Mathematical cranks

Underwood Dudley 

The Mathematical Association of America | 1992 | páginas | djvu |4,6  Mb

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A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem); people who pray in matrices; people who find the American Revolution ruled by the number 57; people who have in common eccentric mathematical views, some mild (thinking we should count by 12s instead of 10s), some bizarre (thinking that second-order differential equations will solve all problems of economics, politics and philosophy). This is a truly unique book. It is written with wit and style and is a part of folk mathematics.

Contents
Introduction v 
Alphabet, Application of Pyramid Height to the 1 
American Revolution, The Role of 57 in the 4 
Applied Mathematics 9 
Base for the Number System, The Best - 20 
Bitterness, Cranks' 32 
Calculus, Celestial 38 
Cantor's Diagonal Process 40 
Congressional Record, Mathematics in the 46 
Constant Society, The 50 
Consultation, Lack of, of Cranks with Experts 53 
Crank, Case Study of a 55. 
Crank, The Making of a 67 
Deduction, The Joy of 78 
Duplication of the Cube 86 
Ellipse, Circumference of an 93 
Encouraging Cranks, The Folly of 97 
Equations, Solving 102 
Fermat's Last Theorem 105 
Fermat's Little Theorem 135 
Fifth Postulate, Euclid's 137 
Four-Color Theorem, The ." 159 
Godel's Theorem 167 
Goldbach Conjecture, The 171 
Greed 179 
Incomprehensibility of Crank's Works 182 
Infinity, Difficulties with 184 
Insanity 189 
Legislating Pi 192 
Linear Programming, Conspiracy Involving 198 
Magic Squares 200 
Mail, Crank 205 
Megalomania 208 
Money to be Made in Mathematics, Lack of 222 
Nines, Casting Out 226 
Nonagons, Regular 231 
Notation, Nonstandard 235 
Number Theory, The Lure of 239 
Perfect Numbers 242 
Phi 245 
Prayer, Matrix 251 
Primes, The Secret of the 254 
Primes, Twin, Existence of Infinitely Many 256 
Prolificity, Crank's 260 
Puzzle, A 269 
Pythagoreans, Neo- 271 
Pythagoreans, The Mystery of the 274 
Quadrature of the Circle 279 
Set Theory 322 
Signs, The Rule of 324 
Solution to a Puzzle 330 
Sphere, Philosophy of the 331 
Statistics, Parameter Estimation in 334 
Taxonomy, Mathematical 337 
Time, Wasted ....! 339 
Topology, Applied 341 
Trisection of the Angle 342 
Van der Pol's Equation 349 
Notes 353 

Index 363

Number words and number symbols a cultural history of numbers

Karl Menninger

Dover Publications Inc. | 1992 | 512 páginas | epub | 15 Mb

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Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.

A problem solving approach to mathematics for elementary school teachers

Rick Billstein, Shlomo Libeskind e Johnny W. Lott

 Pearson | 2012 - 11ª edição | 1042 páginas | rar - pdf | 30,4 Mb

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More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts—it also provides an invaluable reference to future teachers by including professional development features and discussions of today’s standards.

The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments. The Annotated Instructor’s Edition offers new Integrating Mathematics and Pedagogy (IMAP) video annotations, in addition to activity manual and e-manipulative CD annotations, to make it easier to incorporate active learning into your course. MyMathLab® is available to offer auto-graded exercises, course management, and classroom resources for future teachers.

