From Calculus to Computers Using the last 200 years of mathematics history in the classroom

(Mathematical Association of America Notes)

Amy Shell-Gellasch e Dick Jardine

The Mathematical Association of America | 2005 | 268 páginas | rar - pdf | 1,9 Mb

link (password: matav)

To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth- and twentieth-century mathematics, building on the earlier efforts but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines. From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Examples of topics covered are probability in undergraduate statistics courses, logic and programming for computer science, undergraduate geometry to include non-Euclidean geometries, numerical analysis, and abstract algebra.
Emphasizes mathematics history from the nineteenth and twentieth centuries
Provides ideas and material for immediate adoption in the classroom
Topics covered range from Galois theory to using the history of women and minorities in teaching

Table of Contents
Preface
Introduction
Part I. Algebra, Number Theory, Calculus, and Dynamical Systems:
1. Arthur Cayley and the first paper on group theory David J. Pengelley
2. Putting the differential back into differential calculus Robert Rogers
3. Using Galois' idea in the teaching of abstract algebra Matt D. Lunsford
4. Teaching elliptic curves using original sources Lawrence D'Antonio
5. Using the historical development of predator-prey models to teach mathematical modeling Holly P. Hirst
Part II. Geometry:
6. How to use history to clarify common confusions in geometry Daina Taimina and David W. Henderson
7. Euler on Cevians Eisso J. Atzema and Homer White
8. Modern geometry after the end of mathematics Jeff Johannes
Part III. Discrete Mathematics, Computer Science, Numerical Methods, Logic, and Statistics:
9. Using 20th century history in a combinatorics and graph theory class Linda E. MacGuire
10. Public key cryptography Shai Simonson
11. Introducing logic via Turing machines Jerry M. Lodder
12. From Hilbert's program to computer programming William Calhoun
13. From the tree method in modern logic to the beginning of automated theorem proving Francine F. Abeles
14. Numerical methods history projects Dick Jardine
15. Foundations of Statistics in American Textbooks: probability and pedagogy in historical context Patti Wilger Hunter
Part IV. History of Mathematics and Pedagogy:
16. Incorporating the mathematical achievements of women and minority mathematicians into classrooms Sarah J. Greenwald
17. Mathematical topics in an undergraduate history of science course David Lindsay Roberts
18. Building a history of mathematics course from a local perspective Amy Shell-Gellasch
19. Protractors in the classroom: an historical perspective Amy Ackerberg-Hastings
20. The metric system enters the American classroom:
1790-1890 Peggy Aldrich Kidwell
21. Some wrinkles for a history of mathematics course Peter Ross
22. Teaching history of mathematics through problems John R. Prather

Alternative Forms of Knowing (in) Mathematics: Celebrations of Diversity of Mathematical Practices

Swapna Mukhopadhyay e  Wolff-Michael Roth

Sense Publishers |  2012 | 321 páginas | pdf | 24 Mb

link


This book grew out of a public lecture series, Alternative forms of knowledge construction in mathematics, conceived and organized by the first editor, and held annually at Portland State University from 2006. Starting from the position that mathematics is a human construction, implying that it cannot be separated from its historical, cultural, social, and political contexts, the purpose of these lectures was to provide a public intellectual space to interrogate conceptions of mathematics and mathematics education, particularly by looking at mathematical practices that are not considered relevant to mainstream mathematics education. One of the main thrusts was to contemplate the fundamental question of whose mathematics is to be valorized in a multicultural world, a world in which, as Paolo Freire said, "The intellectual activity of those without power is always characterized asnon-intellectual". To date, nineteen scholars (including the second editor) have participated in the series. All of the lectures have been streamed for global dissemination at:http://www.media.pdx.edu/dlcmedia/events/AFK/. Most of the speakers contributed a chapter to this book, based either on their original talk or on a related topic. The book is divided into four sections dealing with: • Mathematics and the politics of knowledge • Ethnomathematics • Learning to see mathematically • Mathematics education for social justice.


