
Concept Map . . . . . . . . . . . . . . . . . . . . . . . 159
Problem-Solution Map. . . . . . . . . . . . . . . . 162
Time Order Map . . . . . . . . . . . . . . . . . . . . 168
Part 2: Writing to Apply
Authoring
Authoring Overview . . . . . . . . . . . . . . . . . . . . 173
Guided Writing Procedure . . . . . . . . . . . . 175
Reading-Writing Workbench . . . . . . . . . . . 178
Author’s Chair . . . . . . . . . . . . . . . . . . . . . . 182
Read, Encode, Annotate, Ponder . . . . . . . . 186
Summarizing
Summarizing Overview . . . . . . . . . . . . . . . . . 191
GIST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Key Words . . . . . . . . . . . . . . . . . . . . . . . . . 197
Guided Reading and Summarizing Procedure .. . . . . 199
Applying Knowledge
Applying Knowledge Overview . . . . . . . . . . . 204
Summary-Writing Microtheme . . . . . . . . . 208
Thesis-Support Microtheme . . . . . . . . . . . 210
Data-Provided Microtheme . . . . . . . . . . . . 212
Quandary-Posing Microtheme . . . . . . . . . 214
RAFT Assignment . . . . . . . . . . . . . . . . . . 216
Business Letter . . . . . . . . . . . . . . . . . . . . . 218
Friendly Letter . . . . . . . . . . . . . . . . . . . . . . 220
Data Report . . . . . . . . . . . . . . . . . . . . . . . . 222
Newspaper Article . . . . . . . . . . . . . . . . . . . 224
Mathematics Fiction Story . . . . . . . . . . . . 226
Research Report . . . . . . . . . . . . . . . . . . . . 228
Part 3: Assessing Writing
Assessing Writing
Assessing Writing Overview . . . . . . . . . . . . . . 230
Holistic Assessment . . . . . . . . . . . . . . . . . . 233
Analytic Assessment . . . . . . . . . . . . . . . . . 235
Primary Trait Assessment . . . . . . . . . . . . . 237
Self-Assessment . . . . . . . . . . . . . . . . . . . . . 239
Peer Assessment . . . . . . . . . . . . . . . . . . . . 242
Teacher Conference . . . . . . . . . . . . . . . . . . 244
Appendix A: Additional Resources . . . . . . . 246
Appendix B: References Cited . . . . . . . . . . . 247
Appendix C: Suggestions for Further Reading . . . 253
Appendix D: Contents of the Digital Resource CD .  . 254

Diamond: A Paradox Logic

Series on Knots and Everything (Book 23)

N. S. Hellerstein


World Scientific Publishing Company; 2nd Revised edition | 2010 |  297 páginas | pdf | 1,8 Mb

link

This book is about 'diamond', a logic of paradox. In diamond, a statement can be true yet false; an 'imaginary' state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book has three sections: Paradox Logic, which covers the classic paradoxes of mathematical logic, shows how they can be resolved in this new system; The Second Paradox, which relates diamond to Boolean logic and the Spencer-Brown modulator"; and Metamathematical Dilemma, which relates diamond to Godelian meta-mathematics and dilemma games.

