Ace your math and measuring science project : great science fair ideas

Robert Gardner

Enslow Pub Inc | 2009 | 132 páginas | rar - pdf | 3,9 Mb


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Math and physics often go hand-in-hand. Math and measurements have even played a big role in scientific discovery since ancient times. Use math and measurement as the tools to successfully complete physical science experiments such as figuring out how big a raindrop is, discovering the first units of measure, and more! Many experiments include ideas students can use for their science fair.

Contents
Introduction ........ 7
The Scientific Method........ 8
Science Fairs ...... 10
Safety First .... 11
Indicates experiments that offer ideas for science fair projects.
CHAPTER 1 Measuring and units of Measure 13
1.1 The First Units of Measure ...... 15
1.2 Your Own Measuring System ...... 18
1.3 Metric Measure...... 24
1.4 Comparing Standard Units of Measure.... 27
1.5 Converting Units Within and Between Measuring Systems .. 30
1.6 Body Parts and Ratios ..... 33
CHAPTER 2 Math and science in Many Places 35
2.1 Great Circles: Measuring on a Sphere and Scaling .... 36
2.2 Testing Apples: Measuring, Averaging, Finding Volumes... 37
2.3 Volume, Mass, and Density ... 41
2.4 What Is the Effect of Surface Area on Heat Loss? .... 45
2.5 The Golden Ratio ........ 51
CHAPTER  3 Measuring Areas and Volumes 57
3.1 Area and Acres .... 61
3.2 Area of a Triangle ..... 63
3.3 Circles: Their Diameters, Circumferences, and Areas ...... 64
3.4 Cylinders: Their Areas and Volumes ... 70
3.5 Cones: Their Surface Areas and Volumes ....... 72
CHAPTER  4 Math, Temperature, and heat 79
4.1 Temperature Scales: Graphs, Conversions ...... 80
4.2 Measuring the Heat Delivered by a Heater ...... 84
4.3 Measuring the Heat to Boil Water (Heat of Vaporization).... 88
4.4 Measuring the Heat to Melt Ice (Heat of Fusion).... 92
4.5 Measuring Specific Heat ......... 94
4.6 Finding Specific Heat by Mixing ....... 97
CHAPTER  5 indirect Measurements and estimation 101
5.1 An Indirect Measurement of Thickness....... 102
5.2 An Indirect Measurement of Height..... 104
5.3 Using a Known Height to Measure Distance Indirectly..... 111
5.4 Scaling: Measuring Long Distances With Maps . 113
5.5 How Big Is a Raindrop? .... 115
5.6 Indirect Measurements of Mass ..... 120
5.7 How to Measure Distance With Your Bik.... 122
Appendix: Conversions Between U.S. Customary and Metric Units ... 123
Further Reading..... 124
Internet Addresses ...... 125
Index ..... 126

Mrs. Perkins's Electric Quilt: And Other Intriguing Stories of Mathematical Physics

Paul J. Nahin
Princeton University Press | 2009 | 424 páginas | pdf | 2,4 Mb

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What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself.

In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end.

Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books.

Contents
Three examples of the mutual embrace
Measuring gravity
Feynman's infinite circuit
Air drag--a mathematical view
Air drag--a physical view
Really long falls
The Zeta function--the physics
Ballistics--with no air drag (yet)
Ballistics--with air drag
Gravity and Newton
Gravity far above the earth
Gravity inside the earth
Quilts & electricity
Random walks
Two more random walks
Nearest neighbors
One last random walk
The big noise
Electricity in the fourth dimension.

Outros livros de Paul J. Nahin:

The logician and the engineer : how George Boole and Claude Shannon created the information age por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, [2013] ©2013

Chases and escapes : the mathematics of pursuit and evasion por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, 2012, ©2007.

Digital dice : computational solutions to practical probability problems por Paul J Nahin Idioma: Inglês   Editora: Princeton : Princeton University Press, ©2008.

Dr. Euler's fabulous formula : cures many mathematical ills por Paul J Nahin Idioma: Inglês   Editora: Princeton, NJ : Princeton University Press, ©2006.

When least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2004.

Duelling idiots and other probability puzzlers por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2000.

An imaginary tale : the story of [the square root of minus one] por Paul J Nahin Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©1998.