CONTENTS
Preface vii
Contributors ix
Celebrating Diversity, Realizing Alternatives: An Introduction 1
Brian Greer, Swapna Mukhopadhyay, & Wolff-Michael Roth
PART I: MATHEMATICS AND POLITICS OF KNOWLEDGE 9
Introduction 11
1 Mathematics and Accounting in the Andes before and after the Spanish Conquest 17
Gary Urton
2 Contemporary Indigenous Education: Thoughts for American Indian Education in a 21st-Century World 33
Gregory Cajete
3 Crisis as a Discursive Frame in Mathematics Education Research and Reform: Implications for Educating Black Children
Delaina Washington, Zayoni Torres, Maisie Gholson, & Danny Bernard Martin
4 Whose Language is it? Reflections on Mathematics Education and Language Diversity from Two Contexts 71
Marta Civil & Núria Planas
PART II: ETHNOMATHEMATICS 91
Introduction 93
5 Consulting the Divine: The (Ethno)mathematics of Divination 97
John Kellermeier
6 Map-Making in São Paulo, Southern Brazil: Colonial History, Social Diversity, and Indigenous Peoples’ Rights 115
Mariana Leal Ferreira
7 Developing an Alternative Learning Trajectory for Rational Number Reasoning, Geometry, and Measuring based on Indigenous Knowledge 159
Jerry Lipka, Monica Wong, Dora Andrew-Ihrke, & Evelyn Yanez
8 In Seeking a Holistic Tool for Ethnomathematics: Reflections on Using Ethnomodeling as a Pedagogical Action for Uncovering Ethnomathematical Practices 183
Daniel Clark Orey & Milton Rosa
9 From Ethnomathematics to Ethnocomputing: Indigenous Algorithms in Traditional Context & Contemporary Simulation 205
Bill Babbitt, Dan Lyles, & Ron Eglash
PART III: LEARNING TO SEE MATHEMATICALLY 221
Introduction 223
10 The Work of Seeing Mathematically 227
Wolff-Michael Roth
11 Running the Numbers: A Conversation 247
Chris Jordan
12 To Know How to See: The Realities of Learning and Teaching Mathematics 261
Frank Swetz
PART IV: MATHEMATICS EDUCATION FOR SOCIAL JUSTICE 277
Introduction 279
13 Quantitative Form in Argument 283
Marilyn Frankenstein
14 Connecting Community, Critical, and Classical Knowledge in Teaching Mathematics for Social Justice 299
Rico Gutstein
Epilogue: Why Bother about Diversity of Mathematical Practices? 313

Swapna Mukhopadhyay, Wolff-Michael Roth, & Brian Greer

Introduction to Cultural Mathematics : With Case Studies in the Otomies and the Incas

Thomas E. Gilsdorf

 Wiley| 2012 | 307 páginas | rar - pdf |  6 Mb


link (password: matav)

Cultural mathematics, or ethnomathematics as it is also known, studies the relationship between mathematics and culture—with the ultimate goal of contributing to an appreciation of the connection between the two. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas integrates both theoretical and applied aspects of the topic, promotes discussions on the development of mathematical concepts, and provides a comprehensive reference for teaching and learning about multicultural mathematical practices.

This illuminating book provides a nontraditional, evidence-based approach to mathematics that promotes diversity and respect for cultural heritages. Part One covers such major concepts as cultural aspects of mathematics, numeration and number symbols, kinship relations, art and decoration, games, divination, and calendars. Part Two takes those concepts and applies them to fascinating case studies of both the Otomies of Central Mexico and the Incas of South America.

Throughout the book, numerous illustrations, examples, and motivational questions promote an interactive understanding of the topic. Each chapter begins with questions that encourage a cooperative, inquiry-based approach to learning and concludes with a series of exercises that allow readers to test their understanding of the presented material.

Introduction to Cultural Mathematics is an ideal book for courses on cultural mathematics, the history of mathematics, and cultural studies. The book is also a valuable resource and reference for anyone interested in the connections between mathematics, culture, anthropology, and history.

