Leveled Texts for Mathematics: Number and Operations

Lori Barker

Shell Education | 2011 | 147 páginas | rar - pdf | 5,42 Mb


link (password : matav)


With a focus on number and operations, this resource provides the know-how to use leveled texts to differentiate instruction in mathematics. A total of 15 different topics are featured in and the high-interest text is written at four different reading levels with matching visuals. Practice problems are provided to reinforce what is taught in the passage. The included Teacher Resource CD features a modifiable version of each passage in text format and full-color versions of the texts and image files.

Table of Contents
What Is Differentiation?......4
How to Differentiate Using This Product......5
General Information About the Student Populations......6
Below-Grade-Level Students.........6
English Language Learners........6
On-Grade-Level Students.......7
Above-Grade-Level Students.........7
Strategies for Using the Leveled Texts........8
Below-Grade-Level Students......8
English Language Learners..... 11
Above-Grade-Level Students..... 14
How to Use This Product...... 16
Readability Chart... 16
Components of the Product..... 16
Tips for Managing the Product......... 18
Correlation to Mathematics Standards...... 19
Leveled Texts............ 21
Understanding Place Value to 6 Digits........ 21
Understanding Place Value to 10 Digits...... 29
Types of Numbers........ 37
Factors and Multiples....... 45
Comparing and Ordering Whole Numbers....... 53
Adding Large Numbers....... 61
Subtracting Large Numbers..... 69
Single-Digit Multiplication...... 77
Understanding Division..... 85
Two-Digit Multiplication.......... 93
Division with Two-Digit Divisors....... 101
Three- and Four-Digit Multiplication..... 109
Division with Three- and Four-Digit Divisors..... 117
Understanding Order of Operations...... 125
Estimation......... 133
Appendices........ 141
References Cited........ 141
Contents of Teacher Resource CD...... 142

Outros livros da mesma série:

Leveled texts for mathematics. Data analysis and probability por Stephanie Paris Idioma: Inglês   Editora: Huntington Beach, CA : Shell Education, ©2011.

Leveled texts for mathematics. Fractions, decimals, and percents por Lori Barker Idioma: Inglês   Editora: Huntington Beach, Calif. : Shell Education, 2011.

Leveled texts for mathematics. Geometry por Lori Barker Idioma: Inglês   Editora: Huntington Beach, Calif. : Shell Education, 2011.

Number Theory Through Inquiry

David C. Marshall, Edward Odell e Michael Starbird

 Mathematical Association of America | 2007 | 151 páginas | rar - pdf | 720 kb

link (password: matav)

Number Theory Through Inquiry; is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy ;Number Theory Through Inquiry.; Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and theydevelop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas. They develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

Contents0. Introduction;
1. Divide and conquer
2. Prime time
3. A modular world
4. Fermat's Little theorem and Euler's theorem
5. Public key cryptography
6. Polynomial congruences and primitive roots
7. The golden rule: quadratic reciprocity
8. Pythagorean triples, sums of squares, and Fermat's Last Theorem
9. Rationals close to irrationals and the Pell equation
10. The search for primes
Appendix A. Mathematical induction: the domino effect
Index.

Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games, Grades PreK-2

Jennifer Taylor-Cox

Routledge | 2009 | páginas | rar - pdf | 2,8 Mb

link (password: matav)

dmpbrockton.files.wordpress (link direto)

Useful for small groups or one-on-one instruction, this book offers successful math interventions and RTI connections. Teachers will learn to target math instruction to struggling students by:- Diagnosing weaknesses- Providing specific, differentiated instruction- Using formative assessments- Offering corrective feedback- Motivating students by using games
Taylor-Cox emphasizes four main goals for math instructors. They must help students achieve: accuracy, efficiency, flexibility, and fluency in solving math problems. Integral to each of these goals is ensuring that students understand math concepts. Taylor-Cox writes, "When concepts are ignored and the focus is solely on rules and procedures, struggling students often develop misconceptions and learning gaps." Math Interventions: Building Number Power, Grades PreK-2 provides math teachers with specific strategies for imparting those concepts.

