Mathematical Connections: A Companion for Teachers

(Classroom Resource Material) 

Al Cuoco

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

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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

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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.

Child's Construction of Quantities

Jean Piaget 

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

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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

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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

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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

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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.