Architecture and Mathematics in Ancient Egypt

Corinna Rossi

Cambridge University Press | 2007 | 300 páginas | pdf | 4,8 Mb

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Corinna Rossi explores the use of numbers and geometrical figures by the Ancient Egyptians in their architectural projects and buildings. Whereas previous architectural studies have searched for "universal rules" to explain the entire history of Egyptian architecture, Rossi reconciles the approaches of architectural historians and archaeologists by testing architectural theories. This book is essential reading for all scholars of Ancient Egypt and the architecture of ancient cultures. 

Contents
List of illustrations page viii
List of tables xiii
Preface xiv
Acknowledgments xvii
List of abbreviations xix
Part I Proportions in ancient Egyptian architecture
Introduction to Part I: Harmony and proportions in architecture 2
1 In search of ‘the rule’ for ancient Egyptian architecture 7
Triangles and other figures 7
Three triangles for ancient Egypt 7
Viollet-le-Duc, Babin and the primeval pyramid 11
Choisy and the introduction of the Golden Section 16
The Golden Section 23
The origin and definitions of the Golden Section 23
The Golden Section and ancient Egyptian art and architecture 28
The theory of Alexander Badawy 32
2 Mathematics and architecture in ancient Egypt 57
Ancient Egyptian mathematics 57
The mathematical sources and their language 57
On , and other anachronisms 60
Intention, coincidence or tendency? 68
Triangles and architecture 68
Psychological experiments and involuntary trends 78
Cases from ancient Egypt 80
Conclusion to Part I: Ancient mathematics and practical operations 87
Part II Ancient Egyptian sources: construction and representation of space
Introduction to Part II: Tradition and variations in ancient Egyptian art and architecture 92
3 Documents on the planning and building process 96
Architectural drawings 96
Representations of buildings and working drawings 96
Drawings with written dimensions: the problem of the scale 101
Full-size geometrical sketches of architectural details 113
The use of square grids and the idea of a module 122
Architectural models 128
Votive objects 128
Working models 135
Projects and works in the Nineteenth and Twentieth Dynasty royal tombs 139
Documents on the works 139
Recording the progress: from the project to the survey 142
4 Foundation rituals 148
Foundation ceremonies 148
The ritual sequence 148
Cords and geometry 154
Building Texts 161
The dimensions of the primeval temples 161
The dimensions of the temples at Edfu and Dendera 166
Conclusion to Part II: From the plan to the building 174
Part III The geometry of pyramids
Introduction to Part III: Combining the knowledge 178
5 Symbolic shape and constructional problems 180
The form 180
Pyramidal form and solar cult 180
Benben and benbenet 182
As high as possible 184
The technique 185
Seked, side-length, diagonals and corners 185
Methods for obtaining the slope 188
Dimensions and proportions 196
6 The proportions of pyramids 200
Analysing true pyramids 200
Numerological theories 200
Lauer’s simple ratios 202
A list of true pyramids 204
Available data 204
Pyramidia as alternative sources 205
7 Pyramids and triangles 212
Geometrical models 212
Approximation and seked 212
Equilateral and b = h triangles 214
Seked 512
palms, generally called 14
11 triangle 215
Pythagorean triplets 216
The evolution of the form 221
Old Kingdom pyramids 221
Middle Kingdom pyramids 228
New Kingdom and Late Period pyramids 231
Conclusion to Part III: Interpreting the slope of pyramids 236
An overview 239
Appendix List of Old and Middle Kingdom true pyramids 242
Bibliography 255
Index 271

The Mathematics of Juggling

 Burkard Polster 

Springer | 2003 | 245 páginas | pdf | 1,8 Mb
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As a juggler the author likes to finish his performances with a stunt that combines props and techniques from a variety of juggling disciplines. Imagine him idling on a giraffe unicycle, while balancing a spinning basketball on a mouth stick, and toss-juggling a sword, a toilet plunger, and a rubber chicken. As a mathematician he is also interested in the treasure trove of beautiful mathematics used to model the different activities in a juggler's repertoire. In this book he provides an intellectually stimulating collection of mostly self-contained mathematical essays that introduce the reader to many elegant results and techniques from a wide range of mathematical disciplines such as combinatorics, graph theory, knot theory, mechanics, differential equations, control theory, and robotics. "The Mathematics of Juggling" is the first comprehensive account summarizing and expanding the results in the literature on juggling tricks and skills, as well as the mathematics behind these tricks and skills. Anybody who is not put off by the word "mathematics" in the title of this book should have a good time reading it.

