Child's Construction of Quantities

Jean Piaget 

Routledge | 1998 | 292 páginas | rar - pdf |4,8 Mb

link (password: matav)

Contents
PART I CONSERVATION
The Conservation of Matter and Deformations of a Ball of Modelling Clay 3
2 The Conservation of Weight upon Deformations ofa Clay Ball 22
3 The Conservation of Volume at Equal Concentrations of Matter 47
PART II FROM CONSERVATION TO ATOMISM
4 The Destruction of Matter and the Dissolution of Sugar 67
5 The Conservation of the Sugar and the Beginning of Atomism 81
6 The Conservation of the Weight and Volume of the Dissolved Sugar and the Completion of Atomism 98
PART III COMPRESSION, DECOMPRESSION AND DENSITY
7 The Expansion of a Maize Seed and of a Column of Mercury 119
8 Differences in Density 137
9 Special Problems Posed by the Relationship between Weight and Quantity of Matter 154
PART IV FORMAL COMPOSITIONS
10 The Composition of Asymmetrical Relations and Differences in Weight 183
11 Simple and Additive Compositions of Equivalent Weights 203
12 Simple and Additive Compositions of Equivalent Volumes and the Discovery of the Displacement Law 232
Conclusion 269
Index 281

Basic Engineering Mathematics

John Bird

Routledge | 2014 - 6ª edição | 457 páginas | rar - pdf | 3,7 Mb

link (password: matav)

Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.

John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses.

This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,600 further questions contained within the practice exercises, and biographical information on the 25 famous mathematicians and engineers referenced throughout the book.

Foundation Maths: with MyMathLab

Anthony Croft e Robert Davison 

Prentice-Hall | 2006 - 4ª edição | 523 pages | PDF | 5,19 Mb

link

Foundation Maths has been written for students taking higher or further education courses, who have not specialised in mathematics on post-16 qualifications and need to use mathematical tools in their courses. It is ideally suited for those studying marketing, business studies, management, science, engineering, computer science, social science, geography, combined studies and design. It will be useful for those who lack confidence and need careful, steady guidance in mathematical methods. Even for those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study or distance learning.

Contents
Preface vii
Guided tour ix
Mathematical symbols xi
1 Arithmetic of whole numbers 1
2 Fractions 14
3 Decimal fractions 26
4 Sets 34
5 Percentage and ratio 46
6 Algebra 54
7 Indices 63
8 Number bases 78
9 Elementary logic 89
10 Simplifying algebraic expressions 100
11 Factorisation 108
12 Algebraic fractions 115
13 Transposing formulae 129
14 Solving equations 135
15 Sequences and series 146
16 Functions 161
17 Graphs of functions 174
18 The straight line 194
19 The exponential function 207
20 The logarithm function 216
21 Angles 234
22 Introduction to trigonometry 244
23 The trigonometrical functions and their graphs 252
24 Trigonometrical identities and equations 265
25 Solution of triangles 277
26 Matrices 294
27 Measurement 300
28 Gradients of curves 316
29 The product and quotient rules of differentiation 333
30 Integration and areas under curves 340
31 Integration by parts 357
32 Functions of more than one variable and partial differentiation 365
33 Tables and charts 382
34 Statistics 399
35 Probability 413
36 Correlation 422
37 Regression 437
Solutions 444
Index 520

Research on mathematical thinking of young children : six empirical studies

Leslie P. Steffe 

 National Council of Teachers of Mathematics | 1975 | 207 páginas | pdf | 3,2 Mb

online: ERIC

This volume includes reports of six studies of the thought processes of children aged four through eight. In the first paper Steffe and Smock outline a model for learning and teaching mathematics. Six reports on empirical studies are then presented in five areas of mathematics learning: (1) equivalence and order relations; (2) classification and seriation; (3) interdependence of classification, seriation, and number concepts; (4) Boolean Algebra; and (5) conservation and measurement. In a final chapter, the main findings of these papers are summarized and implications are discussed, with suggestions for further research.

Table of Contents
Introduction, Leslie P. Sleffe 1
I.On a Model for Learning and Teaching Mathematics, Leslie P. Sleffe and Charles D. Smock 4
II.Learning of Equivalence and Order Relations by Four- and Five-Year-Old Children, Leslie P. Sleffe and Russell L. Carey,19
III.Learning of Equivalence and Order Relations byDisadvantaged Five- and Six-Year-Old Children, Douglas T. Owens 47
IV.Learning of Classification and Seriation by Young Children, R Marlin L. Johnson 73
V.The Generalization of Piagetian Operations as It Relates to the Hypothesized Functional Interdependence between Classification, Seriation, and Number Concepts, Richard A. Lesh 94
VI.Learning of Selected Parts of a Boolean Algebra by Young Children, David C. Johnson 123
VII.The Performance of Mist- and Second -Grade Children on Liquid Conservation and Measurement Problems Employing Equivalence and Order Relations, Thomas P. Carpenter 145
Summary and Implications, Kennelh Lovell 171
References 191

