Raising public awareness of mathematics

Ehrhard Behrends, Nuno Crato e José Francisco Rodrigues

Springer | 2012 | páginas | rar - pdf | Mb

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This collective book aims to encourage and inspire actions directed towards raising public awareness of the importance of mathematical sciences for our contemporary society in a cultural and historical perspective. Mathematical societies, in Europe and around the world, can find ideas, blueprints and suggestions for activities – including concerted actions with other international organizations – directed towards raising public awareness of science, technology and other fields where mathematics plays a strong role. The material is divided into four parts:
• National experiences
• Exhibitions / mathematical museums
• Popularization activities
• Popularization: why and how

Contents
Part I National Experiences
Raising Public Awareness in the UK—Some Snapshots . . . 3
John D. Barrow and Robin Wilson
Raising the Public Awareness of Math: Discussing Recent Initiatives in France  . 11
Jean-Pierre Bourguignon
The GermanWebsite Mathematik.de . . . 23
Wolfram Koepf
Mathematics for the People .. . 37
Günter M. Ziegler and Thomas Vogt
Mathematics in the Public Mind: The USA . . 47
Reinhard Laubenbacher
Balancing Math Popularization with Public Debate: A Mathematical Society’s Continued Efforts to Raise the Public Awareness of Mathematics and for Youth Mathematical Education .. 57
Renata Ramalho and Nuno Crato
The Butterfly Effect and the Popularization of Mathematics: Spain . 67
Raúl Ibáñez Torres
Part II Exhibitions and Mathematical Museums
Mathema—Is Mathematics the Language of Nature?. . 87
Ehrhard Behrends
Lessons Which Can Be Learned from the Mathematikum  . 101
Albrecht Beutelspacher
Atractor .. 109
Manuel Arala Chaves
Mathematics in Action from Lisbon: Engagement with the
Popularization and Communication of Mathematics .. 135
Ana Maria Eiró, Suzana Nápoles, José Francisco Rodrigues, and Jorge Nuno Silva
Playing with Mathematics at Il Giardino di Archimede . . 155
Enrico Giusti
IMAGINARY and the Open Source Math Exhibition Platform . 167
Andreas Daniel Matt
Part III Popularisation Activities
www.mathematics-in-europe.eu  . 189
Ehrhard Behrends
TheMaximin Principle in the Popularisation of Mathematics: Maximum Effect with Minimum Costs .. 197
Franka Miriam Brueckler
WMY 2000: Ten Years on .  . 215
Mireille Chaleyat-Maurel
Some Remarks on Popularizing Mathematics or a Magic Room  . 229
Krzysztof Ciesielski and Zdzisław Pogoda
Mathematics and Interdisciplinarity: Outreach Activities at the University of Coimbra . 241
João Fernandes, Carlos Fiolhais, and Carlota Simões
From PA(X) to RPAM(X) . .. 255
Steen Markvorsen
Promoting the Public Awareness of Mathematics in Developing Countries: A Responsibility and an Opportunity . 269
Yasser Omar
Mathematical Pictures: Visualization, Art and Outreach .. 279
John M. Sullivan
Part IV Popularisation—Why and How
Image, Influence and Importance of Mathematics as Directives for Public Awareness . 297
F. Thomas Bruss
The Importance of Useful Mathematics: On Tools for Its Popularization, from Industry to Art . . 313
Jorge Buescu and José Francisco Rodrigues
WWMD? .331
Barry Cipra
Rigour in Communicating Maths: A Mathematical Feature or an Unnecessary Pedantry? .339
Maria Dedò
Mathematics Between Research, Application, and Communication . . 359
Gert-Martin Greuel
Keeping Mathematical Awareness Alive . . 387
Vagn Lundsgaard Hansen
On the Importance of Useless Mathematics .. 397
António Machiavelo

Cool Flexagon Art: Creative Activities That Make Math & Science Fun for Kids!