Contents
Preface vii
1 Juggling: An Introduction 1
1.1 What Is Juggling? . . 1
1.2 A Very Short History of Juggling .  . . 2
1.3 rec.juggling .. . 4
2 Simple Juggling 7
2.1 Simplifying Juggling Patterns . . 7
2.2 Juggling Diagrams . . 9
2.3 Basic Juggling Patterns . . 11
2.4 Average Theorem . . . 14
2.5 Site Swaps and Flattening Algorithm.  . 17
2.6 Permutation Test . . 22
2.6.1 A Method to Construct All Juggling Sequences .. 24
2.6.2 Inverse of a Juggling Sequence .. 25
2.6.3 Pick a Pattern Procedure . . 28
2.6.4 Converse of the Average Theorem .. 29
2.6.5 Scramblable Juggling Sequences . .. 34
2.6.6 Magic Juggling Sequences .. 35
2.7 HowManyWays to Juggle? . . 37
2.7.1 Juggling Cards .  . 38
2.7.2 Weights of Juggling Sequences .  . 42

2.8 Juggling States and State Graphs . . 44
2.8.1 State Graphs . .. 44
2.8.2 Ground-State and Excited-State Sequences . 47
2.8.3 Throws fromStates . .  49
2.8.4 Prime Juggling Sequences and Loops  . 50
2.8.5 Complements of State Graphs . . 58
2.8.6 Transition Matrices .  . 62
3 Multiplex Juggling 65
3.1 Average Theorem and Permutation Test . . 66
3.2 Number ofMultiplex Juggling Sequences .  68
3.3 Weights ofMultiplex Juggling Sequences . . 73
3.4 Multiplex State Graphs . . . 75
3.4.1 Prime Multiplex Juggling Sequences and Loops . . . 77
3.4.2 Throws fromStates . .. . 81
3.5 Operations Involving Juggling Sequences . . . 81
4 Multihand Juggling 85
4.1 Juggling Matrices . .. . 85
4.2 Average Theorem and Permutation Test . . 88
4.3 Multihand State Graphs .  . 90
4.4 Operations Involving Juggling Matrices .. 92
4.5 Special Classes of JugglingMatrices . . 94
4.6 UniformJuggling and Shannon’s Theorems . . 96
4.7 Shannon’s Theorems for Juggling Sequences .  . 103
4.8 Cascades and Fountains .. 107
4.9 Juggling Balls and Hands . . 110
4.10 Juggling Labeled Balls .. . 112
4.11 Decomposing Simple Juggling Sequences . . 113
5 Practical Juggling 117
5.1 Jugglable Juggling Sequences . . 117
5.2 JugglingMade Easy . 123
5.2.1 Zero-Gravity Juggling. . 124
5.2.2 Bounce Juggling . . 126
5.2.3 Robot Juggling .  . 127
5.3 Real-World Juggling with Gravity and Spin .  129
5.3.1 Accuracy and Dwell Time . . 130
5.3.2 Why Clubs and Balls Line Up . . 132
5.4 What Is All this Numbers JugglingGood for? . 137
6 Jingling, or Ringing the Changes 141
6.1 Enter a Band of Ringers .. 141
6.1.1 Basic Definitions . .. 141
6.1.2 History and Practice of Change Ringing . 144

6.2 Juggling the Changes .. 146
6.2.1 Turning Bells into Balls .  146
6.2.2 Turning Extents into Site Swaps  . 149
6.3 Mathematical Notation and Basic Operations . 150
6.3.1 Notation  . 151
6.3.2 Ringing Sequences from Ringing Sequences  . 152
6.4 Principles and Methods  . . 154
6.4.1 Principles . . 154
6.4.2 Methods . . 155
6.4.3 Extents Based on Principles or Methods .  157
6.5 Graphical Representations of Extents .  . 159
6.5.1 Cayley Graphs .. 159
6.5.2 Four Bells . . 160
6.5.3 Five Bells . . 163
6.5.4 Many Bells . . 166
6.5.5 Names . . . 167
6.6 Extents fromGroups .  . . 168
6.6.1 Left Cosets and Plain Bob . . 169
6.6.2 Right Cosets and No-Call Principles . . 173
6.7 Computers, Bobs, and Singles . . 175
7 Juggling Loose Ends 177
7.1 Does God Juggle? . . 177
7.2 Juggling Braids . . . 181
7.3 Spinning Top of a Palm-Spun Pyramid . . 186
7.4 Useless Juggling .  . 189
7.4.1 Juggling Words . . . 189
7.4.2 Juggling Rational and Irrational Numbers  . 191
7.4.3 Antiballs, Antithrows, and Causal Diagrams . 192
7.5 Juggling and Math Stories. . 197
7.5.1 Riddle . . 197
7.5.2 Lord Valentine’s Castle . . 198
7.5.3 Famous Juggler-Mathematicians .  . 199
7.6 Further Reading .  . 199
Appendix: Stereograms of Hamiltonian Cycles 201