Table of Contents
1. An Introduction to Problem Solving
1-1 Mathematics and Problem Solving
1-2 Explorations with Patterns
1-3 Reasoning and Logic: An Introduction
2. Numeration Systems and Sets
2-1 Numeration Systems
2-2 Describing Sets
2-3 Other Set Operations and Their Properties
3. Whole Numbers and Their Operations
3-1 Addition and Subtraction of Whole Numbers
3-2 Algorithms for Whole-Number Addition and Subtraction
3-3 Multiplication and Division of Whole Numbers
3-4 Algorithms for Whole-Number Multiplication and Division
3-5 Mental Mathematics and Estimation for Whole-Number Operations
4. Number Theory
4-1 Divisibility
4-2 Prime and Composite Numbers
4-3 Greatest Common Divisor and Least Common Multiple
Online Module: Clock & Modular Arithmetic
5. Integers
5-1 Integers and the Operations of Addition and Subtraction
5-2 Multiplication and Division of Integers
6. Rational Numbers and Proportional Reasoning
6-1 The Set of Rational Numbers
6-2 Addition, Subtraction, and Estimation with Rational Numbers
6-3 Multiplication and Division of Rational Numbers
6-4 Ratios, Proportions, and Proportional Reasoning
7. Decimals: Rational Numbers and Percent
7-1 Introduction to Decimals
7-2 Operations on Decimals
7-3 Nonterminating Decimals
7-4 Percents and Interest
8. Real Numbers and Algebraic Thinking
8-1 Real Numbers
8-2 Variables
8-3 Equations
8-4 Functions
8-5 Equations in a Cartesian Coordinate System
Online Module: Using Real Numbers in Equations
9. Probability
9-1 How Probabilities Are Determined
9-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities
9-3 Using Simulations in Probability
9-4 Odds, Conditional Probability, and Expected Value
9-5 Using Permutations and Combinations in Probability
10. Data Analysis/Statistics: An Introduction
10-1 Designing Experiments/Collecting Data
10-2 Displaying Data: Part I
10-3 Displaying Data: Part II
10-4 Measures of Central Tendency and Variation
10-5 Abuses of Statistics
11. Introductory Geometry
11-1 Basic Notions
11-2 Linear Measure
11-3 Curves, Polygons, and Symmetry
11-4 More About Angles
Online Module: Networks
12. Congruence and Similarity with Constructions
12-1 Congruence through Constructions
12-2 Other Congruence Properties
12-3 Other Constructions
12-4 Similar Triangles and Similar Figures
Online Module: Trigonometry Ratios via Similarity
13. Congruence and Similarity with Transformations
13-1 Translations and Rotations
13-2 Reflections and Glide Reflections
13-3 Dilations
13-4 Tessellations of the Plane
14. Area, Pythagorean Theorem, and Volume
14-1 Areas of Polygons and Circles
14-2 The Pythagorean Theorem, Distance Formula, and Equation of a Circle
14-3 Geometry in Three Dimensions
14-4 Surface Areas
14-5 Volume, Mass, and Temperature
Online Appendices
Spreadsheets
Graphing calculators
Geometer’s Sketchpad
GeoGebra

A request from Ramadan Badawi

More Mathematical Puzzles of Sam Loyd

Sam Loyd e Martin Gardner

Dover Publications | 1960 | 201 páginas | djvu | 3,9 Mb

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Gardner's second collection of amusing, thought-provoking problems and puzzles from Loyd's Cyclopedia — perhaps the most exciting collection of puzzles ever assembled in one volume. Arithmetic, algebra, speed and distance problems, game theory, counter and sliding block problems, similar topics. 166 problems.

Contents
Plane Geometry Problems
Geometrical Dissection Problems
Route, Tracing, and Topological Problems
Counter and Sliding Block Problems
Solid Geometry Problems 
Arithmetic and Algebraic Problems 
Speed and Distance Problems 

Game Theory Problems 

Operations Research Problems
Physics and Calculus Problems 

To mock a mockingbird

Raymond M. Smullyan 

Knopf | 1985 | 257 páginas | rar - epub | 2,11 Mb

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In this entertaining and challenging new collection of logic puzzles, Raymond Smullyan—author of What Is the Name of This Book? And The Lady or the Tiger?—continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.
In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell the truth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle (a puzzle about a puzzle), in which Inspector Craig of Scotland Yard gets involved in a search of the Fountain of Youth on the Island of Knights and Knaves.
In the second and larger section, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and—thanks to Gödel’s famous theorem—the final revelation.
To Mock a Mockingbird will delight all puzzle lovers—the curious neophytes as well as the serious students of logic, mathematics, or computer science.

Contents
Other Books by This Author
Title Page
Copyright
Dedication
Acknowledgments
Preface
PART I · LOGIC PUZZLES
1 The Prize—and Other Puzzles
2 The Absentminded Logician
3 The Barber of Seville
4 The Mystery of the Photograph
PART II · KNIGHTS, KNAVES, AND THE FOUNTAIN OF YOUTH
5 Some Unusual Knights and Knaves
6 Day-Knights and Night-Knights
7 Gods, Demons, and Mortals
8 In Search of the Fountain of Youth
PART III · TO MOCK A MOCKINGBIRD
9 To Mock a Mockingbird
10 Is There a Sage Bird?
11 Birds Galore
12 Mockingbirds, Warblers, and Starlings
13 A Gallery of Sage Birds
PART IV · SINGING BIRDS
14 Curry’s Lively Bird Forest
15 Russell’s Forest
16 The Forest Without a Name
17 Gödel’s Forest
PART V · THE MASTER FOREST
18 The Master Forest
19 Aristocratic Birds
20 Craig’s Discovery
PART VI · THE GRAND QUESTION!
21 The Fixed Point Principle
22 A Glimpse into Infinity
23 Logical Birds
24 Birds That Can Do Arithmetic
25 Is There an Ideal Bird?
Epilogue
Who’s Who Among the Birds

Mathematical reasoning for elementary teachers

 Calvin T. Long, Duane W. DeTemple e Richard S. Millman

Pearson | 2011 -6ª edição |  949 páginas | rar - pdf | 21,5 Mb

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Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on whyfuture teachers are learning the content as well as when and how they will use it in the classroom. The Sixth Edition has been streamlined to make it easier to focus on the most important concepts. The authors continue to make the course relevant for future teachers, including the new features like Examining School Book Pages, as well as the hallmark features like Into the Classroom discussions and Responding to Students questions. Activities, classroom videos, and resources for professional development for future teachers are also available at www.pearsonhighered.com/teachingmath