Contents
Introduction xi
Part One: Paradox Logic 1
1. Paradox 3
A. The Liar 3
B. The Anti-Diagonal 7
C. Russell’s Paradox 8
D. Santa and the Grinch 10
E. Antistrephon 17
F. Parity of Infinity 18
G. The Heap 19
H. Finitude 21
I. Game Paradoxes 24
J. Cantor’s Paradox 26
K. Paradox of the Boundary 27
2. Diamond 29
A. The Buzzer 29
B. Diamond Values 31
C. Harmonic Functions 32
D. Gluts and Gaps 35
E. Diamond Circuits 38
F. Brownian Forms 40
G. Boundary Logic 46
3. Diamond Algebra 49
A. Bracket Algebra 49
B. Laws 58
C. Normal Forms 64
D. Completeness 69
4. Self-Reference 71
A. Re-Entrance and Fixedpoints 71
B. Phase Order 74
C. The Outer Fixedpoints 79
5. Fixedpoint Lattices 85
A. Relative Lattices 85
B. Seeds and Spirals 88
C. Shared Fixedpoints 91
D. Examples 93
6. Limit Logic 109
A. Limits 109
B. Limit Fixedpoints 114
C. The Halting Theorem 116
7. Paradox Resolved 119
A. The Liar and the Anti-Diagonal 119
B. Russell’s Paradox 120
C. Santa and the Grinch 122
D. Antistrephon 126
E. Infinity, Finitude and the Heap 128
F. Game Paradoxes 130
8. The Continuum 131
A. Cantor’s Paradox 131
B. Dedekind Splices 132
C. Null Quotients 134
D. Cantor’s Number 136
E. The Line within the Diamond 139
F. Zeno’s Theorem 144
G. Fuzzy Chaos 145
9. Clique Theory 151
A. Cliques 151
B. Clique Equality 156
C. Clique Axioms 160
D. Graph Cliques 164
E. Clique Circuits 166
Part Two: The Second Paradox 169
10. Orthogonal Logics 171
A. Analytic Functions 171
B. Function Types 173
C. Dihedral Conjugation 177
D. Star Logic 180
E. Harmonic Projection 182
F. Diamond Types? 183
11. Interferometry 185
A. Quadrature 185
B. Diffraction 193
C. Buzzers and Toggles 200
D. Analytic Diffraction 204
E. Diffracting “Two Ducks in a Box” 206
12. How to Count to Two 209
A. Brownian and Kauffman Modulators 209
B. Diffracting the Modulators 212
C. Rotors, Pumps and Tapes 218
D. The Ganglion 222
Part Three: Metamathematical Dilemma 225
13. Metamathematics 227
A. Gödelian Quanta 227
B. Meta-Logic 231
C. Dialectic 236
D. Dialectical Dilemma 238
14. Dilemma 241
A. Milo’s Trick 241
B. Prisoner’s Dilemma 245
C. Dilemma Games 249
D. Dilemma Diamond 253
E. Banker’s Dilemma 257
F. The Unexpected Departure 260
Notes 265
Bibliography 287
Index 291

Educational Interfaces between Mathematics and Industry: Report on an ICMI-ICIAM-Study

Alain Damlamian, José Francisco Rodrigues e Rudolf Sträßer

New ICMI studies series, v.16.

Springer | 2013 | 451 páginas | rar - pdf | 4 Mb

link (password : matav)

This book is the “Study Book” of ICMI-Study no. 20, which was run in cooperation with the International Congress on Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organiser of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over world. This content was selected by the editors as especially pertinent to the study each individual chapter represents a significant contribution to current research.

Contents

Part I Discussion Document and Study Report

Discussion Document. . . . . . 3

The International Programme Committee

Report on the Study . . .  . . . 17

Alain Damlamian, José Francisco Rodrigues and Rudolf Sträßer

Part II Plenary and Invited Lectures

Getting Math off the Ground: Applied Mathematics at Boeing . . 27

Stephen P. Keeler and Thomas A. Grandine

Mathematics in the Workplace: Issues and Challenges . . . .. . . 43

Celia Hoyles, Richard Noss, Phillip Kent and Arthur Bakker

Mathematical Modeling Education is the Most Important Educational Interface Between Mathematics and Industry . . . 51

Tatsien Li

Models for Industrial Problems: How to Find and How to Use them—in Industry and in Education . . . . . . .  . 59

Helmut Neunzert

Interfacing Education and Research with Mathematics for Industry: The Endeavor in Japan. 77

Masato Wakayama

Part III WG Education/Training with Industry Participation

Education/Training with Industry Participation . . . . 95

Gail FitzSimons and Tom Mitsui

How it is Possible to Make Real-World Mathematics More Visible: Some Results from Two Italian Projects  . . 109

Cinzia Bonotto

The Project ‘‘Ways to More MINT-Graduates’’ of the Bavarian Business Association (vbw) with Focus on the M (=Mathematics) at the University of Augsburg, Germany . . 119

Matthias Brandl

Mathematics in a Safety–Critical Work Context: The Case of Numeracy for Nursing . 127

Diana Coben and Meriel Hutton

Linking Professional Experiences with Academic Knowledge: The Construction of Statistical Concepts by Sale Manager Apprentices . . 137

Corinne Hahn

Learning Conversation in Mathematics Practice School–Industry Partnerships as Arena for Teacher Education . . 147

Gert Monstad Hana, Ragnhild Hansen, Marit Johnsen-Høines, Inger Elin Lilland and Toril Eskeland Rangnes

The Threefold Dilemma of Missing Coherence: Bridging the Artificial Reef Between the Mainland and Some Isolated Islands. . 57

Guenter Törner, Volker Grotensohn and Bettina Roesken

The Project ‘‘Mathe-Meister’’: A Mathematical Self Assessment Centre with Diagnostic Feedback for Vocational Trainees . . . 165