References 209

Nexus Network Journal: Leonardo da Vinci: Architecture and Mathematics

Sylvie Duvernoy 

Nexus Network Journal, vol. 10, number 1

Birkhäuser | 2008 | 200 páginas | pdf | 24 Mb

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Leonardo da Vinci was well aware of the fundamental importance of mathematics for architecture. This book examines Leonardo’s knowledge of theoretical mathematics, explores how he used concepts of geometry in his designs for architectural projects, and reports on a real-life construction project using Leonardo’s principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass, and Jane Burry.

CONTENTS

Letter from the Guest Editor

5 SYLVIE DUVERNOY. An Introduction to Leonardo’s Lattices Leonardo da Vinci: Architecture and Mathematics

13 KIM WILLIAMS. Transcription and Translation of Codex Atlanticus, fol. 899 v

17 RINUS ROELOFS. Two- and Three-Dimensional Constructions Based on Leonardo Grids

27 BIAGIO DI CARLO. The Wooden Roofs of Leonardo and New Structural Research

39 SYLVIE DUVERNOY. Leonardo and Theoretical Mathematics

51 MARK REYNOLDS. The Octagon in Leonardo’s Drawings

77 JOÃO PEDRO XAVIER. Leonardo’s Representational Technique for Centrally- Planned Temples

101 VESNA PETRESIN ROBERT. Perception of Order and Ambiguity in Leonardo’s Design Concepts

129 CHRISTOPHER GLASS. Leonardo’s Successors Geometer’s Angle

149 RACHEL FLETCHER. Dynamic Root Rectangles Part Two: Root-Two Rectangles and Design Applications Didactics

179 JANE BURRY and ANDREW MAHER. The Other Mathematical Bridge

Book Reviews

195 MICHAEL OSTWALD. A Theory of General Ethics: Human Relationships, Nature and the Built Environment by Warwick Fox

199 SARAH CLOUGH EDWARDS. Inigo Jones and the Classical Tradition by Christy Anderson

203 SYLVIE DUVERNOY. Architecture and Mathematics in Ancient Egypt by Corinna Rossi

Undergraduate Mathematics for the Life Sciences: Models, Processes, and Directions

Glenn Ledder; Jenna P Carpenter; Timothy D Comar

Mathematical Association of America | 2013 | 226 páginas | rar - pdf | 1 Mb

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There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind.
In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.
The authors represent a wide variety of academic institutions, from universities to community colleges, and all of the articles begin with information about the institutional context. Many of the articles also include links to resources that can be found on the internet, and some have associated books in print as well. All emphasize features that could be applied to similar projects at other institutions and offer useful advice for the newcomer to mathematics curriculum development for life science students.

Contents

Foreword: Looking Backward and Moving Forward in Undergraduate Life Science

Quantitative Education vii

Louis J. Gross

Foreword: An Invitation to BIO SIGMAA ix

Eric Marland

Preface xv

General Introduction xvii

Glenn Ledder

I Models 1

1 BioCalc at Illinois 5

J. Jerry Uhl and Judy Holdener

A one-semester biocalculus course at a large university, with emphasis on conceptual learning facilitated by a computer algebra system

2 Biocalculus at Benedictine University 17

Timothy D. Comar

A two-semester biocalculus sequence at a small college

3 Implementation of First Year Biomath Courses at the Ohio State University 25

Laura Kubatko, Janet Best, Tony Nance, and Yuan Lou

A one-year sequence of biocalculus plus statistics at a large university

4 Teaching Calculus, Probability, and Statistics to Undergraduate Life Science Majors: A Unified Approach 33

Frederick R. Adler

A one-year sequence of mixed topics designed for biology students

5 The First Year of Calculus and Statistics at Macalester College 39

Dan Flath, Tom Halverson, Danny Kaplan, and Karen Saxe

A redesigned introductory sequence for all students

6 Biology in Mathematics at the University of Richmond 45

Lester Caudill

A two-semester sequence with calculus and advanced topics

7 A Terminal Post-Calculus-I Mathematics Course for Biology Students 51

Glenn Ledder

Mathematical modeling, probability, and dynamical systems for students with a Calculus I background

