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.

Statistics Explained

Perry R. Hinton

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

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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

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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

Conned Again, Watson!, Cautionary Tales of Logic, Math, and Probability

 Colin Bruce

Perseus Publishing | 2000 | 290 páginas | pdf | 1,4 Mb

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In these cautionary tales of greedy gamblers, reckless businessmen, and ruthless con men, Sherlock Holmes uses his deep understanding of probability, statistics, decision theory, and game theory to solve crimes and protect the innocent.

Contents

Preface vii

Acknowledgments ix

1 The Case of the Unfortunate Businessman 1

2 The Case of the Gambling Nobleman 19

3 The Case of the Surprise Heir 45

4 The Case of the Ancient Mariner 65

5 The Case of the Unmarked Graves 85

6 The Case of the Martian Invasion 115

7 Three Cases of Unfair Preferment 141

8 The Execution of Andrews l6l

9 Three Cases of Relative Honor 181

10 The Case of the Poor Observer 207

11 The Case of the Perfect Accountant 225

12 Three Cases of Good Intentions 247

Afterword 275

Construction Mathematics

Surinder Virdi, Roy Baker e Narinder Kaur Virdi

Routledge |  2014 - 2ª edição |336 páginas | rar - pdf | 3 Mb

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Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines.

• Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components.

• Suitable for beginners and easy to follow throughout.

• Learn the essential basic theory along with the practical necessities.

The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained.

Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in Construction. Additional coverage of the core unit Mathematics in Construction and the Built Environment from BTEC National Construction, Civil Engineering and Building Services courses makes this an essential revision aid for students who do not have Level 2 mathematics experience before commencing their BTEC National studies. This is also the ideal primer for any reader who wishes to refresh their mathematics knowledge before going into a construction HNC or BSc.

Contents

1. Using a Scientific Calculator 
2. Numbers
3.Basic Algebra 
4. Indices and Logarithms 
5. Standard Form, Significant Figures and Estimation 
6. Transposition and Evaluation of Formulae 
7. Fractions and Percentages 
8. Graphs 
9. Units and their Conversion 
10. Geometry 
11. Areas (1) 
12. Volumes (1) 
13. Trigonometry (1) 
14. Setting Out 
15. Costing - Materials and Labour 
16. Statistics 
17. Areas and Volumes (2) 
18. Areas and Volumes (3) 
19. Trigonometry (2) 
20. Computer Techniques 
21. Assignments 
Appendix 1 Concrete Mix 
Appendix 2 Solutions for Excercises 
Appendix 3 Assignment Solutions

The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations

Reviel Netz 

Cambridge University Press | 2007 | páginas | pdf | 731 kb

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The transformation of mathematics from its ancient Greek practice to its development in the medieval Arab-speaking world is approached by focusing on a single problem proposed by Archimedes and the many solutions offered. From a practice of mathematics based on the localized solution (originating in the polemical practices of early Greek science), we see a transition to a practice of mathematics based on the systematic approach (grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). A radically new interpretation is accordingly offered of the historical trajectory of pre-modern mathematics.

CONTENTS
Acknowledgments page viii
Introduction 1
1 The problem in the world of Archimedes 11
1.1 The problem obtained 11
1.2 The problem solved by Archimedes 16
1.3 The geometrical nature of Archimedes’ problem 19
1.4 The problem solved by Dionysodorus 29
1.5 The problem solved by Diocles 39
1.6 The world of geometrical problems 54
2 From Archimedes to Eutocius 64
2.1 The limits of solubility: Archimedes’ text 66
2.2 The limits of solubility: distinguishing Archimedes from Eutocius 71
2.3 The limits of solubility: the geometrical character of Archimedes’ approach 85
2.4 The limits of solubility: Eutocius’ transformation 91
2.5 The multiplication of areas by lines 97
2.6 The problem in the world of Eutocius 121
3 From Archimedes to Khayyam 128
3.1 Archimedes’ problem in the Arab world 129
3.2 A note on Al-Khwarizmi’s algebra 137
3.3 Khayyam’s solution within Khayyam’s algebra 144
3.4 The problem solved by Khayyam 155
3.5 Khayyam’s equation and Archimedes’ problem 160
3.6 Khayyam’s polemic: the world of Khayyam and the world of Archimedes 171
3.7 How did the problem become an equation? 181
Conclusion 187
References 193
Index 196