Kathrin Winter

Part IV WG University and Academic Technical/Vocational Education

University and Academic Technical/Vocational Education . . .  . 173

Nilima Nigam and José Francisco Rodrigues

Mathematics for Engineering and Engineering for Mathematics . .185

Miquel Alberti Palmer, Sergio Amat, Sonia Busquier, Pilar Romero and Juan Tejada

Laboratory for Computational Mathematics: An Interface Between Academia and Industry 199

A. Araújo, S. Barbeiro and J. A. Ferreira

Improving the Industrial/Mathematics Interface.. . 205

Jean P. F. Charpin and Stephen B. G. O’Brien

Two Masters on ‘Mathematics for Industry’ at the Universities of Paris and of Pau . 213

Edwige Godlewski, M. Madaune-Tort and S. Dossou-Gbete

Mathematics in Industry and Teachers’ Training . .  223

Matti Heilio

Interfaces Between Mathematics and Industry and the Use of Technology in Mathematics Education in India  . 229

Ajit Kumar

Modeling Modeling: Developing Habits of Mathematical Minds . . 237

John A. Pelesko, Jinfa Cai and Louis F. Rossi

The Evolution of Graduate Applied Math Courses in the Institute of Mathematics, University of the Philippines. . 247

Carlene P. C. Pilar-Arceo and Jose Maria L. Escaner IV

The Vertical Integration of Industrial Mathematics, the WPI Experience  . 253

Bogdan Vernescu

Part V WG Education in Schools

Educational Interfaces Between Mathematics and Industry at School Level . . 263

Gabriele Kaiser, Henk van der Kooij and Geoff Wake

Mathematical Applications, Modelling and Technology as Windows into Industry Based Mathematical Practice .  . 271

Vince Geiger

Mathematics Education and the Information Society . . . 279

Koeno Gravemeijer

Authentic Complex Modelling Problems in Mathematics Education . . 287

Gabriele Kaiser, Martin Bracke, Simone Göttlich and Christine Kaland

Embedding Authentic Real World Tasks into Secondary Mathematics Curricula .. 299

Gloria Stillman and K. E. D. Ng

Drawing on Understanding of Workplace Practice to Inform Design of General Mathematics Curricula .  . 309

Geoff Wake

Part VI WG Mathematics-Industry Communication

Communication and Collaboration. . .. . 319

Solomon Garfunkel, Rolf Jeltsch and Nilima Nigam

Engineering, Mathematics Communication, and Education: Reflections on a Personal Experience . . . 333

Jorge Buescu

A View on Mathematical Discourse in Research and Development . . . 341

Vasco Alexander Schmidt

Using Popular Science in a Mathematical Modeling Course  . . 351

Burt S. Tilley

Part VII WG Technology Issues

Technology Issues . .  . 359

Helmer Aslaksen and Fadil Santosa

Tackling the Challenges of Computational Mathematics Education of Engineers . . 365

France Caron and André Garon

Integrating Computational Modelling in Science, Technology, Engineering, and Mathematics Education.. . 375

Rui Gomes Neves, Jorge Carvalho Silva and Vítor Duarte Teodoro

Incorporating the Ideas and Methods of Mathematical Modeling into Calculus Teaching .385

Qixiao Ye

Part VIII WG the Mathematics-Industry Interface

The Mathematics–Industry Interface . . 397

Jofré Alejandro and Lutz-Westphal Brigitte

Part IX Selected Papers Linked to More than One Working Group 

Inappropriate Use of Spreadsheets in the Finance Industry . . . . 403

Djordje M. Kadijevich

MITACS Accelerate: A Case Study of a Successful Industrial Research Internship Program . . . 413

Sarah Petersen and Marsh Rebeccah

A Meta-analysis by Mathematics Teachers of the GIFT Program Using Success Case Methodology . . . 421

Richard Millman, Meltem Alemdar and Bonnie Harris

Cultivating an Interface Through Collaborative Research Between Engineers in Nippon Steel & Sumitomo Metal and Mathematicians in University . . . 427

Junichi Nakagawa and Masahiro Yamamoto

An Introduction to CUMCM: China/Contemporary Undergraduate Mathematical Contest in Modeling . . 435

Jinxing Xie

Part X Conclusion

Conclusion on Educational Interfaces Between Mathematics and Industry. . . . . 447

Alain Damlamian, José Francisco Rodrigues and Rudolf Sträßer

Index . . . 453