Table of ContentsIntroduction .........1
What is Math Intervention? ..........1
Focus on Number Sense and Computation .......3
What Makes Math Intervention Successful? ....4
How to Use Formative Assessment ......8
Monitor Progress ......9
Reteach ........11
How to Use this Book ........11
Chapter One: Early Number Concepts ..........15
One-to-one Correspondence .......16
Rote Counting ..........20
Rational Counting ........23
Keeping Track ........27
Cardinality ........31
Conservation of Number......34
Subitizing .........38
Chapter Two: Numbers and Number Relationships Concepts ......45
Representing Numbers .....46
More and Less ......50
Equal and Unequal ........55
Composing and Decomposing Numbers .........59
Understanding Ten ...........64
Ordinal Numbers ..........69
Even and Odd .........74
Basic Place Value .............79
Basic Fractions .........84
Estimation ..............88
Chapter Three: Addition and Subtraction Concepts ......93
Total and Parts ..........94
Counting On and Counting Back ..........100
Joining Sets .............104
Number Line Profi ciency ...........107
Take Away Subtraction ...... 111
Missing Part Subtraction ....... 115
Comparison Subtraction .........118
Adding and Subtracting Tens ......122
Adding Doubles and Near Doubles ......125
Fact Families—Addition and Subtraction .......131
Partial Sums ......137
Partial Differences ........142
Near Tens for Addition and Subtraction .....147
Equal Differences .....152
References .........163

Help Your Kids with Math: A visual problem solver for kids and parents

 

Barry Lewis

DK Publishing | 2010 | 258 páginas | rar - pdf | 9,7 Mb

link (password : matav)

Studying math is often a source of great anxiety for children and also proves troublesome for parents helping with their homework.

Using uniquely accessible illustrated stress-free approach, Help Your Kids with Math looks at every aspect of math, from simple sums to simultaneous equations, and explains each facet in easily understandable language so that adults and kids can master the subject together.

In Help Your Kids with Math tricky concepts are explored and examined step-by-step, so that even the most math-phobic individual will be able to approach and solve complex problems with confidence.

Contents
NUMBERS
Introducing numbers ; Addition ; Subtraction ; Multiplication ; Division ; Prime numbers ; Units of measurement ; Positive and negative numbers ; Powers and roots ; Standard form ; Decimals in action; Fractions, Ratio and proportion, Percentages, Converting fractions, decimals, and percentages ; Mental math ; Rounding off ; Using a calculator ; Personal finance ; Business finance
GEOMETRY
What is geometry?; Angles; Straight lines; Symmetry; Coordinates; Vectors; Translations ; Rotations; Reflections; Enlargements; Scale drawings; Bearings; Constructions; Loci ; Triangles; Constructing triangles; Congruent triangles; Area of a triangle; Similar triangles ; Pythagorean Theorem ; Quadrilaterals; Polygons ; Circles ; Circumference and diameter ; Area of a circle ; Angles in a circle; Chords and cyclic quadrilaterals ; Tangents ; Arcs ; Sectors ; Solids ; Volumes ; Surface area 148
TRIGONOMETRY
What is trigonometry? ; Working with trigonometry ; Finding missing sides ; Finding missing angles 
ALGEBRA
What is algebra?; Sequences; Working with expressions; Expanding and factorizing expressions; Quadratic expressions; Formulas; Solving equations; Linear graphs; Simultaneous equations; Factorizing quadratic equations; The quadratic formula; Quadratic graphs ; Inequalities 
STATISTICS
What is statistics? ; Collecting and organizing data ; Bar charts ; Pie charts ; Line graphs;  Averages; Moving Averages ; Measuring spread ; Histograms ; Scatter diagrams 
PROBABILITY
What is probability? , Expectation and reality ; Multiple probability ; Dependent events ; Tree diagrams 
Reference section 232
Glossary 244
Index 252
Acknowledgments 256

Which Numbers are Real?