Outros livros do mesmo autor:

Ludic proof : Greek mathematics and the Alexandrian aesthetic por Reviel Netz Idioma: Inglês   Editora: Cambridge ; New York : Cambridge University Press, 2009.

The Archimedes codex : how a medieval prayer book is revealing the true genius of antiquity's greatest scientist por Reviel Netz; William Noel Idioma: Inglês   Editora: Da Capo Press 2007

The shaping of deduction in Greek mathematics : a study in cognitive history por Reviel Netz Idioma: Inglês   Editora: Cambridge ; New York : Cambridge University Press, 2003.

A Historian Looks Back: The Calculus as Algebra and Selected Writings

(Spectrum)

Judith V. Grabiner

 Mathematical Association of America |  2010 |304 páginas | rar - pdf | 1,7 Mb

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Judith Grabiner, the author of A Historian Looks Back, has long been interested in investigating what mathematicians actually do, and how mathematics actually has developed. She addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. This book brings together much of what she has had to say to this audience.

The centerpiece of the book is The Calculus as Algebra: J.-L. Lagrange, 1736-1813. The book describes the achievements, setbacks, and influence of Lagrange s pioneering attempt to reduce the calculus to algebra. Nine additional articles round out the book describing the history of the derivative; the origin of delta-epsilon proofs; Descartes and problem solving; the contrast between the calculus of Newton and Maclaurin, and that of Lagrange; Maclaurin s way of doing mathematics and science and his surprisingly important influence; some widely held myths about the history of mathematics; Lagrange s attempt to prove Euclid s parallel postulate; and the central role that mathematics has played throughout the history of western civilization.

The development of mathematics cannot be programmed or predicted. Still, seeing how ideas have been formed over time and what the difficulties were can help teachers find new ways to explain mathematics. Appreciating its cultural background can humanize mathematics for students. And famous mathematicians struggles and successes should interest -- and perhaps inspire -- researchers. Readers will see not only what the mathematical past was like, but also how important parts of the mathematical present came to be.

Contents

Introduction .. . . xi

Part I. The Calculus as Algebra .. . . .1

Preface to the Garland Edition .. .3

Acknowledgement. . . .7

Introduction . . . . .9

1. The Development of Lagrange’s Ideas on the Calculus: 1754–1797 .. . 17

2. The Algebraic Background of the Theory of Analytic Functions . . . 37

3. The Contents of the Fonctions Analytiques . . . 63

4. From Proof-Technique to Definition: The Pre-History of Delta-Epsilon Methods . . 81

Conclusion .  . . .101

Appendix . .103

Bibliography .. . .105

Part II. Selected Writings  . .125

1. The Mathematician, the Historian, and the History of Mathematics . . . .127

2. Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus∗ . . . 135

3. The Changing Concept of Change: The Derivative from Fermat to Weierstrass† . . 147

4. The Centrality of Mathematics in the History of Western Thought† . . . 163

5. Descartes and Problem-Solving† . . . .175

6. The Calculus as Algebra, the Calculus as Geometry: Lagrange, Maclaurin, and Their Legacy . .191

7. Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions∗ . . 209

8. Newton, Maclaurin, and the Authority of Mathematics∗ .. .229

9. Why Should Historical Truth Matter to Mathematicians? Dispelling Myths while PromotinMaths . . .243

10. Why Did Lagrange “Prove” the Parallel Postulate?∗ .  . 257

Index .. . 275

About the Author .  . .287