 

Anders Hanson e Elissa Mann

Checkerboard Library | 2013 | 34 páginas | rar - pdf | 2,45 Mb

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ContentsCOOL FLEXAGON ART
HIDDEN IN THE FOLDS
POLYGON BASICS
SIDES, VERTICES, AND ANGLES
IN THE FOLD
TYPES OF FLEXAGONS
FOLDING TIPS
MAKE IT EASIER!
PROJECT 1
MAKE A HEXA-TETRA FLEXAGON
PROJECT 2
MAKE A HEXA-HEXA FLEXAGON
3-D GEOMETRY
FROM SHAPES TO SOLIDS
PROJECT 3
MAKE A 3-D FLEXAGON
PROJECT 4
TRANSFORMER STAR
MATH TERMS
GLOSSARY
WEB SITES
INDEX

Paradoxes and Sophisms in Calculus

Sergiy Klymchuk e Susan G. Staples

The Mathematical Association of America | 2013 | páginas | rar - pdf |965 kb

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In the study of mathematics, surprising and counterintuitive examples can offer a fascinating insight into the development of the subject, and inspire a learner's passion for discovery. With a carefully chosen selection of so-called paradoxes and sophisms, this book offers a delightful supplementary resource to enhance the study of single variable calculus. By paradox, the authors mean an unexpected statement that looks invalid, but is in fact true. The word sophism describes intentionally invalid reasoning that looks formally correct, but, in fact, contains a subtle mistake or flaw. This collection of over fifty paradoxes and sophisms showcases the subtleties of calculus and leads students to contemplate the underlying concepts. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences and series are explored, with full explanations provided for each example. The book is an ideal resource for those studying or teaching calculus at high school and university level.

Contents
Introduction;
Part I. Paradoxes:
1. Functions and limits;
2. Derivatives and integrals;
Part II. Sophisms:
3. Functions and limits;
4. Derivatives and integrals;
Part III. Solutions to Paradoxes:
5. Functions and limits;
6. Derivatives and integrals;
Part IV. Solutions to Sophisms:
7. Functions and limits;
8. Derivatives and integrals;
References.

Combinatorial Reasoning: An Introduction to the Art of Counting

Duane DeTemple e William Webb

Wiley | 2014 | 484 páginas | rar - pdf | 3,1 Mb

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With a focus on beginning combinatorics, this book features complete exposition of the discussed topics and over 700 exercises that illustrate the presented concepts and methodology. The book covers fundamental topics in enumeration, all of which are explored in great depth. The authors' approach is very reader-friendly and avoids the "scholarly tone" found in many other related books. Abstract ideas are grounded in familiar concrete settings, and there are far more diagrams within the book than are found in most other related texts. In addition, simple cases are treated first before general and advanced cases, and the notations are kept simple and helpful. To help readers learn how combinatorics interacts with other subjects as a tool or as an application, the book provides brief summaries of basic concepts from probability, power series, and group theory. Each chapter begins with an introduction to the topics covered within the chapter, followed by sections that are each accompanied by a large number of exercises that range from basic calculations to more challenging problems. The exercises are carefully structured to range from the routine to the more advanced. The beginning level problems are designed to confirm and develop students' understanding of the fundamental concepts and calculations, where a calculation is most often based on combinatorial reasoning rather than algebraic manipulation. More advanced exercises allow students to explore and more deeply understand the topics in the chapter and apply the techniques to more complex combinatorial situations. Each chapter also contains a brief summary of the most important concepts covered. Finally, each chapter ends with a few additional problems that further synthesize the ideas that were presented in the chapter. Chapter coverage includes: Initial EnCOUNTers with Combinatorial Reasoning; Arrangements, Selections, and Distributions; Binomial Series and Generating Functions; Alternating Sums, Inclusion-Exclusion, and Rook Polynomials; Recurrence Relations; Special Numbers; Linear Spaces and Recurrences Sequences; and Counting Symmetric Arrangements