Michael Henle

The Mathematical Association of America |2012 | 230 páginas | rar - pdf | 1,23 Mb

link (password : matav)

The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and numbers that represent positions in games (surreal numbers). Each system has a well-developed theory with applications in other areas of mathematics and science. They all feature in active areas of research and each has unique features that are explored in this book. Alternative number systems reveal the central role of the real numbers and motivate some exciting and eccentric areas of mathematics. What Numbers Are Real? will be an illuminating read for anyone with an interest in numbers, but specifically for advanced undergraduates, graduate students and teachers of university-level mathematics.

Contents
I. The reals.
1 Axioms for the Reals
2 Construction of the reals
II. Multi-dimensional numbers.
3 The complex numbers
4 The quaternions
III. Alternative lines.
5 The constructive reals
6 The hyperreals
7 The surreals.

The Geometry of Numbers

 C. D. Olds, Anneli Lax and Giuliana P. Davidoff

The Mathematical Association of America | 2000 | 193 páginas | rar - pdf | 786 kb

link (password: matav)

djvu -3,5 Mb link

This is a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice points on lines, circles and inside simple polygons in the plane. A minimum of mathematical expertise is required beyond an acquaintance with elementary geometry. The authors gradually lead up to the theorems of Minkowski and others who succeeded him. On the way the reader will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres.

Contents
Lattice Points and Number Theory
An Introduction to the Geometry of Numbers
Gaussian Integers, by Peter D. Lax
The Closest Packing of Convex Bodies
Brief Biographies
Solutions and Hints.

The Glorious Golden Ratio

Alfred S. Posamentier e Ingmar Lehmann

Prometheus Books | 2011 | 363 páginas | rar - epub | 20 Mb

link (password: matav)

What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded.
Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.

Contents
Acknowledgments
Introduction
Chapter 1: Defining and Constructing the Golden Ratio
Chapter 2: The Golden Ratio in History
Chapter 3: The Numerical Value of the Golden Ratio and Its Properties
Chapter 4: Golden Geometric Figures
Chapter 5: Unexpected Appearances of the Golden Ratio
Chapter 6: The Golden Ratio in the Plant Kingdom
Chapter 7: The Golden Ratio and Fractals
Concluding Thoughts
Appendix: Proofs and Justifications of Selected Relationships
Notes
Index

The Number System

(Dover Books on Mathematics) 

 H. A. Thurston

 Dover Publications | 2007 | 144 páginas | rar - epub | 21 Mb

link (password : matav)

The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.
This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts.


CONTENTS
PART I - EXPLANATORY TREATMENT
CHAPTER I.—COUNTING
CHAPTER II.—WHOLE NUMBERS
CHAPTER III.—THE LAWS OF ARITHMETIC
CHAPTER IV.—FRACTIONS
CHAPTER V.—NEGATIVE NUMBERS
CHAPTER VI.—FIELDS
CHAPTER VII.—IRRATIONAL NUMBERS
CHAPTER VIII.—POWERS
CHAPTER IX—COMPLEX NUMBERS
CHAPTER X.—VERIFICATION OF THE AXIOMS
CHAPTER XI.—ALTERNATIVE TREATMENTS
PART II - SYSTEMATIC TREATMENT
CHAPTER A.—WHOLE NUMBERS: 1 Definition … 3-8 Addition … 9-16 Multiplication.
CHAPTER B.—HEMIGROUPS AND GROUPS: 1 Definition of hemigroup and dyad … 3-15 Properties of dyads … 16-21 Groups … 22 A hemigroup can be embedded in a group.
CHAPTER C.—INTEGERS: 1 Definition … 2-15 Addition … 16-22 Multiplication … 23 The integers contain the whole numbers … 24-31 Positive integers.
CHAPTER D.—FIELDS

Numbers Are Forever

 Liz Strachan

Constable | 2014 | 289 páginas | rar - epub | 873 kb

link (password: matav)

This book is only about numbers - that is, whole numbers and nothing but the whole numbers, which start from from 0, 1, 2, 3, 4... and go on forever. Here you can meet perfect numbers, happy numbers, lucky, untouchable, weird, narcissistic, evil and deficient numbers, not to mention nice Friedmans and multi-legged repunits, as well as primes and their cousins, the sexy primes. It is also full of fascinating facts and curios, prime number conjectures, the sieve of Eratosthenes, the Fibonacci series, and much more besides. This is an accessible, clearly explained approach which will appeal to recreational maths enthusiasts, puzzle solvers, and mathematicians of all ages.