8 Modeling Nature and the Nature of Modeling—an Integrative Modeling Approach 61

Claudia Neuhauser

Dynamical systems, partial differential equations, and stochastic processes for students with a Calculus I background, with emphasis on modeling in Excel and Matlab

9 Mathematical Biology and Computational Algebra at the Sophomore Level 65

Rohan Attele and Dan Hrozencik

Computational linear algebra with student research projects

10 An Interdisciplinary Research Course in Theoretical Ecology for Young Undergraduates 69

Glenn Ledder, Brigitte Tenhumberg, and G. Travis Adams

A research-driven course focusing on connections between theoretical models and experimental data

11 An Interdisciplinary Course, Textbook, and Laboratory Manual in Biomathematics with Emphasis on Current Biomedical Research 83

Raina Robeva, Robin Davies, and Michael L. Johnson

A special topics course on biomedical research

12 Teaching Bioinformatics in a Mathematics Department 89

Steven Deckelman

A mathematically-oriented bioinformatics program and its core capstone course

13 SYMBIOSIS: An Integration of Biology, Math and Statistics at the Freshman Level: Walking

Together Instead of on Opposite Sides of the Street 97

Karl H. Joplin, Edith Seier, Anant Godbole, Michel Helfgott, Istvan Karsai, Darrell Moore, and Hugh A. Miller, III

A complex interdisciplinary freshman curriculum II Processes 105

14 Science One: Integrating Mathematical Biology into a First-Year Program 109

Mark Mac Lean

Designing and maintaining a year-long team-taught interdisciplinary curriculum at a large institution

15 Planning for the Long Term 115

Meredith L. Greer

Retooling a course to meet changing needs and changing personnel

16 Some Lessons from Fifteen Years of Educational Initiatives at the Interface between

Mathematics and Biology: The Entry-Level Course 121

Louis J. Gross

Getting a department to embrace a course

17 A “Wet-Lab” Calculus for the Life Sciences 127

James L. Cornette, Gail B. Johnston, Ralph A. Ackerman, and Brin A. Keller

A cautionary tale about a project that died from lack of institutional support

18 Creating an Interdisciplinary Research Course in Mathematical Biology 133

Glenn Ledder and Brigitte Tenhumberg

Advice on creating interdisciplinary team-taught courses

19 Bioinformatics: An Example of a Cooperative Learning Course 139

Namyong Lee and Ernest Boyd

A biology/mathematics/computer science course at a smaller MS-level institution

20 Integrating Statistics and General Biology I in a Learning Community 143

William Ardis and Sukanya Subramanian

Using learning communities to connect biology with statistics

21 Constructing an Undergraduate BioMath Curriculum at a Large University: Developing

First Year Biomath Courses at The Ohio State University 149

Tony Nance and Laura Kubatko

Curriculum reform at a very large institution

22 Initial Steps Towards an Integration of Qualitative Thinking into the Teaching of Biology at a

Large Public University 155

Carole L. Hom, Eric V. Leaver, and Martin Wilson

An introductory biological modeling course offered by a biology department III Directions 165

23 Integrating Statistics into College Algebra to Meet the Needs of Biology Students 169

Sheldon P. Gordon and Florence Gordon

A call for a college algebra course thought of as pre-statistics rather than pre-calculus

24 Motivating Calculus with Biology 177

Sebastian J. Schreiber

Ideas for introducing more biology and biological modeling into mathematics courses

25 Computational Systems Biology: Discrete Models of Gene Regulation Networks 189

Ana Martins, Paola Vera-Licona, and Reinhard Laubenbacher

Using Boolean network analysis to model complex systems in molecular biology

26 Creating Quantitative Biologists: The Immediate Future of SYMBIOSIS 201

Darrell Moore, Karl H. Joplin, Istvan Karsai, and Hugh A. Miller III

Making introductory biology courses that have more quantitative content and focus more on biological thinking than biological facts

About the Editors 207

Applying Maths in Construction

 Antoinette Tourret e John Humphreys 

Routledge | 1997 | páginas | rar-pdf | 5,3 Mb

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This book and its accompanying Teacher's Pack are the result of a project, supported by the Nuffield Foundation, to provide flexible learning materials for the Basic Application of Number core skill for both the NVQs and GNVQ in construction and the construction crafts.The student book uses a unique approach to explain how mathematical principles apply to construction tasks. Each chapter forms an individual construction project and uses the full range of number skills from the fundamentals of addition and subtraction to statistics, trigonometry and technical drawing. Successfully completed projects provide the student with the required portfolio of evidence for their course. Notes throughout the text refer the student to the relevant module in the Teacher's Pack, which contains assessments, tests and detailed explanations of the number skills needed to complete the projects.