Table of Contents
1. Thinking Critically
1.1 An Introduction to Problem Solving
1.2 Pólya's Problem-Solving Principles
1.3 More Problem-Solving Strategies
1.4 Algebra as a Problem-Solving Strategy
1.5 Additional Problem-Solving Strategies
1.6 Reasoning Mathematically
2. Sets and Whole Numbers
2.1 Sets and Operations on Sets
2.2 Sets, Counting, and the Whole Numbers
2.3 Addition and Subtraction of Whole Numbers
2.4 Multiplication and Division of Whole Numbers
3. Numeration and Computation
3.1 Numeration Systems Past and Present
3.2 Nondecimal Positional Systems
3.3 Algorithms for Adding and Subtracting Whole Numbers
3.4 Algorithms for Multiplication and Division of Whole Numbers
3.5 Mental Arithmetic and Estimation
4. Number Theory
4.1 Divisibility of Natural Numbers
4.2 Tests for Divisibility
4.3 Greatest Common Divisors and Least Common Multiples
5. Integers
5.1 Representations of Integers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers
6. Fractions and Rational Numbers
6.1 The Basic Concepts of Fractions and Rational Numbers
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions
6.4 The Rational Number System
7. Decimals, Real Numbers, and Proportional Reasoning
7.1 Decimals and Real Numbers
7.2 Computations with Decimals
7.3 Proportional Reasoning
7.4 Percent
8. Algebraic Reasoning and Connections with Geometry
8.1 Algebraic Expressions, Functions, and Equations
8.2 Graphing Points, Lines, and Elementary Functions
8.3 Connections Between Algebra and Geometry
9. Geometric Figures
9.1 Figures in the Plane
9.2 Curves and Polygons in the Plane
9.3 Figures in Space
9.4 Networks
10. Measurement: Length, Area, and Volume
10.1 The Measurement Process
10.2 Area and Perimeter
10.3 The Pythagorean Theorem
10.4 Surface Area and Volume
11. Transformations, Symmetries, and Tilings
11.1 Rigid Motions and Similarity Transformations
11.2 Patterns and Symmetries
11.3 Tilings and Escher-like Designs
12. Congruence, Constructions, and Similarity
12.1 Congruent Triangles
12.2 Constructing Geometric Figures
12.3 Similar Triangles
13. Statistics: The Interpretation of Data
13.1 Organizing and Representing Data
13.2 Measuring the Center and Variation of Data
13.3 Statistical Inference
14. Probability
14.1 Experimental Probability
14.2 Principles of Counting
14.3 Permutations and Combinations
14.4 Theoretical Probability
Appendices
A. Manipulatives in the Mathematics Classroom
B. Getting the Most out of Your Calculator
C. A Brief Guide to the Geometer's Sketchpad
D. Resources

Women and Mathematics: Balancing the Equation

Susan F. Chipman, Lorelei R. Brush e Donna M. Wilson

Psychology Press | 1985 | 396 páginas | rar - pdf | Mb

link (password: matav)

Contents
Foreword
1. Women’s Participation in Mathematics: Outlining the Problem
Susan F. Chipman and Veronica G. Thomas
2. Project TALENT: Mathematics Course Participation in the 1960s and its Career Consequences
Lauress L. Wise
3. A National Assessment of Participation and Achievement of Women in Mathematics
Jane M. Armstrong
4. Self-Perceptions, Task Perceptions, Socializing Influences, and the Decision to Enroll in Mathematics Jacquelynne Eccles (Parsons), Terry F. Adler, Robert Futterman, Susan B. Goff, Caroline M. Kaczala, Judith L. Meece, and Carol Midgley
5. Cognitive and Affective Determinants of Course Preferences and Plans
Lorelei ft. Brush
6. Visual-Spatial Skill: Is it Important for Mathematics? Can it be Taught?
Jane M. Connor and Lisa A. Serbin
7. The Influence of Sex-Role Stereotyping on Women’s
Attitudes and Achievement in Mathematics
Sally L. Boswell
8. School, Classroom, and Home Influences on Women’s Decisions to Enroll in Advanced Mathematics Courses
Jane Stallings
9. Factors Related to Young Women’s Persistence and Achievement in Advanced Placement Mathematics
Patricia L. Casserly and Donald Rock
10. The Impact of Early Intervention Programs Upon Course-Taking and Attitudes in High School
Lynn H. Fox, Linda Brody, and Dianne Tobin
11. Understanding Mathematics Course Enrollment and Mathematics Achievement: A Synthesis of the Research
Susan F. Chipman and Donna M. Wilson
12. Strategies to Increase Mathematics Enrollments
Alma Lantz
References
Author Index
Subject Index 375