CONTENTS
PREFACE ix
PART I THE BASICS OF ENUMERATIVE COMBINATORICS
1 Initial EnCOUNTers with Combinatorial Reasoning 3
1.1 Introduction, 3
1.2 The Pigeonhole Principle, 3
1.3 Tiling Chessboards with Dominoes, 13
1.4 Figurate Numbers, 18
1.5 Counting Tilings of Rectangles, 24
1.6 Addition and Multiplication Principles, 33
1.7 Summary and Additional Problems, 46
References, 50
2 Selections, Arrangements, and Distributions 51
2.1 Introduction, 51
2.2 Permutations and Combinations, 52
2.3 Combinatorial Models, 64
2.4 Permutations and Combinations with Repetitions, 77
2.5 Distributions to Distinct Recipients, 86
2.6 Circular Permutations and Derangements, 100
2.7 Summary and Additional Problems, 109
Reference, 112
3 Binomial Series and Generating Functions 113
3.1 Introduction, 113
3.2 The Binomial and Multinomial Theorems, 114
3.3 Newton’s Binomial Series, 122
3.4 Ordinary Generating Functions, 131
3.5 Exponential Generating Functions, 147
3.6 Summary and Additional Problems, 163
References, 166
4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim 167
4.1 Introduction, 167
4.2 Evaluating Alternating Sums with the
DIE Method, 168
4.3 The Principle of Inclusion–Exclusion (PIE), 179
4.4 Rook Polynomials, 191
4.5 (Optional) Zeckendorf Representations and Fibonacci Nim, 202
4.6 Summary and Additional Problems, 207
References, 210
5 Recurrence Relations 211
5.1 Introduction, 211
5.2 The Fibonacci Recurrence Relation, 212
5.3 Second-Order Recurrence Relations, 222
5.4 Higher-Order Linear Homogeneous Recurrence Relations, 233
5.5 Nonhomogeneous Recurrence Relations, 247
5.6 Recurrence Relations and Generating Functions, 257
5.7 Summary and Additional Problems, 268 
References, 273
6 Special Numbers 275
6.1 Introduction, 275
6.2 Stirling Numbers, 275
6.3 Harmonic Numbers, 296
6.4 Bernoulli Numbers, 306
6.5 Eulerian Numbers, 315
6.6 Partition Numbers, 323
6.7 Catalan Numbers, 335
6.8 Summary and Additional Problems, 345
References, 352
PART II TWO ADDITIONAL TOPICS IN ENUMERATION
7 Linear Spaces and Recurrence Sequences 355
7.1 Introduction, 355
7.2 Vector Spaces of Sequences, 356
7.3 Nonhomogeneous Recurrences and Systems
of Recurrences, 367
7.4 Identities for Recurrence Sequences, 378
7.5 Summary and Additional Problems, 390
8 Counting with Symmetries 393
8.1 Introduction, 393
8.2 Algebraic Discoveries, 394
8.3 Burnside’s Lemma, 407
8.4 The Cycle Index and P´olya’s Method of Enumeration, 417
8.5 Summary and Additional Problems, 430
References, 432
PART III NOTATIONS INDEX, APPENDICES, AND SOLUTIONS TO SELECTED ODD PROBLEMS
Index of Notations 435
Appendix A Mathematical Induction 439
A.1 Principle of Mathematical Induction, 439
A.2 Principle of Strong Induction, 441
A.3 Well Ordering Principle, 442
Appendix B Searching the Online Encyclopedia of Integer Sequences (OEIS) 443
B.1 Searching a Sequence, 443
B.2 Searching an Array, 444
B.3 Other Searches, 444
B.4 Beginnings of OEIS, 444
Appendix C Generalized Vandermonde Determinants 445
Hints, Short Answers, and Complete Solutions to Selected Odd Problems 449
INDEX 467

The Music of Reason: Experience the Beauty of Mathematics Through Quotations

Theoni Pappas

Wide World Publishing | 1995 | 145 páginas | pdf | 3,3 Mb

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ContentsMathematics 1
Mathematics & Imagination 16
Mathematics & Humor 26
Mathematicians 32
Mathematics & the Arts 40
Mathematics & Infinity 4&
Mathematics & History 56
Mathematics & Nature 64
Keality, Truth & Mathematics 74
Numbers 86
Logic, Intuition, & Thought 96
Mathematics & the Universe 106
Mathematical Things 116
Mathematics & the Sciences 124
Computers 130
Epilogue 138
about the author 139

Livro relacionado:

Mathematically speaking : a dictionary of quotations por Carl C Gaither; Alma E Cavazos-Gaither; Idioma: Inglês   Editora: Bristol ; Philadelphia : Institute of Physics Pub., ©1998.

Mathematical Achievements of Pre-modern Indian Mathematicians

T.K Puttaswamy

Elsevier | 2012 | 768 páginas | rar - pdf |2,2 Mb 

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Mathematics in India has a long and impressive history. Presented in chronological order, this book discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic period (800 B.C.) to the 17^th Century of the Christian era. These contributions range across the fields of Algebra, Geometry and Trigonometry. The book presents the discussions in a chronological order, covering all the contributions of one Pre-Modern Indian Mathematician to the next. It begins with an overview and summary of previous work done on this subject before exploring specific contributions in exemplary technical detail. This book provides a comprehensive examination of pre-Modern Indian mathematical contributions that will be valuable to mathematicians and mathematical historians.