Contents
Introduction vii
Project 1
Decorating a room 1
A: Number skills 1
B: Job description and analysis of tasks 1
C: Cost of materials 2
D: Other considerations 3
1.1 Sketching the room 4
1.2 Stripping and sizing the walls 5
1.3 Wall-papering the walls 9
1.4 Cleaning and texturing the ceiling 13
1.5 Fitting the coving 15
1.6 Painting the ceiling and coving with the emulsion 17
1.7 Working on the doors, windows, skirting boards and architrave 19
1.8 Preparing the estimate 26
Project 2
Designing a staircase 28
A: Number skills 28
B: Job description and analysis of tasks 28
C: Cost of materials 29
D: Other considerations 29
2.1 Calculating the riser and the going 30
2.2 Calculating the slope of the staircase 34
2.3 Calculating the string length 37
2.4 Scale drawing of the stairs 38
2.5 Preparing the cutting list 40
2.6 Calculating costs 41
2.7 Preparing the estimate 43
Project 3
Planning kitchens 44
A: Number skills 44
B: Job description and analysis of tasks 44
C: Cost of materials 45
D: Other considerations 46
3.1 Drawing a scaled plan of the kitchen 46
3.2 Planning the units 49
3.3 Specialist fittings 52
3.4 Calculating the cost of the units 55
3.5 Calculating the cost of the specialist fittings 56
3.6 Doing a pictorial representation of the kitchen 61
3.7 Preparing the estimate 62
Project 4
Excavation for a swimming pool 64
A: Number skills 64
B: Job description and analysis of tasks 64
C: Cost of materials 65
D: Other considerations 66
4.1 Using ratios and bearings 66
4.2 Calculating the volume of the pool 68
4.3 How long will the digger be needed? 72
4.4 Cost of hire of the digger 74
4.5 Number of lorry journeys 75
4.6 Cost of earth removal 76
Project 5
Material requirements for a detached garage 77
A: Number skills 77
B: Job description and analysis of tasks 77
C: Cost of materials 78
D: Other considerations 78
5.1 Materials required for foundations and floor 79
5.2 Materials required for the walls 82
5.3 Calculating mortar requirements 86
5.4 Materials for the flat roof construction 88
5.5 The bill of quantities 92
Index 95

Teaching Secondary Mathematics as if the Planet Matters

Alf Coles, Richard Barwell, Tony Cotton, Jan Winter e Laurinda Brown

Routledge | 2013 |190 páginas | rar - pdf | 1,2 Mb

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‘This book moves us beyond a theoretical pondering of the issues and makes concrete suggestions for teachers and students for how things can be different in mathematics classrooms. This is long overdue.’
Peter Gates, University of Nottingham

Teaching Mathematics as if the Planet Matters explores how Mathematics teachers can develop approaches to curriculum and learning which help students understand the nature of the contemporary world. It sets out a model for teaching and learning that allows teachers to examine existing approaches to teaching and draw upon the insights of mathematics as a discipline to help students relate classroom mathematics to global issues such as climate change, the economy, food supplies, biodiversity, human rights, and social justice.

Including practical examples, suggestions for teaching activities and detailed further reading sections, the book covers:

• the mathematics of description in the measuring, recording and statistical analysis that informs our knowledge of climate change, consumption and sustainability;

• the mathematics of prediction in the modelling used by governments, scientists and businesses to plan roads, power stations and food supplies and their effects;

• the mathematics of communication in the news reports, blogs and environmental campaigns, incomplete without graphs, charts and statistics.

The true worth of a school subject is revealed in how far it can account for and respond to the major issues of the time. The issue of the environment cuts across subject boundaries and requires an interdisciplinary response. Mathematics teachers are part of that response and they have a crucial role in helping students to respond to environmental issues and representations.