Contents
Introduction; 
The Very Beginning Starts with Zero; 
Prime Numbers; 
Goldbach's Conjecture; 
1; 2; 
The Binary System; Square Numbers; 
Indices; 
Standard Form; 
A Twentieth-century Conjecture; 
3; 
Cubes and Cube Roots; 
Mersenne Numbers; 
Fermat's Last Theorem; 
4; 5; 
The Fibonacci Sequence; 
6; 
Perfect Numbers; 
7; 
Happy Numbers; 
8; A
 Review of Polygonal Numbers; 
Factorial!; 
∞; 
9; 11; 12; 
Abundant Numbers; 
Deficient Numbers; 
13; 
16 and the Luhn Algorithm; 
Leyland Numbers; 
17; 19; 27; 28; 29; 
30 and the Giuga Numbers; 
31; 37; 41; 
47, 497, 4997 et al. 
The Magic 48^2
70 and Other Weird Numbers; 
71; 74; 75; 81; 89; 97; 
Reciprocals; 
100; 
101 and Its Other Palindromic Pals; 
105; 109; 
112 and the Rest of the Family; 
118; 
The 123 Curiosity; 
127: De Polignac's Great Disappointment; 
132; 136; 144; 
Factorial Fun with 145; 
153 and the Narcissistic Numbers; 
The Friedman Numbers; 
197; 199; 
220 and Amicable Pairs; Pascal's Triangle; 
232, 233 and 234; 
2642 and Other Palindromic Squares; 
365; 512; 
561 and the Carmichael Numbers; 
593; 
642 and 643: The Amazing Difference between 2 Cubes; 
648 and the Other Members of the Club; 
666 703 and the Kaprekar Numbers 1000; 
The Effect of Multiplying by 1001; 
1033 and Other Constant Base Powers; 
1089; 
1138 Comes Full Circle After a 4th Power Journey; 
1233 and Special Relationships; 
1676; 
Harshad Numbers; 
Self Numbers; 
Ramanujan and the Taxi Cab Number 1729; 
Brocard's Problem; 
Lucky Numbers; 
1961; 
The Untouchables; 
2187 and Family Members; 
2519; 2592; 
The Amazing 2880; 
3367; 
435 and Münchhausen; 
4884, Palindrome by Reversal; 
4913; 
5777 and 5993 (2 Flies in the Ointment); 
9109; 
12,496 and the Sociable Set; 
19,937: 
A Circular Prime; 
27,594; 40,585; 
Easy Adding; 
142,857; 147,852 221,859510,510; 
2,646,798; 87,539,318 --Another Taxi Cab Number; 
Interesting 8-Digit Numbers; 
123,456,789; 
'Miracle' Numbers; 
One Billion (1,000,000,000); 
1,000,000,007; 
Postscript; 
Glossary

Mathematical Connections: A Companion for Teachers

(Classroom Resource Material) 

Al Cuoco

The Mathematical Association of America | 2005 | 261 páginas | pdf | 6,3 Mb

link
link1

This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self-study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book.

Contents
1. Difference tables and polynomial fits. Doing it with sums
Doing it with differences
Finding a formula: combinatorial polynomials
Making it formal: the [delta] operator
Going the other way: polynomials to tables
Conversions
From Newton to Lagrange
Agreeing to disagree
2. Form and function: the algebra of polynomials. Polynomials
The basic theorems
Coefficients and values
Up a level
Transformations
Coefficients and zeros.
3. Complex numbers, complex maps, and trigonometry. Complex numbers
The complex plane
The geometry behind multiplying
Trigonometric identities
Complex maps
Julia sets and the Mandelbrot set.
4. Combinations and locks. Combinatorial proofs and identities
The simplex lock
Some approaches to the simplex lock problem
Connections to the Mahler basis.
5. Sums of powers. Summatory polynomials
Bernoulli's method.