Mathematical Interest Theory

Leslie Vaaler e James Daniel

Mathematical Association of America | 2008 -2ª edição | 493 páginas | rar - pdf | 2 Mb

link (password : matav)

Mathematical Interest Theory gives an introduction of how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. On the other hand, Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The content is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course. Mathematical Interest Theory includes more than 240 carefully worked examples. There are over 430 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to the Texas Instruments BA II Plus and BA II Plus Professional calculators can be used to efficiently solve the problems. This is important for readers wishing to pass the SOA/CAS joint financial mathematics exam FM/2. However, this part of the book can be skipped without disturbing the flow of the exposition

Contents
An introduction to the Texas Instruments BA II Plus
The growth of money
Equations of value and yield rates
Annuities (annuities certain)
Annuities with different payment and conversion periods
Loan repayment
Bonds
Stocks and financial markets
Arbitrage, term structure of interest rates, and derivatives
Interest rate sensitivity.

Statistics Explained

Perry R. Hinton

Routledge | 2014 - 3ª edição | 377 páginas | rar - pdf | Mb

link (password: matav)

Statistics Explained is an accessible introduction to statistical concepts and ideas. It makes few assumptions about the reader’s statistical knowledge, carefully explaining each step of the analysis and the logic behind it. The book:

• provides a clear explanation of statistical analysis and the key statistical tests employed in analysing research data
• gives accessible explanations of how and why statistical tests are used
• includes a wide range of practical, easy-to-understand worked examples

Building on the international success of earlier editions, this fully updated revision includes developments in statistical analysis, with new sections explaining concepts such as bootstrapping and structural equation modelling. A new chapter - ‘Samples and Statistical Inference’ - explains how data can be analysed in detail to examine its suitability for certain statistical tests.

The friendly and straightforward style of the text makes it accessible to all those new to statistics, as well as more experienced students requiring a concise guide. It is suitable for students and new researchers in disciplines including Psychology, Education, Sociology, Sports Science, Nursing, Communication, and Media and Business Studies.

Presented in full colour and with an updated, reader-friendly layout, this new edition also comes with a companion website featuring supplementary resources for students. Unobtrusive cross-referencing makes it the ideal companion to Perry R. Hinton’s SPSS Explained, also published by Routledge.

Perry R. Hinton has many years of experience in teaching statistics to students from a wide range of disciplines and his understanding of the problems students face forms the basis of this book.

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

Nerida Ellerton e M. A. (Ken) Clements

Springer | 2014 | 383 páginas | rar - pdf | 31 Mb

link (password: matav)

This well-illustrated book provides strong qualitative and comparative support for the main arguments developed by Nerida Ellerton and Ken Clements in their groundbreaking Rewriting this History of School Mathematics in North America 1607–1861: The Central Role of Cyphering Books. Eleven extraordinary handwritten school mathematics manuscripts are carefully analyzed—six were prepared entirely in Great Britain, four entirely in North America, and 1 partly in Great Britain and partly in North America. The earliest of the 11 cyphering books was prepared around 1630, and the latest in 1835. Seven of the manuscripts werearithmetic cyphering books; three were navigation cyphering books, and one was a mensuration/surveyingmanuscript.
One of the cyphering books examined in this book was prepared, over the period 1819–1826, by a young Abraham Lincoln, when he was attending small one-teacher schools in remote Spencer County, Indiana. Chapter 6 in this book provides the first detailed analysis of young Abraham’s cyphering book—which is easily the oldest surviving Lincoln manuscript. Another cyphering book, this one prepared by William Beattie in 1835, could have been prepared as a special gift for the King of England. The analyses make clear the extent of the control which the cyphering tradition had over school mathematics in North America and Great Britain between 1630 and 1840.
In their final chapter Ellerton and Clements identify six lessons from their research into the cyphering tradition which relate to present-day circumstances surrounding school mathematics. These lessons are concerned with sharp differences between intended, implemented and attained curricula, the remarkable value that many students placed upon their cyphering books, the ethnomathematical circumstances which surrounded the preparations of the extraordinary cyphering books, and qualitative differences between British and North American school mathematics.

Contents
Abstracts
Preface
Foreword
1 Cyphering Books and the Cyphering Tradition in North America and Great Britain, 1630–1880
2 Primitive Beginnings, Circa 1667
3 “Thomas Prust his Booke Amen 1702”
4 Daughters of the Revolution: Martha and Elisabeth Ryan’s Cyphering Book, Circa 1780
5 With a Tinge of Green: Mary Walters’ Cyphering Book, 1820
6 He would be Good: Abraham Lincoln’s Early Mathematics, 1819–1826
7 Sacrobosco’s Heritage: Thomas Dixson’s Cyphering Book, 1630–1632
8 Writing as if Arithmeticke: George Bickham’s Cyphering Book, Circa 1740
9 Bound for Botany Bay? Circa 179
10 From the Royal Mathematical School: Charles Page, 1825
11 Fit for a King? William Beattie, Circa 1810 and 1835–1836
12 Lessons from Extraordinary Cyphering Books
Author Biographies
Author Index
Subject Index