Contents
List of figures vii
List of tables ix
Preface xi
Part I: A critical stance on global issues 1
1 The role of mathematics in shaping our world 3
Richard Barwell
2 The economy 16
Laurinda Brown
3 Climate change 31
Richard Barwell
4 Food 50
Jan Winter
5 Biodiversity 60
Alf Coles
6 Towards a mathematics for human rights and social justice 73
Tony Cotton
Part II: Into the classroom as if the planet matters 85
7 Critical mathematics education: from theory to practice 87
Tony Cotton
8 Starting from handling data 98
Tony Cotton
9 Starting from algebra 108
Alf Coles
10 Starting from number 121
Jan Winter
11 Starting from geometry 134
Alf Coles and Laurinda Brown
12 Starting from probability 148
Richard Barwell
Conclusion: the planet matters – does mathematics teaching? 162
Index 168

Codes The Guide to Secrecy from Ancient to Modern Times

(Discrete Mathematics and Its Applications)

Richard A. Mollin

Chapman and Hall/CRC | 2005 | 700 páginas | pdf | 4,1 Mb

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From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems. Codes: The Guide to Secrecy from Ancient to Modern Times explores the depth and breadth of the field, remaining accessible to the uninitiated while retaining enough rigor for the seasoned cryptologist.
The book begins by tracing the development of cryptology from that of an arcane practice used, for example, to conceal alchemic recipes, to the modern scientific method that is studied and employed today. The remainder of the book explores the modern aspects and applications of cryptography, covering symmetric- and public-key cryptography, cryptographic protocols, key management, message authentication, e-mail and Internet security, and advanced applications such as wireless security, smart cards, biometrics, and quantum cryptography. The author also includes non-cryptographic security issues and a chapter devoted to information theory and coding. Nearly 200 diagrams, examples, figures, and tables along with abundant references and exercises complement the discussion.
Written by leading authority and best-selling author on the subject Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times is the essential reference for anyone interested in this exciting and fascinating field, from novice to veteran practitioner.

Contents
From the riddles of ancient Egypt to cryptography in the Renaissance - 3500 years in the making
From sixteenth-century cryptography to the new millennium - the last 500 years
Symmetric-key cryptography
Public-key cryptography
Cryptographic protocols
Key management
Message authentication
Electronic mail and internet security
Applications and the future
Noncryptographic security issues
Information theory and coding
Appendix A: Mathematical facts
Appendix B: Pseudorandom number generation
Appendix C: Factoring large integers
Appendix D: Technical and advanced details
Appendix E: Probability theory
Appendix F: Recognizing primes
Appendix G: Exercises

The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse

Jennifer Ouellette

Penguin Books | 2010 | 338 páginas | rar - pdf | 1,5 Mb

link (password : matav)

epub - 1,7 Mb - link

Jennifer Ouellette never took math in college, mostly because she-like most people-assumed that she wouldn't need it in real life. But then the English-major-turned-award-winning-science-writer had a change of heart and decided to revisit the equations and formulas that had haunted her for years. The Calculus Diaries is the fun and fascinating account of her year spent confronting her math phobia head on. With wit and verve, Ouellette shows how she learned to apply calculus to everything from gas mileage to dieting, from the rides at Disneyland to shooting craps in Vegas-proving that even the mathematically challenged can learn the fundamentals of the universal language.


CONTENTS
Acknowledgments xiii
Prologue: I Could Be Mathier 1
To Infinity and Beyond 11
Drive Me Crazy 40
Casino Royale 65
The Devil’s Playground 93
Show Me the Money 119
A Pox upon It 140
Body Heat 171
The Catenary Tales 202
123456789 Surfi n’ Safari 225
Epilogue: The Mimetics of Math 249
Appendix 1 : Doing the Math 263
Appendix 2: Calculus of the Living Dead 293
Bibliography 299
Index 309

Mathematics and Politics: Strategy, Voting, Power, and Proof

 Alan D. Taylor e Allison M. Pacelli 

Springer | 2010 -2ª edição | 382 páginas | pdf | 1,2 Mb

link
link1

As a text for an undergraduate mathematics course for nonmajors, Mathematics and Politics requires no prerequisites in either area while the underlying philosophy involves minimizing algebraic computations and focusing instead on some conceptual aspects of mathematics in the context of important real-world questions in political science.

Five major topics are covered including a model of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. Each topic is discussed in an introductory chapter and revisited in more depth in a later chapter. This new edition has added co-author, Allison Pacelli, and two new chapters on "Fairness" and "More Fairness." The examples and the exercises have been updated and enhanced throughout.