Mathematical Mysteries: the beauty and magic of numbers

 Calvin C. Clawson

Plenum Press | 1996 | 322 páginas | rar - pdf | 7,7 Mb

link (password: matav)

Why seemingly unrelated mathematical truths are connected in simple and beautiful equations continues to stump even mathematicians. This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician’s treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements,Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

CONTENTS
Introduction 1
CHAPTER 1 Discovery of the Number Sequence 8
CHAPTER 2 Numbers and the Occult 39
CHAPTER 3 Sequences and Series 53
CHAPTER 4 The Family of Numbers 77
CHAPTERS Story for a Rich Man 95
CHAPTER 6 Exotic Connections 116
CHAPTER 7 Closing in on the Primes 145
CHAPTER 8 Primes in Depth 164
CHAPTER 9 Primes and Secret Codes 184
CHAPTER 10 The Remarkable Ramanujan
CHAPTER 11 Ramanujan's Equations
CHAPTER 12 Goldbach's Conjecture
CHAPTER 13 Deepest Mysteries
CHAPTER 14 Into the Stratosphere
EndNotes
Suggested Reading
Index

Outros livros do mesmos autor:

Mathematical sorcery : revealing the secrets of numbers por Calvin C Clawson Idioma: Inglês   Editora: New York : Plenum, ©1999.

The mathematical traveler : exploring the grand history of numbers por Calvin C Clawson Idioma: Inglês   Editora: New York : Plenum Press, ©1994.

Children's Logical and Mathematical Cognition Progress in Cognitive Development Research

 C.J. Brainerd

Springer | 2011 - reprint of the original 1st ed. 1982 edition | páginas | pdf | 6,6 Mb

link

Contents
Chapter 1 Conservation - Nonconservation: Alternative Explanations .. 1
Curt Acredolo
Conservation and the Appreciation of an Identity Rule ....
Operational and Nonoperational Conservation .. 2
Nonconservation and the Overreliance on Perceptual Cues .... 4
Pseudononconservation .... 5
Nonoperational Conservation .... 14
Conclusions ....... 21
Future Research: The Development of the Identity Rule ..... 24
Reference Notes ..... 27
References ...... 27
Chapter 2 The Acquisition and Elaboration of the Number Word Sequence .... 33
Karen C. Fuson, John Richards, and Diane J. Briars
Acquisition of the Sequence .... 35
Elaboration of the Sequence ... 55
Conclusion ......... 89
Reference Notes ...... 89
References ..... 91
Chapter 3 Children's Concepts of Chance and Probability
Harry W. Hoemann and Bruce M. Ross
Piagetian Theory ... 94
Subsequent Studies .... 99
Theoretical Implications ... 116
References .... 120
Chapter 4 The Development of Quantity Concepts: Perceptual and Linguistic Factors .. 123
Linda S. Siegel
Linguistic Factors and the Development of Quantity Concepts ..... 123
A Taxonomy of Quantity Concepts .... 124
The Relationship between Language and Thought in the Child .... 128
Study 1: Concept versus Language ....... 129
Study 2: Does Language Training Facilitate Concept Acquisition? ... 132
Study 3: Visual versus Verbal Functions .... 138
Study 4: Training of Cognitive and Language Abilities ...... 140
Study 5: Cognitive Development of Children with Impaired Language Development ... 141
Study 6: The Abstraction of the Concept of Number ....... 144
Conclusion ........ 152
Reference Notes... 153
References ..... 153
Chapter 5 Culture and the Development of Numerical Cognition: Studies among the Oksapmin of Papua New Guinea ... 157
Geoffrey B. Saxe
Methodology and Cross-Cultural Number Research .... 158
The Oksapmin Community ..... 159
Studies on Numerical Cognition among the Oksapmin ... 160
Concluding Remarks
Chapter 6 Children's Concept Learning as Rule-Sampling Systems with Markovian Properties . 177
Charles J. Brainerd
Concept Learning as Rule Sampling ....179
Some Questions about Concept Learning ... 185
Some Experimental Evidence ...192
Remark ......202
Appendix ... 203
References .. 208
Index ..... 213

