International Mathematical Olympiads 1959-1977

(New Mathematical Library)
Samuel L. Greitzer

Mathematical Association of America (MAA) | 1979 | 204 páginas | rar - pdf | 7,2 Mb

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The International Olympiad has been held annually since 1959; the U.S. began participating in 1974, when the Sixteenth International Olympiad was held in Erfurt, G.D.R.
In 1974 and 1975, the National Science Foundation funded a three week summer training session with Samuel L. Greitzer of Rutgers University and Murray Klamkin of the University of Alberta as the U.S. teams' coaches. Summer training sessions in 1976, 1977 were funded by grants from the Army Research Office and Office of Naval Research. To date the U.S. teams have consistently placed among the top three national scores: second in 1974(the USSR was first), third in 1975 (behind Hungary and the G.D.R) and 1976 (behind the USSR and Great Britain) and first in 1977.
Members of U.S. team are selected from the 100 top scorers on the Annual High School Examinations (see NML vols. 5, 17, 25) by subsequent competition in the U.S. Mathematical Olympiad.
In this volume the demonstrably effective coach and prime mover in planning the participation of the U.S.A. in the I.M.O., Samuel L. Greitzer, has compiled all the IMO problems from the First through the Nineteenth (1977) IMO and their solutions, some based on the contestants' papers.
The problems ae solvable by methods accessible to secondary school students in most nations, but insight and ingenuity are often required. A chronological examination of the questions throws some light on the changes and trends in secondary school mathematics curricula.

Five Hundred Mathematical Challenges

Edward J. Barbeau

The Mathematical Association of America | 1997 | 238 | rar - pdf | 1,5 Mb

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The organization of the book makes it a superb pedagogical instrument... Throughout the book are interspersed fables concerning mathematicians and occasional "bons mots." They are wonderful...The book is a paperback, done in a large elegantly printed format. I suggest you try it out on some of your talented undergraduate students. — The Mathematical Intelligencer

The book is an excellent source of problems for high school or college teachers who wish to challenge mathematically oriented students. The problems cover a wide range of topics, including geometry, algebra, number theory, trigonometry, probability and combinatorics...I recommend this book highly for mathematics teachers as a source of nontrivial precalculus problems. — AAAS, Science Books and Films

This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied.

Teachers at both the college and secondary levels will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques.

This collection provides a solid base for students who wish to enter competitions at the Olympiad level. They can begin with easy problems and progress to more demanding ones. A special mathematical tool chest summarizes the results and techniques needed by competition-level students.

Robert Recorde: The Life and Times of a Tudor Mathematician

Gareth Roberts e Fenny Smith
University of Wales Press | 2012 | 252 páginas | rar - pdf |3 Mb

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Robert Recorde was the first person to write an original book on arithmetic in English, rather than in the then-standard Latin or Greek—and thus the first to write about math in a way that ordinary people could understand. He was, in effect, the first mathematics teacher in the English-speaking world. This biography, which provides a comprehensive overview of Recorde’s life and work, traces the major influences on his study and his writing and charts his contribution to the development of mathematical and scientific thinking in Europe.


Contents 
List of illustrations vii
Notes on contributors ix
Acknowledgements xi
Preface xiii
Editorial conventions xvii
Introduction 1
1 The lives and works of Robert Recorde 7
Jack Williams
2 Robert Recorde and his remarkable Arithmetic 25
John Denniss and Fenny Smith
3 Recorde and The Vrinal of Physick: context, uroscopy and the practice of medicine 39
Margaret Pelling
4 The Pathway to Knowledg and the English Euclidean tradition 57
Jacqueline Stedall
5 The Castle of Knowledge: astronomy and the sphere 73
Stephen Johnston
6 The Whetstone of Witte: content and sources 93
Ulrich Reich
7 The Welsh context of Robert Recorde 123
Nia M. W. Powell
8 Commonwealth and Empire: Robert Recorde in Tudor England 145
Howell A. Lloyd
9 Data, computation and the Tudor knowledge economy 165
John V. Tucker
Appendix : From Recorde to relativity: a speculation 189
Gareth Wyn Evans
Bibliography 201
Index 219

Infinite ascent : a short history of mathematics

David Berlinski

Modern Library | 2008 | 224 páginas | epub | 2,63 Mb

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In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure.
Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt.
The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors. 

CONTENTS
1 Number
2 Proof
3 Analytic Geometry
4 The Calculus
5 Complex Numbers
6 Groups
7 Non-Euclidean Geometry
8 Sets
9 Incompleteness
10 The Present
About the Author

Outros livros do mesmo autor:

The king of infinite space : Euclid and his Elements por David Berlinski Idioma: Inglês   Editora: New York : Basic Books, [2013]

One, two, three : absolutely elementary mathematics por David Berlinski Idioma: Inglês   Editora: New York : Pantheon Books, ©2011.

Calculator Puzzles, Tricks and Games

Norvin Pallas

Sterling Pub. Co | 1976 | 98 páginas | djvu | 98 páginas

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Perform amazing feats of mathematical magic, answer clever riddles, and much more with this book and a handy pocket calculator. Scores of brain-teasers, puzzles, mathematical oddities, games, and recreations to fill dozens of hours with fun and excitement. Answers to problems.