CONTENTS

PREFACE ix

INTRODUCTION xi

PART I GENERAL CONCEPTS

1 Understanding the Culture in Mathematics 3

2 Numeration Systems 24

3 Number Gestures and Number Symbols 39

4 Kinship and Social Relations 57

5 Art and Decoration 73

6 Divination 103

7 Games 123

8 Calendars 142

PART II - CASE STUDIES

9 Hñähñu Math: The Otomies 181

10 Tawantinsuyu Math: The Incas 211

HINTS TO SELECTED EXERCISES 253

A Mathematical Orchard: Problems and Solutions

(MAA Problem Book Series)

Mark I. Krusemeyer, George T. Gilbert e Loren C. Larson

The Mathematical Association of America | 2012 | 410 páginas | rar - pdf | 1,9 Mb

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This volume is a republication and expansion of the much-loved Wohascum County Problem Book, published in 1993. The original 130 problems have been retained and supplemented by an additional 78 problems. The puzzles contained within, which are accessible but never routine, have been specially selected for their mathematical appeal, and detailed solutions are provided. The reader will encounter puzzles involving calculus, algebra, discrete mathematics, geometry and number theory, and the volume includes an appendix identifying the prerequisite knowledge for each problem. A second appendix organises the problems by subject matter so that readers can focus their attention on particular types of problems if they wish. This collection will provide enjoyment for seasoned problem solvers and for those who wish to hone their skills.

• An entertaining collection of problems, tried and tested by experienced educators
• Detailed solutions are included and some problems are solved in multiple ways
• Accessible to those of advanced secondary school/high school level, through to undergraduate and above

Table of Contents
Preface
1. The problems
2. The solutions
Appendix 1. Prerequisites by problem number
Appendix 2. Problem numbers by subject
Index.

Journey through Mathematics Creative Episodes in Its History

Enrique A. González-Velasco

Springer | 2011| 478 páginas | pdf | 4,4 Mb

link direto
link

This book offers an accessible and in-depth look at some of the most  important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation.

The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.

TABLE OF CONTENTS
Preface ix
1 TRIGONOMETRY 1
1.1 The Hellenic Period 1
1.2 Ptolemy’s Table of Chords 10
1.3 The Indian Contribution 25
1.4 Trigonometry in the Islamic World 34
1.5 Trigonometry in Europe 55
1.6 From Viète to Pitiscus 65
2 LOGARITHMS 78
2.1 Napier’s First Three Tables 78
2.2 Napier’s Logarithms 88
2.3 Briggs’ Logarithms 101
2.4 Hyperbolic Logarithms 117
2.5 Newton’s Binomial Series 122
2.6 The Logarithm According to Euler 136
3 COMPLEX NUMBERS 148
3.1 The Depressed Cubic 148
3.2 Cardano’s Contribution 150
3.3 The Birth of Complex Numbers 160
3.4 Higher-Order Roots of Complex Numbers 173
3.5 The Logarithms of Complex Numbers 181
3.6 Caspar Wessel’s Breakthrough 185
3.7 Gauss and Hamilton Have the Final Word 190
4 INFINITE SERIES 195
4.1 The Origins 195
4.2 The Summation of Series 203
4.3 The Expansion of Functions 212
4.4 The Taylor and Maclaurin Series 220
5 THE CALCULUS 230
5.1 The Origins 230
5.2 Fermat’s Method of Maxima and Minima 234
5.3 Fermat’s Treatise on Quadratures 248
5.4 Gregory’s Contributions 258
5.5 Barrow’s Geometric Calculus 275
5.6 From Tangents to Quadratures 283
5.7 Newton’s Method of Infinit Series 289
5.8 Newton’s Method of Fluxions 294
5.9 Was Newton’s Tangent Method Original? 302
5.10 Newton’s First and Last Ratios 306
5.11 Newton’s Last Version of the Calculus 312
5.12 Leibniz’ Calculus: 1673–1675 318
5.13 Leibniz’ Calculus: 1676–1680 329
5.14 The Arithmetical Quadrature 340
5.15 Leibniz’ Publications 349
5.16 The Aftermath 358
6 CONVERGENCE 368
6.1 To the Limit 368
6.2 The Vibrating String Makes Waves 369
6.3 Fourier Puts on the Heat 373
6.4 The Convergence of Series 380
6.5 The Difference Quotient 394
6.6 The Derivative 401
6.7 Cauchy’s Integral Calculus 405
6.8 Uniform Convergence 407
BIBLIOGRAPHY 412