The Mathematical Traveler: Exploring The Grand History Of Numbers

Calvin C. Clawson

Springer | 1994 | 310 páginas | rar - pdf | 11,6 Mb

link (password: matav)

This classic work by Calvin Clawson examines the remarkable co-evolution of numbers and human culture. From the early clay beads and ropes that our ancestors used as primitive counting tools to the influence of fractals and complex number systems on chaos theory, The Mathematical Traveler takes us on a journey over continents and through time to discover how mathematics has become an integral part of our world. We stop at ancient Sumeria, China, Greece, Italy, and England, where we learn about the discovery of our current counting system, the golden mean, pi, irrational numbers, and other mathematical innovations. More than just an overview of the history of numbers, The Mathematical Traveler explores how the understanding of mathematics helped humanity to create the underpinnings of art, technology, economics, and science that shaped the world we live in today.

Contents
INTRODUCTION 1
CHAPTER 1 How Do We Count? 5
CHAPTER 2 Early Counting 19
CHAPTER 3 Counting in Other Species 37
CHAPTER 4 Ancient Numbers 49
CHAPTER 5 Chinese and New World Numbers 77
CHAPTER 6 Problems in Paradise 95
CHAPTER 7 The Negative Numbers 121
CHAPTER 8 Dealing with the Infinite 135
CHAPTER 9 Dedekind's Cut: Irrational Numbers 161
CHAPTER 10 Story of 'IT: Transcendental Numbers 181
CHAPTER 11 Expanding the Kingdom: Complex Numbers 207
CHAPTER 12 Really Big: Transfinite Numbers 223
CHAPTER 13 The Genius Calculators 233
CHAPTER 14 What Does It All Mean? 247
CHAPTER 15 Numbers: Past, Present, and Future 263
End Notes 281
Glossary 289
Bibliography 299
Index 3

Outro livro do mesmo autor:

Mathematical sorcery : revealing the secrets of numbers por Calvin C Clawson Idioma: Inglês   Editora: New York : Plenum, ©1999.

Leveled Texts for Mathematics: Fractions, Decimals, and Percents

 Lori Barker

Shell Education | 2011 | 147 páginas | rar -pdf | 58,4 Mb

link (password: matav)


With a focus on fractions, decimals, and percents, this resource provides the know-how to use leveled texts to differentiate instruction in mathematics. A total of 15 different topics are featured in and the high-interest text is written at four different reading levels with matching visuals. Practice problems are provided to reinforce what is taught in the passage

sample pages

Table of Contents
What Is Differentiation?..4
How to Differentiate Using This Product......5
General Information About the Student Populations.......6
Below-Grade-Level Students.....6
English Language Learners.....6
On-Grade-Level Students....7
Above-Grade-Level Students......7
Strategies for Using the Leveled Texts.......8
Below-Grade-Level Students....8
English Language Learners.. 11
Above-Grade-Level Students...... 14
How to Use This Product...... 16
Readability Chart...... 16
Components of the Product..... 16
Tips for Managing the Product... 18
Correlation to Standards...... 19
Leveled Texts.... 21
What Is a Fraction?...... 21
Fractions Have Their Place..... 29
Finding a Place for Decimals.... 37
Some Are More, Some Are Less...... 45
Different but the Same...... 53
As Simple as Possible.... 61
When It’s Greater Than One....... 69
Together or Apart....... 77
Thinking About Different Sizes..... 85
Multiplication and Division of Fractions..... 93
Addition and Subtraction of Decimals.... 101
Multiplying and Dividing Decimals...... 109
Fractions to Decimals....... 117
Understanding Percents.... 125
Fractions, Decimals, and Percents..... 133
Appendices...... 141
References Cited....... 141
Contents of Teacher Resource CD... 142