Contents
Introduction 5
Upside-Down Displays 8
A Few Lines About Nines 10
Sports Figures 12
Hit It! 13
ESP 14
Making Allowances 18
Calculator Mathemetrics .20
Treasure Hunt 25
The Root of the Matter 26
Explosion! 28
Strictly for Squares 29
More Upside-Down Displays 30
Three Complementary Lessons 32
Subtraction . . . Addition . . . Division
Family Finances 35
Shopping Spree 36
The Calculator Murders 39
The Minotaur 40
Much Ado About Decimals 43
Problems to Tax You 46
Timely Problems 47
Magicalculations 48
Climbing the Corporate Calculadder 53
Problems of Interest 57
Home Improvements 58
Calculated Risk 60
More Magicalculations 62
Where There's a Will 64
Oranges and Doughnuts 66
What Is Going On Inside? 68
Fuelish Figures 71
Peasant Multiplication 72
Car-ful Calculations 74
Answers 76
Index 96

Early Mathematics Learning Selected Papers of the POEM 2012 Conference

Ulrich Kortenkamp, Birgit Brandt, Christiane Benz e Götz Krummheuer 

Springer | 2014 | 321 páginas | rar - pdf | 4,9 Mb

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​This book will gather current research in early childhood mathematics education. A special focus will be the tension between instruction and construction of knowledge. The book includes research on the design of learning opportunities, the development of mathematical thinking, the impact of the social setting and the professionalization of nursery teachers.​

Contents
Part I Introduction
1 Introduction 3
Christiane Benz, Birgit Brandt, Ulrich Kortenkamp, Götz
Krummheuer, Silke Ladel and Rose Vogel
2 A Dance of Instruction with Construction in Mathematics Education  9
Norma Presmeg
Part II  Case Studies
3 It is quite confusing isn’t it?  21
Judy Sayers and Patti Barber
4 Mathematical Teaching Moments: Between Instruction and Construction  37
Troels Lange, Tamsin Meaney, Eva Riesbeck and Anna Wernberg
5 “I have a little job for you”  55
Birgit Brandt
6  The Relationship between Cultural Expectation and the Local Realization of a Mathematics Learning Environment 71
Götz Krummheuer
7 The Reflection of Spatial Thinking on the Interactional Niche in the Family  85
Ergi Acar Bayraktar
Part III Children’s Constructions
8 The Roots of Mathematising in Young Children’s Play  111
Bert van Oers
9 Non-canonical Solutions in Children-Adult Interactions—A Case Study of the Emergence of Mathematical Creativity 125
Melanie Münz
10 The Interplay Between Gesture and Speech: Second Graders Solve Mathematical Problems 147
Melanie Huth
11 Children’s Constructions in the Domain of Geometric Competencies (in Two Different Instructional Settings) 173
Andrea Simone Maier and Christiane Benz
12 Identifying quantities—Children’s Constructions to Compose Collections from Parts or Decompose Collections into Parts  189
Christiane Benz
Part IV Tools and Interaction
13 Children’s Engagement with Mathematics in Kindergarten Mediated by the Use of Digital Tools 207
P.S. Hundeland, M. Carlsen and I. Erfjord
14 Mathematical Situations of Play and Exploration as an Empirical Research Instrument 223
Rose Vogel
15 Number Concepts—Processes of Internalization and Externalization by the Use of Multi-Touch Technology 237
Silke Ladel and Ulrich Kortenkamp
Part V Intervention
16 Intentional Teaching: Integrating the Processes of Instruction and Construction to Promote Quality Early Mathematics Education 257
Jie-Qi Chen and Jennifer McCray
17 Professionalization of Early Childhood Educators with a Focus on Natural Learning Situations and Individual Development of Mathematical Competencies: Results from an Evaluation Study  275
Hedwig Gasteiger
18 Employing the CAMTE Framework: Focusing on Preschool Teachers’ Knowledge and Self-efficacy Related to Students’ Conceptions  291
Pessia Tsamir, Dina Tirosh, Esther Levenson, Michal Tabach and Ruthi Barkai
19 Early Enhancement of Kindergarten Children Potentially at Risk in Learning School Mathematics—Design and Findings of an Intervention Study  307
Andrea Peter-Koop and Meike Grüßing

The mathematics of harmony : from Euclid to contemporary mathematics and computer science

 (Series on Knots and Everything)

 Alexey Stakhov e Scott Olsen

World Scientific Publishing Company | 2009 | 745 páginas | pdf | 8 Mb

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This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has its origins in "The Elements" of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the "golden" algebraic equations, the generalized Binet formulas, Fibonacci and "golden" matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and "golden" matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

Contents
Three "key" problems of mathematics on the stage of its origin
Classical golden mean, Fibonacci numbers, and platonic solids
The golden section
Fibonacci and Lucas numbers
Regular polyhedrons
Mathematics of harmony
Generalizations of Fibonacci numbers and the golden mean
Hyperbolic Fibonacci and Lucas functions
Fibonacci and golden matrices
Application in computer science
Algorithmic measurement theory
Fibonacci computers
Codes of the golden proportion
Ternary mirror-symmetrical arithmetic
A new coding theory based on a matrix approach 
Dirac's principle of mathematical beauty and the mathematics of harmony : clarifying the origins and development of mathematics
Appendix : Museum of harmony and the golden section.