• Contains more than 160 original Sanskrit verses with English translations giving historical context to the contributions

• Presents the various proofs step by step to help readers understand

• Uses modern, current notations and symbols to develop the calculations and proofs

Contents
Preface
Foreword
Introduction
1 A Glance at Ancient India and the Decimal System of Numeration
2 The Sulvasutras
3 Mathematics of Jains
4 The Bakshali Manuscript
5 Aryabhata I
6 Varahamihira and Bhaskara I
7 Brahmagupta
8 Sridhara and Prthudakaswami Caturveda
9 Mahavira
10 Aryabhata II and Sripati
11 Bhaskara II
12 Narayana Pandita
13 Kerala Astronomers
14 Sixteenth and Seventeenth Century Commentators of Bhaskara II
Appendix
Bibliography

 

International Perspectives on Gender and Mathematics Education

Helen J. Forgasz, Joanne Rossi Becker e Kyeong-Hwa Lee

Information Age Publishing | 2010 | 467 páginas | rar - pdf | 2,1 Mb

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A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the "boy problem," with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.

Contents
Section I History, Policy, and Non-School Factors
1 International Perspectives on Gender and Mathematics Education: An Overview...1
Joanne Rossi Becker, Helen Forgasz, Olof Bjorg Steinthorsdottir, and Kyeong-Hwa Lee
Section I History, Policy, and Non-School Factors
2 The Ladies’ Diary or Woman’s Almanack, 1704–1841..... 15
Teri Perl
3 Conversations of Parents and Children Working on Mathematics.... 33
Melfried Olson, Judith Olson, Claire Okazaki, and Thuy La
4 Out-of-School-Time (OST) Programs as Mathematics Support for Females.. 55
Lynda R. Wiest
5 Freedom to Choose?: Girls, Mathematics and the Gendered Construction of Mathematical Identity... 87
Fiona Walls
6 Gender Mainstreaming: Maintaining Attention on Gender Equality...111
Colleen Vale
Section II National Focus
7 Studies in Mexico on Gender and Mathematics...... 147
Sonia Ursini, Martha P. Ramírez, and Claudia Rodríguez, María Trigueros, and Ma. Dolores Lozano
8 Gender Differences When Working with Algebraic Variables: A Study with Mexican Secondary School Students.... 173
Carolina Rubí Real Ortega and Sonia Ursini
9 Factors Contributing to Gender Differences in Mathematics Performance of United States High School Students....203
Pamela L. Paek
10 Gender Differences in Mathematics Achievement: Evidence from Regional and International Student Assessments.... 225
Xin Ma
11 Mathematics Achievement in Icelandic Playschools: Examining When Gender Differences Emerge..... 249
Olof Bjorg Steinthorsdottir, Kimberly Dadisman, Dylan L. Robertson, and Kristjana Steinthorsdottir
12 Mathematics Teacher Education and Gender Effects... 263
Sigrid Blömeke and Gabriele Kaiser
Section III High Achievers
13 Discovering the Potential of Gifted Females in Mathematics.... 287
Kyeong-Hwa Lee, Eun-Jung Lee, Seoung-Hey Paik, and HeiSook Lee
14 Gender and High Achievers in Mathematics: Who and What Counts?.... 315
Gilah C. Leder and Helen J. Forgasz
15 What Are High Achieving Young Women’s Perceptions of Mathematics Over Time?.... 341
Amanda Lambertus, Susan Bracken, and Sarah Berenson
Section IV Tertiary Students
16 The Influence of High School and University Experiences on Women’s Pursuit of Undergraduate Mathematics Degrees in Canada......365
Jennifer Hall
17 Try and Catch the Wind: Women Who Do Doctorates at a Mature Stage in Their Lives.... 391
Ansie Harding, Leigh Wood, and Michelle Muchatuta With Barbara Edwards, Lucia Falzon, Sibba Gudlaugsdottir, Belinda Huntley, Jillian Knowles, Barbara Miller-Reilly,and Tobia Steyn
18 Recognizing Gender in Mathematics Relationships: A Relational Counseling Approach Helps Teachers and Students Overcome Damaging Perceptions..... 421
Jillian M. Knowles
Contributors.......451