God Created The Integers: The Mathematical Breakthroughs that Changed History

Stephen Hawking

Running Press | 2007 | 1375 páginas | rar - pdf | 6,9 Mb


link (password: matav)

epub - 46 Mb
link
link1


Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

CONTENTS
Introduction xiii
EUCLID (C. 325BC–265BC)
His Life and Work 01
Selections from Euclid’s Elements
Book I: Basic Geometry—Definitions, Postulates, Common Notions; and Proposition 47, (leading up to the Pythagorean Theorem) 07
Book V: The Eudoxian Theory of Proportion—Definitions & Propositions 25
Book VII: Elementary Number Theory—Definitions & Propositions 63
Book IX: Proposition 20: The Infinitude of Prime Numbers 101
Book IX: Proposition 36: Even Perfect Numbers 102
Book X: Commensurable and Incommensurable Magnitudes 104
ARCHIMEDES (287BC–212BC)
His Life and Work 119
Selections from The Works of Archimedes
On the Sphere and Cylinder, Books I and II 126/168
Measurement of a Circle 194
The Sand Reckoner 200
The Methods 209
DIOPHANTUS (C. 200–284)
His Life and Work 241
Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra
Book II Problems 8–35 246
Book III Problems 5–21 255
Book V Problems 1–29 265
RENÉ DESCARTES (1596–1650)
His Life and Work 285
The Geometry of Rene Descartes 292
ISAAC NEWTON (1642–1727)
His Life and Work 365
Selections from Principia
On First and Last Ratios of Quantities 374
LEONHARD EULER (1707–1783)
His Life and Work 383
On the sums of series of reciprocals (De summis serierum reciprocarum) 393
The Seven Bridges of Konigsberg 400
Proof that Every Integer is A Sum of Four Squares 407
PIERRE SIMON LAPLACE (1749–1827)
His Life and Work 411
A Philosophical Essay on Probabilities 418
JEAN BAPTISTE JOSEPH FOURIER (1768–1830)
His Life and Work 519
Selection from The Analytical Theory of Heat
Chapter III: Propagation of Heat in an Infinite Rectangular Solid (The Fourier series) 528
CARL FRIEDRICH GAUSS (1777–1855)
His Life and Work 591
Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions)
Section III Residues of Powers 599
Section IV Congruences of the Second Degree 625
AUGUSTIN-LOUIS CAUCHY (1789–1857)
His Life and Work 663
Selections from Oeuvres complètes d’Augustin Cauchy
Résumé des leçons données à l’École Royale Polytechnique sur le calcul infinitésimal (1823), series 2, vol. 4
Lessons 3–4 on differential calculus 671
Lessons 21–24 on the integral 679
NIKOLAI IVANOVICH LOBACHEVSKY (1792–1856)
His Life and Work 813
Geometrical Researches on the Theory of Parallels 820
JÁNOS BOLYAI (1802–1860)
His Life and Work 743
The Science of Absolute Space 750
ÉVARISTE GALOIS (1811–1832)
His Life and Work 797
On the conditions that an equation be soluble by radicals 807
Of the primitive equations which are soluble by radicals 820
On Groups and Equations and Abelian Integrals 828
GEORGE BOOLE (1815–1864)
His Life and Work 835
An Investigation of the Laws of Thought 842
BERNHARD RIEMANN (1826–1866)
His Life and Work 979
On the Representability of a Function by Means of a Trigonometric Series (Ueber die Darstellbarkeit eine Function durch einer trigonometrische Reihe) 992
On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypothesen, welche der Geometrie zu Grunde liegen) 1031
On the Number of Prime Numbers Less than a Given Quantity (Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse) 1042
KARL WEIERSTRASS (1815–1897)
His Life and Work 1053
Selected Chapters on the Theory of Functions, Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857
§ 7 Gleichmässige Stetigkeit (Uniform Continuity) 1060
RICHARD DEDEKIND (1831–1916)
His Life and Work 1067
Essays on the Theory of Numbers 1072
GEORG CANTOR (1848–1918)
His Life and Work 1131
Selections from Contributions to the Founding of the Theory of Transfinite Numbers
Articles I and II 1137
HENRI LEBESGUE (1875–1941)
His Life and Work 1207
Selections from Integrale, Longeur, Aire (Intergral, Length, Area) Preliminaries and Integral 1212
KURT GÖDEL (1906–1978)
His Life and Work 1555
On Formally Undecidable Propositions of Principia Mathematica and Related Systems 1263
ALAN TURING (1912–1954)
His Life and Work 1285
On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society 1293