The Mathematics of Games and Gambling

Edward Packel

The Mathematical Association of America | 2006 - 2.ª edição| 190 páginas | rar - pdf | 880 kb

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password: matav


The first edition of this book was reprinted eight times! This book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, , blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing, etc.) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory. The Second Edition includes new material on: sports betting and the mathematics behind it; Game theory applied to bluffing in poker and related to the “Texas Holdem phenomenon”: The Nash equilibrium concept and its emergence in the popular culture: Internet links to games and to Java applets for practice and classroom use. The only formal mathematics background the reader needs is some facility with high school algebra. Game-related exercises are included at the end of most chapters for readers interested in working with and expanding ideas treated in the text. Solutions to some of the exercises appear at the end of the book.

Contents
Preface to the First Edition ix
Preface to the Second Edition xiii
1 The Phenomenon of Gambling 1
1.1 A selective history . . . 1
1.2 The gambler in fact and fiction . . . 5
2 Finite Probabilities and Great Expectations 13
2.1 The probability concept and its origins . . 13
2.2 Dice, cards, and probabilities  . . 15
2.3 Roulette, probability and odds. . 17
2.4 Compound probabilities: The rules of the game  . . 20
2.5 Mathematical expectation and its application .. . 22
2.6 Exercises  . . 26
3 Backgammon and Other Dice Diversions 29
3.1 Backgammon oversimplified  . . 29
3.2 Rolling spots and hitting blots  . . 32
3.3 Enteringand bearingoff .  . 34
3.4 The doubling cube  . . 36
3.5 Craps  . . 40
3.6 Chuck-a-Luck . . . 45
3.7 Exercises . . 47
4 Permutations, Combinations, and Applications 51
4.1 Careful counting: Is order important? . . 51
4.2 Factorials and other notation  . . 53
4.3 Probabilities in poker  . . 55
4.4 Betting in poker: A simple model  . . 59
4.5 Distributions in bridge  . . 67
4.6 Keno type games . . 71
4.7 Exercises . . 73
5 Play it Again Sam: The Binomial Distribution 79
5.1 Games and repeatedtrials . . 79
5.2 The binomial distribution . . 79
5.3 Beating the odds and the “law” of averages  . . 83
5.4 Betting systems  . . 90
5.5 A brief blackjack breakthrough. . 93
5.6 Exercises  . . 95
6 Elementary Game Theory 99
6.1 What isgame theory?  . . 99
6.2 Games in extensive form . . 100
6.3 Two-persongames in normal form  . . 105
6.4 Zero-sumgames . . 107
6.5 Nonzero-sum games, Nash equilibria and the prisoners’ dilemma  . 113
6.6 Simple n-persongames . . 118
6.7 Power indices. . 120
6.8 Games computers play  . . . 123
6.9 Exercises . . . 129
7 Odds and Ends 135
7.1 The mathematics of bluffing and the Texas Holdem invasion . . 135
7.2 Off to the races  . . 141
7.3 Lotteries and your expectation . . . 147
7.4 The gambler’s ruin  . 158

The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability

John Venn

Macmillan And Company | 1888

online:
archive.org
books.google

CHELSEA PUBLISHING | 1962 - 4ª edição 

online:
catalog.hathitrust.org

No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used for teaching elementary mathematics. In The Logic of Chance, he employs the same directness that makes his diagrams so effective.
The three-part treatment commences with an overview of the physical foundations of the science of probability, including surveys of the arrangement and formation of the series of probability; the origin or process of causation of the series; how to discover and prove the series; and the conception of randomness. The second part examines the logical superstructure on the basis of physical foundations, encompassing the measurement of belief; the rules of inference in probability; the rule of succession; induction; chance, causation, and design; material and formal logic; modality; and fallacies. The final section explores various applications of the theory of probability, including such intriguing aspects as insurance and gambling, the credibility of extraordinary stories, and approximating the truth by means of the theory of averages.