Contents
Preface vii
......................................................................................
1 SOCIAL CHOICE
1.1. Introduction 1
1.2. May’s Theorem for Two Alternatives 4
1.3. Six Examples of Social Choice Procedures 5
1.4. Five Desirable Properties of Social Choice Procedures 10
1.5. Positive Results—Proofs 13
1.6. Negative Results—Proofs 20
1.7. A Glimpse of Impossibility 28
1.8. Approval Voting 31
1.9. Conclusions 34
Exercises 35
......................................................................................
2 YES–NO VOTING
2.1. Introduction 49
2.2. Four Examples of Yes–No Voting Systems 50
2.3. Weighted Voting and the U.N. Security Council 53
2.4. Swap Robustness and the Nonweightedness of the Federal System 56
2.5. Trade Robustness and the Nonweightedness of the Canadian System 59
2.6. Statement of the Characterization Theorem 62
2.7. Conclusion 63
Exercises 64
......................................................................................
3 POLITICAL POWER
3.1. Introduction 71
3.2. The Shapley-Shubik Index of Power 73
3.3. Calculations for the European Economic Community 78
3.4. The Banzhaf Index of Power 83
3.5. Two Methods of Computing Banzhaf Power 85
3.6. The Power of the President 90
3.7. The Chair’s Paradox 98
3.8. Conclusions 104
Exercises 105
......................................................................................
4 CONFLICT
4.1. Introduction 112
4.2. Two-By-Two Games 113
4.3. Dominant Strategies and Nash Equilibria 116
4.4. Prisoner’s Dilemma and the Arms Race 117
4.5. Chicken and the Cuban Missile Crisis 122
4.6. The Yom Kippur War 126
4.7. The Theory of Moves 128
4.8. Conclusions 137
Exercises 137
......................................................................................
5 FAIRNESS
5.1. Introduction 152
5.2. The Problem of Apportionment 153
5.3. Divisor Methods of Apportionment 155
5.4. A Glimpse of Impossibility 157
5.5. Dispute Resolution and Fair Division 159
5.6. An Alternative to Divide-and-Choose 163
5.7. Adjusted Winner 165
5.8. Adjusted Winner and the Middle East 171
5.9. Conclusions 173
Exercises 174
......................................................................................
6 ESCALATION
6.1. Introduction 179
6.2. The Dollar Auction 180
6.3. Game-Tree Analyses 181
6.4. Limitations and Back-of-the-Envelope Calculations 188
6.5. Statement of O’Neill’s Theorem 192
6.6. Vickrey Auctions 195
6.7. Conclusions 199
Exercises 200
......................................................................................
7 MORE SOCIAL CHOICE
7.1. Introduction 205
7.2. Social Welfare Functions 206
7.3. A Generalization of May’s Theorem 209
7.4. Arrow’s Impossibility Theorem 211
7.5. The Gibbard-Satterthwaite Theorem 222
7.6. Single Peakedness—Theorems of Black and Sen 231
7.7. Conclusions 240
Exercises 240
......................................................................................
8 MORE YES–NO VOTING
8.1. Introduction 247
8.2. A Magic Square Voting System 248
8.3. Dimension Theory and the U.S. Federal System 251
8.4. Vector-Weighted Voting Systems 255
8.5. Conclusions 260
Exercises 261
......................................................................................
9 MORE POLITICAL POWER
9.1. Introduction 264
9.2. The Johnston Index of Power 265
9.3. The Deegan–Packel Index of Power 271
9.4. Ordinal Power: Incomparability 275
9.5. Ordinal Power: Comparability 279
9.6. A Theorem On Voting Blocs 285
9.7. Conclusions 288
Exercises 289
......................................................................................
10 MORE CONFLICT
10.1. Introduction 293
10.2. Models of Deterrence 293
10.3. A Probabilistic Model of Deterrence 298
10.4. Two-Person Zero-Sum Games 303
10.5. Conclusions 309
Exercises 309
......................................................................................
11 MORE FAIRNESS
11.1. Introduction 314
11.2. Efficiency in Adjusted Winner 315
11.3. Adjusted Winner and Manipulability 319
11.4. Fair Division Procedures for Three or More Parties 322
11.5. Envy-Free Procedures 325
11.6. Envy-Free Procedures for Four or More Parties 328
11.7. Another Impossibility Result 330
11.8. Conclusions 331
Exercises 332
Contents xv
......................................................................................
12 MORE ESCALATION
12.1. Introduction 337
12.2. Statement of the Strong Version of O’Neill’s Theorem 337
12.3. Proof (By Mathematical Induction) of the Strong Version of O’Neill’s Theorem 344
12.4. Vickrey Auctions as a Generalized Prisoner’s Dilemma 346
12.5. Conclusions 348
Exercises 349
Attributions 350